f



:: towards a constructive education :: (news server friendly)

I posted this earlier this week, but discovered that many news servers
(and Google) would not carry it, due to the number of newsgroups
posted to, and this also prevented some who could access it from
replying.  I feel this is an important topic to discuss in an
interdisciplinary style, and I still believe that there is much
benefit to all newsgroups and their respective professions which I
posted to, but have broken the linking up in order to expose this to a
wider audience of news servers.  I appologise if you received both
postings on your news server, and I hope that you do not consider it
spam.  I have read all charters and FAQs I could find and the only
thing that is troubling is the double post, as the content applies to
all fields in a quite straightforward way.

-=-=-=-=-=-=-=-=--=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

While you are reading this, your retinal rods and cones are
interpreting images projected onto them.  Each letter, like the

W

that begins this post is given a neural focus, an "attention", as
rhythmic waves refresh the focus regularly.  The transmission through
the optic ganglions and along the optic fibres of the raw inforation
of the

W

goes through a processing which has been well studied in the
literature.  One successful modeling approach is that of the
connectionists or found in the neural net literature.  The oculomotor
loop and the importance of saccades is established.  We have many
models on how neural nets detect edges, identify topological
components in their optic information, determine orientation.  The
retinotopic map is formed.

These models are useful to the extent that there is actual technology
built with these models, and they make good money today.  They agree
with our experiments extremely well.  We can usefully pattern match
the shape

W

with a fair degree of accuracy.

The logic of propositions in the models on shape theory, the theory of
the topological, metrical, and orientation-based classification
calculus, the dynamical logic of the attractor spaces in neural net
models, the region-connection calculus, all of these logics are
Heyting.

Of course, human pattern matching involves much additional information
processing.  When the

W

is blurry, when the information is vague, we may look to the
surrounding

*hile

and call on recollections of known forms of full words.  We've learned
to attach meanings to utterances and visual shapes, and while you are
reading this you are building structures of meaning to the words which
can assist in the recognition, determining patterns of abstractions
connected in a mental system of relationship which is still poorly
understood. But every year more information is gathered.  The
schematic decomposition of the process is being studied, and regularly
receives more insight towards the architectonic basis of the function
and dynamics of thought.

And, we can formalise the game of language.  Formal languages have a
well studied mathematical foundation, and the reasoning in a semantic
system can be formalised in a model theory.  When we look to the many
sources of "reasoning about", from necessities and modalities to
counterfactual possible worlds, satisfaction (semantic), operational
resolution, etc. we find many different logics.  But they are all
Heyting, and this substructure common to all semantic theory allows
for a rich functor structure of equivalences and dualities amongst
these logics.  There are common dictionaries to translate between
various related semantics.

And there appears to be a very important reason this Heyting
substructure is found so predominantly in the formal languages and
foundations of mathematics.  Formal reasoning has a structure of a
state and its transitions, it is in many ways the analysis of an
automaton whose transition graph is specified by the logic of the
reasoning.  Proof theory is very intimately related to the theory of
computation and the lambda calculus.  The lambda calculus has a well
known Heyting structure, and we have the Church-Turing thesis over our
shoulders hinting that this may very well be the most primary
structure found in all algorithmics.

When we look to topics like Martin-Lof type theory to explain the
evolution of the objects of or conceptions and the structure of
describing our world, again we have its Heyting structure well known
and studied.

Constructivism is very much the study of process and information, of
the logic of propositions on information structures.  Processing
information allows us to channel it to useful decision making.  It
appears to be prior epistemically to the abstraction of a "reality".

And we use this structure in our theories about the world around us. 
In general, the semantics of evolving collections of objects and
causality is known to be Heyting.  Applications of Heyting semantics
have been detailed for antigen-antibody interactions or the deviation
of a cancer process, but one of the most fascinating applications for
me has always been the analysis of quantum propositions and the
evolution of quantum systems.  In fact, the work of von Neumann and
Birkhoff is one of the most stark expressions of this generality,
where it was shown that contrary to much early physics, the logic of
the universe may very well be that of a Heyting algebra that is not
Boolean.

Now, I appologise for the large crossposting, but I believe this post
to be topical to all newsgroups in my list.  I earnestly feel that
there is a common thread which needs to be discussed amongst all of
these communities. I am concerned about the education of constructive
theory and Heyting semantics prior to the study of classical logic and
Boole (and Aristotle when you lack quantifiers, etc.).  And when I say
Heyting here, prior, and to come, I also intend co-Heyting, for
obviously there are semantics mentioned who have more reasonable
interpretations in the dual algebras, but that is of course a
contravariant functor away.

For some reason, I feel that this sounds like a radical idea, even
though I also get the impression that Heyting algebras are not the
controversy they were when associated more strongly with Brouwer and
intuitionism.  There are obviously many communities using them.  They
appear to be intimately related with conceptualisation and the thought
process.

Yet, going through the college system, I found it rare for
non-specialists to be aware of the more general Heyting structures
found in their respective fields, though they were often well prepared
in classical logic.  And I often found that this presented a much
_less_ useful tool in which to evaluate the structures of their
fields.  The application of Boolean logics to quantum systems is one
of the major sources of "strangeness" under which quantum mechanics is
commonly described, and understanding how to properly make
propositions about quantum systems can clear up much confusion here.
In linguistics and formal foundations, there is regular rediscovery of
basic results on the difficulty of identity and the ambiguity of
negation which are well described by constructive semantics.  From the
theory of Cohen forcing to slaving principles and thermodynamic
process, from topoi to decoherence-function-consistent histories, our
fields have many Heyting structures lying just an analysis away.

I am not of the opinion that the Boolean has _no_ use, nor would I
even advocate giving up the Axiom of Choice as a useful tool.  But I
do believe that prior to exposing a student to these particular models
of mathematical reasoning, the more constructive foundations should be
explained more thoroughly.  Because I do find that alot of
misconceptions about constructivism get propagated at times.  In
particular, on these newsgroups I find that questions concerning
issues particularly involved with the general theory around
applications of Heyting algebras get a much diminished audience to
that of more classical analyses of reasoning.  Sometimes there is even
derision.

John Baez once stated that,

"Intuitionism proceeds by a method known as Winnowing the Audience. 
Essentially, one can avoid the use of formal proofs by making the
proofs so long, tedious, and bewildering that only those in agreement
bother to read them."

Obviously, I have placed this without context, and recent comments by
Baez in support of some of Lawvere's programme may comment to possible
changes in position, but the statement is certainly indicative of a
trend.  Many pop-foundations (pop-philosophy, pop-mathematics, etc.)
books still mention the various constructive schools of thought as
minor players, sometimes with actual dismissal and often without much
detail.  Now, this may only point to a failing of pop books, and
although I think most professionals deride the pop books of their
professions, there is certainly a community attitude that such books
commonly intend to convey.

Yet, I also find that there is quite a large group of communities
using many different faces of Heyting structures.  And I find that
mathematicians as a whole do seem to appreciate constructive proofs
over nonconstructive ones where they can get them.  And on some of
these newsgroups I even find most constructive expositions are well
received at times.  I just find that those with a good understanding
of the field are either self-trained or studied directly under a
contributer to the field, and there is often lamentation that the
field is more widely applicable.  In fact, the field surely seems more
widely applicable than the study of classical Boolean logic, it being
only one form of Heyting structure and not applicable to many of the
structures mentioned or, for example, the well known theory of
decidability founded by Godel or the theory of Kleene truth.

For me, constructivist theories have always been computational
theories in general.  For me, I never found anything "tedious, and
bewildering" and certainly have not noticed that it might be common to
"avoid the use of formal proofs" in intuitionism or other constructive
programmes.  But this was because I read early on about intuitionism
and constructivist theories as my notions of logic were developing. 
By accidents of choices and self-education, I learned constructive
logics at about the same time as learning classical logics. 
Certainly, constructivist math can be more difficult since you lack
some common tools for proof, and I have found myself joking about
difficulty and obscurity many times in my studies when I first entered
certain topics (like algebraic geometry and the analysis of varieties
and schemes, as an example which I still clearly remember making
similar comments), when the pantheon of objects and their
transformation structure was still poorly known by myself, and I find
that quotes like those of Baez above are often indicative of this
early apprehension.  So I get concerned about education.

And these are the questions I have for all of our communities out
there:

-  is it, with so many applications so fundamentally related in our
fields unified by the common Heyting thread, perhaps time to start
teaching our students more about the theory of the Heyting algebra
structure prior to adding axioms forcing bivalence or existence?
-  if not, why not?
-  and, somewhat to get a better picture for myself, why do you
believe the more widely applicable Heyting structures and their
semantic analysis is found to be less important to the education of
our students than the lesser applicable Boolean particular case
currently taught?

Obviously, I am of the "yes" opinion to the first question.  For the
third question, I do see the historical contigencies that have guided
modern education, but after more than a hundred years of
constructivist thought being advocated, from early rumblings of
Kroenecker and Poincare, through Brouwer, Weyl, Heyting, Tarski, and
the eventual use of the logical structure and its semantic analysis in
numerous foundational fields, and its modern ubiquity, such
explanations still seem to fail for me for modern education. 
Obviously, mathematics is an easier enterprise with the additional
tools of excluded middle and transfinite choice, but again I am not an
advocate of _not_ teaching those tools.  I am only curious about why
the constructive logics which seem in numerous ways to be prior to
such tools are not taught prior.  They certainly can help in the
understanding of the more classical approaches.  My hunch for the
third question is that the desire for classical logic is very similar
to the desire to believe in monotheism, that there is this insecurity
in many people concerning the "absolute" and "reality", and questions
of truth and falseness, like questions of good and evil, should be
knowable to some form of completion.  I know that is certainly a
controversial opinion in some circles, but I wanted to throw it out
there to give a better view of where I come from and perhaps to
stimulate discussion on the third topic.  Paradoxically, I have found
that although I am drawn to multivalent logics and find monotheism
anathema (ironic considering the words origins), I also enjoy studying
the realist interpretations of quantum mechanics, which I suspect are
guided by very similar desires, so perhaps I just like to be
contrary...

In philosophy, epistemics, cognition, linguistics, formal models,
computation, and the possible structure of our world, there are
unifying principles of expressability that I find more and more
useful.  It confuses me that I find them still poorly understood in
crowds where, at least to me, it has always seemed they should be more
well known.  So I thought I'd try to bring some of the more relevant
communities together and see if I could start some discussion on
broadening education along these important lines, for I feel that such
is urgently needed to prevent a lot of "wheel grinding" and repition
of already known results in the separate fields.  I really believe
that such a consolidation of logical education is needed in all of our
fields to place more focus on our respective advances.

-=-=-=--=-=-=--==-=-=-=-=-=-=-=-=-=-=-=-=-=-=

The newsgroups I have broken this up into are divided into 3 groups of
5.  They cover the major newgroups discussing issues mentioned, and
whom collectively, I felt, could have the most impact on the
educational concerns I mention.  I included two fan newsgroups which I
felt contained overlap with many of the ideas presented as well.  For
those interested in all sides of the debate, I wanted to list my
divisions here.  I will be participating in all of them.

1
-=-
alt.consciousness
alt.fan.hofstadter
comp.theory
sci.cognitive
sci.logic

2
-=-
alt.philosophy
comp.lang.functional
sci.lang
sci.physics
sci.psychology.theory

3
-=-
alt.fan.noam-chomsky
comp.ai.neural-nets
sci.edu
sci.philosophy.meta
sci.math


-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar
0
galathaea1 (62)
2/6/2004 12:06:39 AM
comp.lang.functional 2791 articles. 0 followers. Post Follow

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galathaea wrote:
 > known Heyting structure, and we have the Church-Turing thesis over our
 > shoulders hinting that this may very well be the most primary
 > structure found in all algorithmics.
 >
 > When we look to topics like Martin-Lof type theory to explain the
 >
<remaining verbal diarrhea snipped>


Could it be... Jack Sarfatti in drag?





0
willyjeff (1)
2/6/2004 3:56:28 AM
"Slick Willy" wrote:
:
: galathaea wrote:
:  > known Heyting structure, and we have the Church-Turing thesis over our
:  > shoulders hinting that this may very well be the most primary
:  > structure found in all algorithmics.
:  >
:  > When we look to topics like Martin-Lof type theory to explain the
:  >
: <remaining verbal diarrhea snipped>
:
:
: Could it be... Jack Sarfatti in drag?

Can you please tell me where anything I mentioned is factually incorrect?  I
am not using big words to impress anyone here.  In these communities I am
speaking to, I expect some reasonable understanding of the concepts I
mentioned.  I'm sorry that doesn't include yourself.


-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar



0
galathaea1 (62)
2/6/2004 4:10:50 AM

Slick Willy wrote:

> galathaea wrote:
>  > known Heyting structure, and we have the Church-Turing thesis over our
>  > shoulders hinting that this may very well be the most primary
>  > structure found in all algorithmics.
>  >
>  > When we look to topics like Martin-Lof type theory to explain the
>  >
> <remaining verbal diarrhea snipped>
>
> Could it be... Jack Sarfatti in drag?

Out of curiosity...

What actual historical references that pertain to any of these subjects have
you bothered to read?

:-)

mitch



0
mitchs (45)
2/6/2004 7:31:07 AM
"galathaea" <galathaea@excite.com> wrote in message
news:b22ffac3.0402051606.f6de9b1@posting.google.com...

You waffled too long before coming to anything substantive, so I snipped all
without reading further.
Verbal diarrhoea is curable.  See a doctor.

Franz


0
2/6/2004 2:44:00 PM
galathaea wrote:
> I posted this earlier this week, but discovered that many news servers
> (and Google) would not carry it, due to the number of newsgroups
> posted to, and this also prevented some who could access it from
> replying.  I feel this is an important topic to discuss in an
> interdisciplinary style, and I still believe that there is much
> benefit to all newsgroups and their respective professions which I
> posted to, but have broken the linking up in order to expose this to a
> wider audience of news servers.  I appologise if you received both
> postings on your news server, and I hope that you do not consider it
> spam.  I have read all charters and FAQs I could find and the only
> thing that is troubling is the double post, as the content applies to
> all fields in a quite straightforward way.
> 
> -=-=-=-=-=-=-=-=--=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

I find three things to say after a relatively quick reading, and a fourth 
after looking up the definition of a Heyting Algebra, that I insert on top of 
list as item

0) the best Manifesto Slogan in favor of Heyting Algebras, that I can invent, is :

666 ? - 666 ~ .666 ~ 2/3 ~ 1 - 1/3 ~ tertium non datur ~ the excluded middle
             ~ "either you are with us, or you are against us"

An apparent consequence is that, if you find this slogan too intimidating for 
your purposes, you might instead go the way to think of Heyting algebras as 
describing no less than Irony across the domains where they pop up. This in 
the sense that this presence of Irony would explain schools are dissuaded to 
follow track.

1) your choice of the W I find deserves reading as allusion to the python 
expression :

python >>> filter(lambda W : W not in "ILLITERATE", "BULLSHIT")

this expression, discovered at the occasion of the 2000 US elections, produces

'BUSH'

as standard answer on a standard Python interpretor. We know a priori that 
more or less readable variants of the same expression should be possible in 
other languages, but it looks a priori dubious that the miraculous property of 
the Python language of allowing this expression to shine on the standard in 
such a deliciously ambiguous form - we know at once that this miraculous 
property will be difficult to duplicate by another language.

Python being btw well in the top 10 of programming languages. While we believe 
the above syntax may well end up deprecated by Python's Benevolent Dictator 
For Life Creator, Guido van Rossum, a key part of the Beauty of the above 
ambiguous structure is that it allows the current Python standard distribution 
a claim to success in the Turing Test !

2) I've tried to track down what I would find most important to place well 
when zooming out over a panorama as extended as your pick, which is the idea 
of "braking computers". ie we believe that what we can obtain as a *speedup* 
facilitated by the computer, we can also obtain at times by the *slowdown* 
produced by a Universe-wide "anticomputer" doing miracles while remaining 
totally passive, not helping the computation, collaborating over the cosmos to 
stop or slow down computation and physiology. A distributed cosmos-wide 
anti-computer, democratically as capable as the swarm of the real computers, 
to provide intelligence service to us by its influence over the evolution of 
computation. Given how the majority of users of the name of God use it in a 
way that is incompatible with the correct usage of a name for that "universal 
anticomputer", we can't say the latter is God. Secretely nevertheless, we 
believe many of the best claims of "seeing God" are cases of people 
instinctively finding a collaborative connection with the universal 
anticomputer, but then at once confused about *what exactly saw them* and 
fantasizing around it. The above Python example can be viewed as witness to 
the friendlyness of the universal anticomputer to the Python programming language.

3) To summarize what I learn at once from what you write : this is the 
proposition that "ambiguity of negation" gives rise to "Heyting algebras" 
while the latter pop up here and there without ourselves uniting their study, 
work, and exploitation. But can't a very similar case be made while 
substituting "Complex Numbers" to "Heyting Algebras", except perhaps at the 
level of elementary pedagogics ? If a single class action of such a form was 
permitted, with the purpose of education reform in a broad sense, would the 
wise attorney choose "Complex Numbers" or "Heyting Algebras" ? Or are we in 
fact by any chance talking of one and the same thing ?

0
borcis (46)
2/6/2004 4:20:43 PM
"Franz Heymann" wrote:
: You waffled too long before coming to anything substantive, so I snipped
all
: without reading further.
: Verbal diarrhoea is curable.  See a doctor.

This is the second comment on bowel movements associated to my post.  Yet I
do not see any "waffling" when I read it.  Can you please explain why I get
such responses, when I have taken time to carefully write my post?  I have
followed many of your posts on the sci.physics forum and do respect your
opinion, but do not understand from where you are coming.

In case you didn't read it, my post is about education, something I feel is
very important.

In fact, I am getting the impression that many don't read the post, perhaps
because reading hurts their head.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/6/2004 5:10:06 PM
"Franz Heymann" wrote
: You waffled too long before coming to anything substantive, so I snipped
all
: without reading further.
: Verbal diarrhoea is curable.  See a doctor.

In fact, I find it difficult to see how I can broach my topic amongst all
groups without taking the path I chose.  Is it that you feel I shouldn't
mention any results from fields outside your own?  Or did you not even get
through the part about recognition, and find out that I was talking about
Heyting algebras?

I am interested, as I do want to know how I can get the various communities
talking about the importance of the education I mention.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/6/2004 5:34:13 PM
On Fri, 6 Feb 2004 09:10:06 -0800, "galathaea" <galathaea@excite.com>
wrote:

>Can you please explain why I get such responses, when I have taken time
>to carefully write my post?

It has been said that unless you are able to explain an idea in such a
way that a three-year-old can understand it, you don't truly understand
it yourself. I wouldn't go quite that far, but the thought does have
some merit.

A couple of specific criticisms:

You haven't laid any framework for your discussion. You launch right
into elaboration without even stating the topic, and so your readers are
guaranteed to be lost from the very beginning. _You_ may know what
you're talking about, but nobody else does. It's a bit like the three
rules of thumb for a scientific paper or presentation: (1) Tell them
what you're going to tell them. (2) Tell them. (3) Tell them what you
just told them.

Your long-winded prose is so meandering (and occasionally convoluted)
that it's difficult to figure out what the hell you're trying to say,
sometimes even within a single paragraph. On the surface, it begins to
sound like the meaningless drivel that so often passes for literary
criticism these days, and which Alan Sokol so successfully parodied a
few years back. (Note that I'm not saying that your writing _is_
meaningless drivel, only that it _looks_ like meaningless drivel.)

You may very well have some worthwhile ideas, but until you learn to
organize your thoughts more carefully and express them more clearly and
concisely, no one else is going to be able to tell.

-Steve

0
see94 (37)
2/6/2004 6:42:36 PM

galathaea wrote:

>
> In case you didn't read it, my post is about education, something I feel is
> very important.
>

Unfortunately, I think many people are somewhat cynical about this particular
topic.  If they perceive fortunate circumstance because of education, they have
no reason to question its value.  If they are ambivalent there is nothing to be
concerned about except, perhaps, the skeptical question concerning the agenda
behind a reformer's motivation.

On sci.logic, George Greene observed that constructive mathematics was
difficult.  So what you are describing would increase a burden already
perceived as onerous for many.

Galathaea, I have several journal articles on things like constructive e-sets
and solvable Boolean algebras.  But I do not have the background to read them
directly.  Do you know of any expository texts that would help introduce me to
the methodologies for constructive mathematics?

You might also wish to visit the pages,

 http://plato.stanford.edu/entries/logic-paraconsistent/

 http://plato.stanford.edu/entries/mathematics-inconsistent/

although you are probably aware of them.

I find the fact that these concepts are contrasted with consistency somewhat
amusing.  Since my background concerning these questions is closely associated
with Kantian epistemology, I am still waiting for someone to convince me that
what is taught as "logic" is anything but the fixed delusion of certain
influential narcissists and those who mistakenly investigated their program.

Here is one other site that you might find more interesting.  The Polish school
of mathematics (along with Paul Halmos and a few others) pursued algebraic
semantics along the lines of Tarski's cylindrical algebras.  Jacek Malinowski
has a number of interesting papers.  Algebraic semantics allows for a natural
distinction between equivalential and non-equivalential logics in contrast to
the kind of investigation begun by Heyting.

 http://www.uni.torun.pl/~jacekm/publications.htm

Still, I would like to see someone discussing the details of Heyting algebras
with you.  I am now aware that many of my own former computer tasks were based
on the structure of Brouwerian semilattices.  Had I been aware of that at the
time, I probably could have done a number of things far more effectively.

:-)

mitch



0
mitchs (45)
2/6/2004 7:00:01 PM

Franz Heymann wrote:

> "galathaea" <galathaea@excite.com> wrote in message
> news:b22ffac3.0402051606.f6de9b1@posting.google.com...
>
> You waffled too long before coming to anything substantive, so I snipped all
> without reading further.
> Verbal diarrhoea is curable.  See a doctor.
>

Shallowness, however, rarely finds relief.

:-)

mitch



0
mitchs (45)
2/6/2004 7:03:07 PM

Morris Carr� wrote:

> A distributed cosmos-wide
> anti-computer, democratically as capable as the swarm of the real computers,
> to provide intelligence service to us by its influence over the evolution of
> computation.

You overestimate your ability with the part that reads "as capable as."

Carnegie-Mellon University began the development of Capability Maturity Models because
the swarm to which you refer had been undependable, unreliable, and costly.  The
paradigm of Extreme Programming is an ad hoc implementation of certain parts of the
Capability Maturity Models for people who cannot read technical documentation for lack
of illustrations.

I suspect, however, that the companies for which you worked depended on the very
religious faith that you have so willfully disrespected.  It is likely that they
failed to demonstrate any productivity from their computer investments until recession
forced them to institute sound business practices once again--that is, if they
survived.

:-)

mitch



0
mitchs (45)
2/6/2004 7:11:59 PM
"Steve Schafer" wrote:
: On Fri, 6 Feb 2004 09:10:06 -0800, "galathaea" <galathaea@excite.com>
: wrote:
:
: >Can you please explain why I get such responses, when I have taken time
: >to carefully write my post?
:
: It has been said that unless you are able to explain an idea in such a
: way that a three-year-old can understand it, you don't truly understand
: it yourself. I wouldn't go quite that far, but the thought does have
: some merit.

I actually felt that what I wrote was dumbing things down quite a bit.  I am
getting the feeling that is more a problem of attention defecit and the
length of the post more than anything else.  All of the comments so far have
made it quite clear that the negativity was due to having not read any
furthur than the first few paragraphs.

: A couple of specific criticisms:
:
: You haven't laid any framework for your discussion. You launch right
: into elaboration without even stating the topic, and so your readers are
: guaranteed to be lost from the very beginning. _You_ may know what
: you're talking about, but nobody else does. It's a bit like the three
: rules of thumb for a scientific paper or presentation: (1) Tell them
: what you're going to tell them. (2) Tell them. (3) Tell them what you
: just told them.

I rarely see the abstract/paper/conclusion format on these groups, but if
you think it would help, maybe I will try that approach.  It does seem
apparent that some people are having a difficult time reading far enough to
see any of the points made.

: Your long-winded prose is so meandering (and occasionally convoluted)
: that it's difficult to figure out what the hell you're trying to say,
: sometimes even within a single paragraph. On the surface, it begins to
: sound like the meaningless drivel that so often passes for literary
: criticism these days, and which Alan Sokol so successfully parodied a
: few years back. (Note that I'm not saying that your writing _is_
: meaningless drivel, only that it _looks_ like meaningless drivel.)

I don't find it too meandering.  It has a fairly linear outline.  It first
introduces the point that Heyting algebras are currently considered very
likely to be our logic of perception and found in the way that we build our
conceptual framework.  It then goes on to point out that formalising these
theories of language leads to model theory and the foundations of
mathematical reasoning, and that this too has a well established Heyting
structure.  I point to the fact that this is intimately related to the lamda
calculus, again possessing a well known Heyting logic, and this leads quite
naturally into type theories of computation.  It is only here I find a major
turn, where I jump from formalised computation to models of science,
pointing out the established theories of evolving collections and quantum
logic both have a Heyting structure, and even mention in passing some of the
biological work of Leguizamon.  I think it is fairly clear that this first
part is basically just recapitulating the ubiquity of Heyting form in modern
research, if someone actually reads it.

Then I ask my question about education.  I won't spoil the surprise on that
one, though.

Sokol's little prank on that post-modernist magazine was obvious to me the
first time I read it, and should be to anybody who calls themselves a
scientist.  What I wrote has a well established bibliography, the math is
well known and has contributers with names like Tarski, von Neumann,
Kolmogorov, and others quite well respected in their fields, and the overall
theory covers all the groups I posted to.

I am still having difficulty seeing how any of this would not be obvious by
reading the piece completely, but I do see how someone who stops reading the
post will not have read the post.  That one is obvious to me.

: You may very well have some worthwhile ideas, but until you learn to
: organize your thoughts more carefully and express them more clearly and
: concisely, no one else is going to be able to tell.

I still don't see the need for more clarity, but it is obvious that
conciseness is necessary for some.  I have "dumbed" down my explanation to
the point of summary, and I even felt that the introduction might be
appreciated for its interesting introduction into the logic of perception.

I do appreciate your comments, by the way.  I am sore at the lack of a
complete reading by some who still felt competent to reply to my post, and
maybe some of this comes through in my reply to you, but I do recognise the
importance of the comments you have made, and will very likely approach the
issue in a more formalised (yet simple!) way, with abstract and all.  I do
feel that the issue sincerely needs to be talked about, for the very
practical reasons I mention.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/6/2004 7:35:41 PM
mitch wrote:
> 
> Morris Carr� wrote:
> 
> 
>>A distributed cosmos-wide
>>anti-computer, democratically as capable as the swarm of the real computers,
>>to provide intelligence service to us by its influence over the evolution of
>>computation.
> 
> 
> You overestimate your ability with the part that reads "as capable as."
> 
> Carnegie-Mellon University began the development of Capability Maturity Models because
> the swarm to which you refer had been undependable, unreliable, and costly.  The
> paradigm of Extreme Programming is an ad hoc implementation of certain parts of the
> Capability Maturity Models for people who cannot read technical documentation for lack
> of illustrations.

Did they try to do something for people who can't read illustrations for lack 
of technical documentation ?

> 
> I suspect, however, that the companies for which you worked depended on the very
> religious faith that you have so willfully disrespected.It is likely that they
> failed to demonstrate any productivity from their computer investments until recession
> forced them to institute sound business practices once again--that is, if they
> survived.

Well, last I worked seriously for somebody it was a school of psychology and 
indeed the most spectacular thing was how computer displays got the majority 
of attention of paid workers, an evolution that I think in the case of 
psychology allows reading as a recession, if not financial.

> 
> :-)

;)) MC

0
borcis (46)
2/6/2004 8:49:51 PM
"galathaea" <galathaea@excite.com> wrote in message
news:10200ukiinuv083@corp.supernews.com...

> : COLOR VISION
> :
> : According to the Young-Helmholtz theory of color vision, the sensation
> : of any color can be achieved by the superposition of pure red,
> : green and blue colors.

> I am uncertain as to your intent with this material, but I would mention
> that our visible spectrum covers just under one full octave (frequency
> doubling), so chord space is constrained.  But more importantly, we do not
> have the resolution of our auditory senses, visual being a basic 4 point
> interpolation (a rod type plus 3 cone types).  This does contribute to the
> recognition problem mathematically, and does cause some recognition
problems
> to be undecidable (thus Boolean propositions fail to be satisfactory), and
> it also makes it difficult to determine any consonance / dissonance
> relationships as found in auditory theory.  However, some of the more
> developed research has focused on similar effects in spatial pattern
> organisation, where the wave studied is the optic wave over the retinal
> receptors and not the electromagnetic.  Interesting stuff, but I fear not
> relevant to my post.
>

I was providing setup for the notion of ongoing patterns interacting.
Interference and resulting changes and all that.

> : As concerns a summary of Heyting and Brouwer.

> These certainly illustrate some of the difficulties encountered by the
early
> constructivists, and some of the origins of the thought in the area.  Of
> course, theories usually migrate from the initial position some as the
> theory matures, and I believe that modern theory of constructivism would
> make some distinctions not made in the above discussion.
>

> : "The suggestion that the auditory cortex is inherently suited to analyze
> : visual input is not far-fetched. I mentioned that frequency (pitch) in
> : hearing behaves a lot like space in vision. The mind treats soundmakers
> : with different pitches as if they were objects at different locations,
> : and it treats jumps in pitch like motions in space" [page 96]
> :
> : The Blank Slate: The Modern Denial of Human Nature
> : by Steven Pinker
> : http://www.amazon.com/exec/obidos/tg/detail/-/0142003344/

> Neural plasticity is one of the wonders of the biological world.  It is my
> belief that the conceptual space of all inputs, be they the classical
> senses, proprioception, internal and external thermo- or chemo- reception,
> body positioning and muscle feedback, and much of the autoregulatory
systems
> are all abstracted during the neural transmission to attractor spaces of
> concepts.  The shape and domain of the attractors are adjusted through
> learning, and as I mentioned, the logic of propositions on them is
Heyting.
> Very often, the attractors use "local" information in their dynaimcs, the
> neuron's neighborhood creating short-term local memories that cause the
> processing to be determined on only very recent states.  This is found,
for
> example, in "pitch relativism", along with many other phenomena.

Here plasicity wasn't the point but relativistic attribution of scaled
models and their tunings. If someone is plaing a piece of music on a guitar
and someone else is slowely tightening the 6 strings evenly tighter, it
would be like spining a record faster and hearing strange but consistent
versions.

As with different languages how we can tune our sounds, particular words,
and definitions, to what is to be described.

When we tune neural activities to a problem.

> The shape and domain of the attractors are adjusted through
> learning, and as I mentioned...

John McCrone has argued recently that some areas of the brain have
completely different operating systems and programming languages with
sophisticated schemata or drivers for translating between devices. These
attractors you mention, are you saying the brain is a single fractal or
saying like the avant guard that each area harbor groups of possible
fractals each with their zillions of point of attraction or repulsion. And
that as in geometry how we iterate a formula and draw the entire space, that
these fractals in each area draw that space by consequent interference [and
the other musical interferences]?

Competing fractals from poly-sensory percetion. THe balancing of the
competing attractions, extended through magnitudal and distributed levers,
is like a musical composition, explained by an economicist in multitudal
jargons, explaing the relations between various parts of the brain.

John McCrones Page
http://www.btinternet.com/~neuronaut/webtwo_articles.html


> : As concerns comments from Kevin Kelley's; Out of Control
> : http://www.kk.org/outofcontrol/contents.php

> Actually, I have done much research myself along the lines of Stuart A.
> Kauffman's brilliant "The Origins of Order: Self-Organisation and
Selection
> in Evolution" and the Nocolis / Prigogine classic "Self-Organisation in
> Nonequilibrium Systems: From Dissipative Structures to Order through
> Fluctuations", in particular looking at the boundaries between
controllable
> and chaotic behavior and the phase transition the boundary represents.
>
> In regards to my post's topic, this is an important area because the
> proposition space becomes altered in a fundamentally interesting way.
> Although both sides of the boundary are represented by Heyting algebras,
the
> analysis on either side changes and this, I believe, is an important
> approach to elucidating the semantic origins of the Heyting structure.
>
> [...]

> : As concerns trends in Acedemia

> : DaDaPaPa. All that shit is now in the process of being railroaded
> : and anhilated by systems_theory entering the gates of aCedemia,
> : all in suit and tie, they will intellectually die or absorb the
> : complex and chaotic! The job is getting done well now and itz all
> : melting, ahhhhh, I'm melting Dorthy.
>
> Every field has its own pet name for the final unifying principle of the
> sciences.  Now with social structures being successfully mathematically
> modeled, along with ecologies, biological systems, complex materials, etc.
> and many mathematical fields being brought in to organise the information
> being recovered, there are many terms springing up in the literature for
> this new holism.  Rene Thom, for example, implies at times that
catastrophe
> theory could also take this name.  Synergetics and control theory claimed
> this as theirs.  And so on.
>
> I'm more of the opinion that models in general are the foundation, but
many,
> if not most, areas of math will make their contributions along the way.
>
> [...]

> : As concerns the book:
> : Consilience : The Unity of Knowledge
> : by Edward O. Wilson
> : http://www.amazon.com/exec/obidos/tg/detail/-/0679450777/
>
> I often believe that the Greeks (along with certain scientific
> personalities) were very good at PR.  The origin of order and the
"ordering"
> of nature goes far back prior to the greeks as a principle of research.
> Earlier numerology was used, as was the basic use of mythology in general.
> And I believe there have always been those who have tried to unite many of
> the sciences.  Interdisciplinarians have been around throughout history,
and
> I do not believe our era has any larger proportions statistically than,
say,
> the early 1900s or the 19th and 18th centuries.  The interdisciplinarians
of
> today, though, have more information at their disposal, so more of them
are
> successful in the models they build being useful to us.
>


---------------------------------

Origional response...

> While you are reading this, your retinal rods and cones are interpreting
> images projected onto them.  Each letter, like the
>
> W
>
> that begins this post is given a neural focus, an "attention", as rhythmic
> waves refresh the focus regularly.  The transmission through the optic
> ganglions and along the optic fibres of the raw inforation of the
>
> W
>
> goes through a processing which has been well studied in the literature.
> One successful modeling approach is that of the connectionists or found in
> the neural net literature.  The oculomotor loop and the importance of
> saccades is established.  We have many models on how neural nets detect
> edges, identify topological components in their optic information,
> determine orientation.  The retinotopic map is formed.
>
> These models are useful to the extent that there is actual technology
> built with these models, and they make good money today.  They agree
> with our experiments extremely well.  We can usefully pattern match
> the shape
>
> W
>
> with a fair degree of accuracy.
>

I have been trying to look at 12 tonal musical systems and comparing this
with optics and wave interference, and trying to see if neural activity is
constrained in scale and meter as notes and chords increase, decrease, and
more or less self regulate themseves. So I begin with junk found with a
click.

-------------------------------

COLOR VISION

According to the Young-Helmholtz theory of color vision, the sensation of
any color can be achieved by the superposition of pure red, green and blue
colors. This fact was proved experimentally and indicates that in the eye
there are three types of receptors, which are sensitive separately to red,
green and blue light. These receptors are excited in proportions that
correspond to the color of the visible light. Red light excites only the red
light receptors, green light excites the receptors responsible for green
light, and blue light receptors of blue light. If all receptors are excited
to an equal degree, we have the sensation of white light, and if the
receptors are not excited, the sensation of darkness. For this reason, the
overlapped spots of the red, green and blue light shown in the figure look
like a white spot. Additionally, the superposition of red and blue lights
appears magenta, superposition of the green and blue lights appears cyan,
and superposition of red and green colors appears as a yellow color.

http://physics.nad.ru/Physics/English/rgb_txt.htm
http://physics.nad.ru/Physics/English/optics.htm

---------------------------------

Superposition of Waves

The principle of superposition may be applied to waves whenever two (or
more) waves travelling through the same medium at the same time. The waves
pass through each other without being disturbed. The net displacement of the
medium at any point in space or time, is simply the sum of the individual
wave dispacements. This is true of waves which are finite in length (wave
pulses) or which are continuous sine waves.

http://www.kettering.edu/~drussell/Demos/superposition/superposition.html
http://www.kettering.edu/~drussell/demos.html

--------------------------------

Constructive Wave Interference

During the time when one wave passes through another we say that the waves
interfere. It is really not correct to say that the waves collide or hit,
although this is often how such an interaction is termed.

When the crest of one wave passes through, or is superpositioned upon, the
crest of another wave, we say that the waves constructively interfere.
Constructive interference also occurs when the trough of one wave is
superpositioned upon the trough of another wave.

During any wave interference the shape of the medium is determined by the
sum of the separate amplitudes of each wave. We often say that when waves
interfere, amplitudes add.

http://tinyurl.com/27l4z

-------------------------------

Destructive Wave Interference

When the crest of one wave passes through, or is superpositioned upon, the
trough of another wave, we say that the waves destructively interfere.

During any wave interference the shape of the medium is determined by the
sum of the separate amplitudes of each wave. We often say that when waves
interfere, amplitudes add. During destructive interference, since the
positive amplitudes from one crest are added to the negative amplitudes from
the other trough, this addition can look like a subtraction.

http://tinyurl.com/3ep37

--------------------------------

Two Source Interference Pattern

Although both sources are repeatedly producing waves which move across the
medium, a stable, that is, motionless, pattern is set up. As it turns out,
the regions of constructive interference do not move, nor do the regions of
destructive interference.

These motionless regions have a shape, or pattern, which can be measured.
These measurements can be used to calculate the wavelength of the waves
which are producing the pattern. In this way one can find the wavelength of
a moving wave.

http://tinyurl.com/2frv9

--------------------------------

RESONANCE

When you push a person on a swing, a series of small pushes makes the person
swing through a large amplitude. To accomplish this, you time your pushes to
match the swing's natural frequency, the rate at which the swing tends to
move back and forth.

....most objects tend to vibrate at certain frequencies. You may have noticed
that parts of your car rattle at a certain speed or that certain objects
vibrate and buzz in response to a particular note from your stereo. These
are everyday examples of resonance.

Resonance has also been responsible for some spectacular destruction. In
earthquakes, buildings are often damaged when the frequency at which the
ground is shaking comes very close to or matches one of the resonant
frequencies of the buildings. The Tacoma Narrows Bridge vibrated itself to
pieces when a strong wind pushed it at just the right frequency. The wing of
the Lockheed Electra jet failed repeatedly until engineers discovered that
the wing's resonant frequency was responsible for its destruction. A
suspended walkway at a Kansas City hotel collapsed when people dancing on
the structure caused resonant vibration.

In the army, troops always march across a bridge out of step; army vehicles
are spaced at irregular intervals when crossing a bridge. These practices
avoid setting up vibrations at the bridge's resonant frequency.

Not all objects resonate. Any object that dissipates energy faster than the
energy is added will not resonate.

http://www.exploratorium.edu/snacks/resonator.html

--------------------------------

This here would be some of the math involved with musical instuments like
the guitar or piano. Like with light waves, sound waves of differring
frequencies produce other sounds and stop yet other sounds. Scales and
chords. Something strange happens when we strike three or four notes all in
the same scale but of different 12 tone note values. You could say the body
of the instrument is ringing in all frequencies but the lambda calculus
[amplifies some sounds and diminishes others]

Acoustics II: Sound and Vibration

1. Vibration of 1-DOF Simple Oscillators

Comparing Circular and Sinusoidal Motion - how is circular motion in the
complex plane (magnitude and phase) related to sine and cosine functions?

Simple Harmonic Oscillator - with and without damping, transfer of energy
between kinetic and potential forms

Damped Harmonic Oscillator - underdamped, overdamped, and critically damped

Forced Harmonic Oscillator - transient and steady state response to a force
applied to the mass

Base Motion - transient and steady state response of an oscillator to
displacement of its support

The Simple Pendulum - comparing the linear approximation (small angle) with
a real pendulum

2. Vibration of Multi-DOF Systems

Coupled Oscillators - energy transfer between two mass-spring systems
coupled together

Dynamic Absorbers - J.P. Den Hartog's classical undamped tuned dynamic
absorber

Vibrational modes of a multi-dof system - progression of mode shapes from
single degree-of-freedom to continuous structure

3. Vibrational Modes of Continuous Systems

Vibrational Modes of a Hanging Chain - mode shapes for a hanging chain

Vibration of a Fixed-Fixed String - mode shapes, and frequency spectra for a
plucked string

Rectangular Membrane - and degenerate modes of a square membrane [no text
yet, but movies work]

Circular Membrane - or how a drum head vibrates

Vibration of Baseball Bats - bending modes (sweet spot) and cylinder modes
(ping)

Vibrational Modes of an Electric Guitar - actual experimental Modal Analysis
data

Vibrational Modes of an Acoustic Guitar - actual experimental Modal Analysis
data

Tacoma Narrows Bridge - (0.668 MB mpeg movie) - when engineers don't account
for resonance when designing structures

http://www.kettering.edu/~drussell/demos.html

> The logic of propositions in the models on shape theory, the theory of the
> topological, metrical, and orientation-based classification calculus, the
> dynamical logic of the attractor spaces in neural net models, the
> region-connection calculus, all of these logics are Heyting.
>

Heyting attended the Erkenntnis Symposium at Konigsberg in September 1930.
There he represented intuitionism while Carnap and von Neumann represented
logicism and formalism respectively. Each argued their own case and against
that of the other two. Although Heyting's version of intuitionist logic
differed somewhat from that of Brouwer, it is clear that one of his main
aims was to make Brouwer's ideas more accessible and better known. Brouwer
had presented his ideas in a deliberately non-formal, and very personal,
way.

http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Heyting.html

------------------------------

From an early stage Brouwer was interested in the philosophy of mathematics,
but he was also fascinated by mysticism and other philosophical questions
relating to human society. He published his own ideas on this topic in 1905
in his treatise Leven, Kunst, en Mystiek (Life, art, and mysticism). In this
work he [1]:-

.... considers as one of the important moving principles in human activity
the transition from goal to means, which after some repetitions may result
in activities opposed to the original goal.

Brouwer's doctoral dissertation, published in 1907, made a major
contribution to the ongoing debate between Russell and Poincar� on the
logical foundations of mathematics. His doctoral thesis [13]:-

.... revealed the twin interests in mathematics that dominated his entire
career; his fundamental concern with critically assessing the foundations of
mathematics, which led to his creation of intuitionism, and his deep
interest in geometry, which led to his seminal work in topology ...

He quickly discovered that his ideas on the foundations of mathematics would
not be readily accepted [13]:-

Brouwer quickly found that his philosophical ideas sparked controversy.
Korteweg, his thesis advisor, had not been pleased with the more
philosophical aspects of the thesis, and had even demanded that several
parts of the original draft be cut from the final presentation. Korteweg
urged Brouwer to concentrate on more "respectable" mathematics, so that the
young man might enhance his mathematical reputation and thus secure an
academic career. Brouwer was fiercely independent and did not follow in
anybody's footsteps, but he apparently took his teacher's advice ...

Brouwer continued to develop the ideas of his thesis in The Unreliability of
the Logical Principles published in 1908.

The research which Brouwer now undertook was in two areas. He continued his
study of the logical foundations of mathematics and he also put a very large
effort into studying various problems which he attacked because they
appeared on Hilbert's list of problems proposed at the Paris International
Congress of Mathematicians in 1900. In particular Brouwer attacked Hilbert's
fifth problem concerning the theory of continuous groups. He addressed the
International Congress of Mathematicians in Rome in 1908 on the topological
foundations of Lie groups. However, after studying Sch�nflies' report on set
theory, he wrote to Hilbert:-

I discovered all of a sudden that the Schoenfliesian investigations
concerning topology of the plane, on which I had relied in the fullest way,
could not be taken as correct in all parts, so that my group-theoretic
results also became doubt...

....When Brouwer was beginning his career as a mathematician, set-theoretic
topology was in a primitive state. Controversy surrounded Cantor's general
set theory because of the set-theoretic paradoxes or contradictions. Point
set theory was widely applied in analysis and somewhat less widely applied
in geometry, but it did not have the character of a unified theory. There
were some perceived benchmarks. For example; the generally held view that
dimension was invariant under one-to-one continuous mappings ...

Van der Waerden, in the above quote, said that Brouwer would not lecture on
his own topological results since they did not fit with mathematical
intuitionism. In fact Brouwer is best known to many mathematicians as the
founder of the doctrine of mathematical intuitionism, which views
mathematics as the formulation of mental constructions that are governed by
self-evident laws. His doctrine differed substantially from the formalism of
Hilbert and the logicism of Russell. His doctoral thesis in 1907 attacked
the logical foundations of mathematics and marks the beginning of the
Intuitionist School. His views had more in common with those of Poincar� and
if one asks which side of the debate between Russell and Poincar� he came
down on then it would have with the latter...

Kneebone writes ... about Brouwer's contributions to the philosophy of
mathematics:-

Brouwer is most famous ... for his contribution to the philosophy of
mathematics and his attempt to build up mathematics anew on an Intuitionist
foundation, in order to meet his own searching criticism of hitherto
unquestioned assumptions. Brouwer was somewhat like Nietzsche in his ability
to step outside the established cultural tradition in order to subject its
most hallowed presuppositions to cool and objective scrutiny; and his
questioning of principles of thought led him to a Nietzschean revolution in
the domain of logic. He in fact rejected the universally accepted logic of
deductive reasoning which had been codified initially by Aristotle, handed
down with very little change into modern times, and very recently extended
and generalised out of all recognition with the aid of mathematical
symbolism.

Kneebone also writes in [3] about the influence that Brouwer's views on the
foundations of mathematics had on his fellow mathematicians:-

Brouwer's projected reconstruction of the whole edifice of mathematics
remained a dream, but his ideal of constructivism is now woven into our
whole fabric of mathematical thought, and it has inspired, as it still
continues to inspire, a wide variety of inquiries in the constructivist
spirit which have led to major advances in mathematical knowledge.

Despite failing to convert mathematicians to his way of thinking, Brouwer
received many honours for his outstanding contributions. We mentioned his
election to the Royal Dutch Academy of Sciences above. Other honours
included election to the Royal Society in London, the Preussische Akademie
der Wissenschaften in Berlin, and the Akademie der Wissenschaften in
G�ttingen. He was awarded honorary doctorates the University of Oslo in
1929, and the university of Cambridge in 1954. He was made Knight in the
Order of the Dutch Lion in 1932.

http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Brouwer.html

-----------------------------------

Heyting published a paper on intuitionistic algebra in 1941 and
intuitionistic Hilbert spaces in the 1950's. These were ground-breaking
works. Another major treatise which has presented intuitionism to both
mathematicians and logicians was Intuitionism: an Introduction (1956, second
edition 1966). Gilmore begins his excellent review of this book as follows:-

This is an introduction to intuitionistic mathematics for mature
mathematicians. The reader is taken rapidly to the heart of several
different branches of intuitionistic mathematics. The speed of development
is achieved by condensing the proofs and by presuming familiarity with the
classical counterparts to the theories discussed.

The book is written as a dialogue between Class (a classical mathematician),
Form (a formalist), Int (an intuitionistic mathematician), Letter (a
finitistic nominalist), Prag (a pragmatist), and Sign (a significist). In
the first chapter Int defends intuitionistic mathematics against the
criticism of the others, asking them finally to judge for themselves. In the
remaining chapters Int presents mathematics for them to judge. In these
chapters Class, except for Int, is the most loquacious; he frequently
compares classical results with corresponding intuitionistic results and his
questions lead Int to a more detailed discussion of some points. The device
of dialogue allows abbreviation of statements without loss of clarity.

The article [4] shows the major influence that Heyting has had on the study
of the foundations of mathematics and in so doing shows the importance of
Heyting's contributions. Franchella argues that Heyting has been the cause
of two major changes of direction. Firstly, at least partly because of him,
the topic has moved away from trying to answer the big problems such as
"what is mathematics?". Heyting moved away from these big problems,
concentrating on trying to identify formal, intuitive, and logical concepts
in the study of mathematics. The second change which Franchella argues that
Heyting brought about was a realisation that there exist degrees of evidence
in mathematics. This is a particularly important aspect of mathematics today
when computer programs are being used to verify mathematical proofs:-

What was specific to intuitionism, however, was the thesis that mathematics
is an activity, a process of becoming, the exhaustive description of which
is impossible, just as it is impossible to define once and for all its
elementary concepts.

http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Heyting.html

------------------------------------


> Of course, human pattern matching involves much additional information
> processing.  When the
>

Researchers rewired ferret's eyes and into the hearing cortex. It works and
they can walk around seeing through their ears.....

Pinker goes on to defend the idea of 'reference by relations' in sound where
"pitch" is like location in space. Adjusting the framework to the -key- of
the music [or other successions] at the consequence of other unatural
attempts?

"The suggestion that the auditory cortex is inherently suited to analyze
visual input is not far-fetched. I mentioned that frequency (pitch) in
hearing behaves a lot like space in vision. The mind treats soundmakers with
different pitches as if they were objects at different locations, and it
treats jumps in pitch like motions in space" [page 96]

The Blank Slate: The Modern Denial of Human Nature
by Steven Pinker
http://www.amazon.com/exec/obidos/tg/detail/-/0142003344/

I mention this because as in music there is alot of self adjusting to the
location markers of "pitch relativism."

> W
>
> is blurry, when the information is vague, we may look to the surrounding
>
> *hile
>
> and call on recollections of known forms of full words.  We've learned to
> attach meanings to utterances and visual shapes, and while you are reading
> this you are building structures of meaning to the words which can assist
in
> the recognition, determining patterns of abstractions connected in a
mental
> system of relationship which is still poorly understood. But every year
more
> information is gathered.  The schematic decomposition of the process is
> being studied, and regularly receives more insight towards
the -architectonic
> basis of the function and dynamics of thought.
>
> And, we can formalise the game of language.  Formal languages have a well
> studied mathematical foundation, and the reasoning in a semantic system
can
> be formalised in a model theory.  When we look to the many sources of
> "reasoning about", from necessities and modalities to counterfactual
> possible worlds, satisfaction (semantic), operational resolution, etc. we
> find many different logics.  But they are all Heyting, and this
substructure
> common to all semantic theory allows for a rich functor structure of
> equivalences and dualities amongst these logics.  There are common
> dictionaries to translate between various related semantics.
>
> And there appears to be a very important reason this Heyting substructure
is
> found so predominantly in the formal languages and foundations of
> mathematics.  Formal reasoning has a structure of a state and its
> transitions, it is in many ways the analysis of an automaton whose
> transition graph is specified by the logic of the reasoning.  Proof theory
> is very intimately related to the theory of computation and the lambda
> calculus.  The lambda calculus has a well known Heyting structure, and we
> have the Church-Turing thesis over our shoulders hinting that this may
very
> well be the most primary structure found in all algorithmics.
>

From his experiments in artificial life in swarm models, Chris Langton,
Kauffman's Santa Fe Institute colleague, derived an abstract quality (called
the lambda parameter) that predicts the likelihood that a particular set of
rules for a swarm will produce a "sweet spot" of interesting behavior.
Systems built upon values outside this sweet spot tend to stall in two ways.
They either repeat patterns in a crystalline fashion, or else space out into
white noise. Those values within the range of the lambda sweet spot generate
the longest runs of interesting behavior.

By tuning the lambda parameter Langton can tune a world so that evolution or
learning can unroll most easily. Langton describes the threshold between a
frozen repetitious state and a gaseous noise state as a "phase
transition"-the same term physicists use to describe the transition from
liquid to gas or liquid to solid. The most startling result, though, is
Langton's contention that as the lambda parameter approaches that phase
transition-the sweet spot of maximum adaptability-it slows down. That is,
the system tends to dwell on the edge instead of zooming through it. As it
nears the place it can evolve the most from, it lingers. The image Langton
likes to raise is that of a system surfing on an endless perfect wave in
slow motion; the more perfect the ride, the slower time goes.

This critical slowing down at the "edge" could help explain why a precarious
embryonic vivisystem could keep evolving. As a random system neared the
phase transition, it would be "pulled in" to rest at that sweet spot where
it would undergo evolution and would then seek to maintain that spot. This
is the homeostatic feedback loop making a lap for itself. Except that since
there is little "static" about the spot, the feedback loop might be better
named "homeodynamic."

Stuart Kauffman also speaks of "tuning" the parameters of his simulated
genetic networks to the "sweet spot." Out of all the uncountable ways to
connect a million genes, or a million neurons, some relatively few setups
are far more likely to encourage learning and adaptation throughout the
network. Systems balanced to this evolutionary sweet spot learn fastest,
adapt more readily, or evolve the easiest. If Langton and Kauffman are
right, an evolving system will find that spot on its own.

Langton discovered a clue as to how that may happen. He found that this spot
teeters right on the edge of chaotic behavior. He says that systems that are
most adaptive are so loose they are a hairsbreadth away from being out of
control. Life, then, is a system that is neither stagnant with
noncommunication nor grid-locked with too much communication. Rather life is
a vivisystem tuned "to the edge of chaos"-that lambda point where there is
just enough information flow to make everything dangerous.

Out of Control
Chapter 20: THE BUTTERFLY SLEEPS
- Self-Tuning Vivisystems
http://www.kk.org/outofcontrol/ch20-e.html

---------------------------------------

This set of math techniques that Kauffman, Holland and others devised is
still without a proper name, but I'll call it here "net math." Some of the
techniques are known informally as parallel distributed processing, Boolean
nets, neural nets, spin glasses, cellular automata, classifier systems,
genetic algorithms, and swarm computation. Each flavor of net math
incorporates the lateral causality of thousands of simultaneous interacting
functions. And each type of net math attempts to coordinate massively
concurrent events-the kind of nonlinear happenings ubiquitous in the real
world of living beings. Net math is in contradistinction to Newtonian math,
a classical math so well suited to most physics problems that it had been
seen as the only kind of math a careful scientist needed. Net math is almost
impossible to use practically without computers.

The wide variety of swarm systems and net maths got Kauffman to wondering if
this kind of weird swarm logic-and the inevitable order he was sure it
birthed-were more universal than special. For instance, physicists working
with magnetic material confronted a vexing problem. Ordinary
ferromagnets-the kind clinging to refrigerator doors and pivoting in
compasses-have particles that orient themselves with cultlike uniformity in
the same direction, providing a strong magnetic field. Mildly magnetic "spin
glasses," on the other hand, have wishy-washy particles that will
magnetically "spin" in a direction that depends in part on which direction
their neighbors spin. Their "choice" places more clout on the influence of
nearby ones, but pays some attention to distant particles. Tracing the
looping interdependent fields of this web produces the familiar tangle of
circuits in Kauffman's home image. Spin glasses used a variety of net math
to model the material's nonlinear behavior that was later found to work in
other swarm models. Kauffman was certain genetic circuitry was similar in
its architecture.

Unlike classical mathematics, net math exhibits nonintuitive traits. In
general, small variations in input in an interacting swarm can produce huge
variations in output. Effects are disproportional to causes-the butterfly
effect.

Even the simplest equations in which intermediate results flow back into
them can produce such varied and unexpected turns that little can be deduced
about the equations' character merely by studying them. The convoluted
connections between parts are so hopelessly tangled, and the calculus
describing them so awkward, that the only way to even guess what they might
produce is to run the equations out, or in the parlance of computers, to
"execute" the equations. The seed of a flower is similarly compressed. So
tangled are the chemical pathways stored in it, that inspection of a unknown
seed-no matter how intelligent-cannot predict the final form of the unpacked
plant. The quickest route to describing a seed's output is therefore to
sprout it.

Equations are sprouted on computers. Kauffman devised a mathematical model
of a genetic system that could sprout on a modest computer. Each of the
10,000 genes in his simulated DNA is a teeny-weeny bit of code that can turn
other genes either on or off. What the genes produced and how they were
connected were assigned at random.

This was Kauffman's point: that the very topology of such complicated
networks would produce order-spontaneous order!-no matter what the tasks of
the genes.

Out of Control
Chapter 20: THE BUTTERFLY SLEEPS
- Net math: a counter-intuitive style of math
http://www.kk.org/outofcontrol/ch20-b.html

> When we look to topics like Martin-Lof type theory to explain the
evolution
> of the objects of or conceptions and the structure of describing our
world,
> again we have its Heyting structure well known and studied.
>
> Constructivism is very much the study of process and information, of the
> logic of propositions on information structures.  Processing information
> allows us to channel it to useful decision making.  It appears to be prior
> epistemically to the abstraction of a "reality".
>
> And we use this structure in our theories about the world around us.  In
> general, the semantics of evolving collections of objects and causality is
> known to be Heyting.  Applications of Heyting semantics have been detailed
> for antigen-antibody interactions or the deviation of a cancer process,
but
> one of the most fascinating applications for me has always been the
analysis
> of quantum propositions and the evolution of quantum systems.  In fact,
the
> work of von Neumann and Birkhoff is one of the most stark expressions of
> this generality, where it was shown that contrary to much early physics,
the
> logic of the universe may very well be that of a Heyting algebra that is
not
> Boolean.
>
> Now, I appologise for the large crossposting, but I believe this post to
be
> topical to all newsgroups in my list.

I offer me rants! Its music with feeling.

> I earnestly feel that there is a
> common thread which needs to be discussed amongst all of these
communities.
> I am concerned about the education of constructive theory and Heyting
> semantics prior to the study of classical logic and Boole (and Aristotle
> when you lack quantifiers, etc.).  And when I say Heyting here, prior, and
> to come, I also intend co-Heyting, for obviously there are semantics
> mentioned who have more reasonable interpretations in the dual algebras,
but
> that is of course a contravariant functor away.
>
> For some reason, I feel that this sounds like a radical idea, even though
I
> also get the impression that Heyting algebras are not the controversy they
> were when associated more strongly with Brouwer and -intuitionism.  There
are
> obviously many communities using them.  They appear to be intimately
related
> with conceptualisation and the thought process.
>

Intuitionism
From Wikipedia, the free encyclopedia.

In the philosophy of mathematics, intuitionism, or neointuitionism (opposed
to preintuitionism), is an approach to mathematics as the constructive
mental activity of humans.

Any mathematical object is considered to be a product of a construction of a
mind, and therefore, the existence of an object is equivalent to the
possibility of its construction. This contrasts with the classical approach,
which states that the existence of an entity can be proved by refuting its
non-existence. For the intuitionist, this is invalid; the refutation of the
non-existence does not mean that it is possible to find a constructive proof
of existence. As such, intutionism is a variety of mathematical
constructivism; but it is not the only kind.

Intuitionism takes the validity of a mathematical statement to be equivalent
to its having been proved; what other criteria can there be for truth (an
intuitionist would argue) if mathematical objects are merely mental
constructions? This means that an intuitionist may not believe that a
mathematical statement has the same meaning that a classical mathematician
would. For example, to say A or B, to an intuitionist, is to claim that
either A or B can be proved. In particular, the law of excluded middle, A or
not A, is disallowed since one cannot assume that it is always possible to
either prove the statement A or its negation. (See also intuitionistic
logic.)

Intuitionism also rejects the abstraction of actual infinity; i.e., it does
not consider as given objects infinite entities such as the set of all
natural numbers or an arbitrary sequence of rational numbers. This requires
the reconstruction of the most part of set theory and calculus, leading to
theories highly different from their classical versions.

http://en.wikipedia.org/wiki/Intuitionism

> Yet, going through the college system, I found it rare for non-specialists
> to be aware of the more general Heyting structures found in their
respective
> fields, though they were often well prepared in classical logic.  And I
> often found that this presented a much _less_ useful tool in which to
> evaluate the structures of their fields.  The application of Boolean
logics
> to quantum systems is one of the major sources of "strangeness" under
which
> quantum mechanics is commonly described, and understanding how to properly
> make propositions about quantum systems can clear up much confusion here.
In
> linguistics and formal foundations, there is regular rediscovery of basic
> results on the difficulty of identity and the ambiguity of negation which
> are well described by constructive semantics.  From the theory of Cohen
> forcing to slaving principles and thermodynamic process, from topoi to
> decoherence-function-consistent histories, our fields have many Heyting
> structures lying just an analysis away.
>
> I am not of the opinion that the Boolean has _no_ use, nor would I even
> advocate giving up the Axiom of Choice as a useful tool.  But I do believe
> that prior to exposing a student to these particular models of
mathematical
> reasoning, the more constructive foundations should be explained more
> thoroughly.  Because I do find that alot of misconceptions about
> constructivism get propagated at times.  In particular, on these
newsgroups
> I find that questions concerning issues particularly involved with the
> general theory around applications of Heyting algebras get a much
diminished
> audience to that of more classical analyses of reasoning.  Sometimes there
> is even derision.
>
> John Baez once stated that,
>
> "Intuitionism proceeds by a method known as Winnowing the Audience.
> Essentially, one can avoid the use of formal proofs by making the proofs
so
> long, tedious, and bewildering that only those in agreement bother to read
> them."
>

(3) One-Sided vs Two-Sided Arguments

....It depends to some extent upon how well informed the audience is: The
more well informed the members of the audience are, the less likely they are
to be persuaded by a one-sided argument and the more likely they are to be
persuaded by an argument that brings out the important opposing arguments
and then proceeds to refute them. This makes sense: A well-informed person
is more likely to know some of the counterarguments. When the communicator
avoids mentioning these, the knowledgeable members of the audience are
likely to conclude that the communicator is either unfair or unable to
refute such arguments. On the other hand, an uninformed person is less apt
to know of the existence of opposing arguments. If the counterargument is
ignored, the less-informed members of the audience are persuaded; if the
counterargument is presented, they may get confused...

http://tinyurl.com/27hce

> Obviously, I have placed this without context, and recent comments by Baez
> in support of some of Lawvere's programme may comment to possible changes
in
> position, but the statement is certainly indicative of a trend.  Many
> pop-foundations (pop-philosophy, pop-mathematics, etc.) books still
mention
> the various constructive schools of thought as minor players, sometimes
with
> actual dismissal and often without much detail.  Now, this may only point
to
> a failing of pop books, and although I think most professionals deride the
> pop books of their professions, there is certainly a community attitude
that
> such books commonly intend to convey.
>

DaDaPaPa. All that shit is now in the process of being railroaded and
anhilated by systems_theory entering the gates of aCedemia, all in suit and
tie, they will intellectually die or absorb the complex and chaotic! The job
is getting done well now and itz all melting, ahhhhh, I'm melting Dorthy.

> Yet, I also find that there is quite a large group of communities using
many
> different faces of Heyting structures.  And I find that mathematicians as
a
> whole do seem to appreciate constructive proofs over nonconstructive ones
> where they can get them.  And on some of these newsgroups I even find most
> constructive expositions are well received at times.  I just find that
those
> with a good understanding of the field are either self-trained or studied
> directly under a contributer to the field, and there is often lamentation
> that the field is more widely applicable.  In fact, the field surely seems
> more widely applicable than the study of classical Boolean logic, it being
> only one form of Heyting structure and not applicable to many of the
> structures mentioned or, for example, the well known theory of
decidability
> founded by Godel or the theory of Kleene truth.
>
> For me, constructivist theories have always been computational theories in
> general.  For me, I never found anything "tedious, and bewildering" and
> certainly have not noticed that it might be common to "avoid the use of
> formal proofs" in intuitionism or other constructive programmes.  But this
> was because I read early on about intuitionism and constructivist theories
> as my notions of logic were developing.  By accidents of choices and
> self-education, I learned constructive logics at about the same time as
> learning classical logics.  Certainly, constructivist math can be more
> difficult since you lack some common tools for proof, and I have found
> myself joking about difficulty and obscurity many times in my studies when
I
> first entered certain topics (like algebraic geometry and the analysis of
> varieties and schemes, as an example which I still clearly remember making
> similar comments), when the pantheon of objects and their transformation
> structure was still poorly known by myself, and I find that quotes like
> those of Baez above are often indicative of this early apprehension.  So I
> get concerned about education.
>
> And these are the questions I have for all of our communities out there:
>

> -  is it, with so many applications so fundamentally related in our fields
> unified by the common Heyting thread, perhaps time to start teaching our
> students more about the theory of the Heyting algebra structure prior to
> adding axioms forcing bivalence or existence?

> -  if not, why not?

> -  and, somewhat to get a better picture for myself, why do you believe
the
> more widely applicable Heyting structures and their semantic analysis is
> found to be less important to the education of our students than the
lesser
> applicable Boolean particular case currently taught?
>

Bell Telephone and Microsoft?

> Obviously, I am of the "yes" opinion to the first question.  For the third
> question, I do see the historical contigencies that have guided modern
> education, but after more than a hundred years of constructivist thought
> being advocated, from early rumblings of Kroenecker and Poincare, through
> Brouwer, Weyl, Heyting, Tarski, and the eventual use of the logical
> structure and its semantic analysis in numerous foundational fields, and
its
> modern ubiquity, such explanations still seem to fail for me for modern
> education.  Obviously, mathematics is an easier enterprise with the
> additional tools of excluded middle and transfinite choice, but again I am
> not an advocate of _not_ teaching those tools.  I am only curious about
why
> the constructive logics which seem in numerous ways to be prior to such
> tools are not taught prior.  They certainly can help in the understanding
of
> the more classical approaches.  My hunch for the third question is that
the
> desire for classical logic is very similar to the desire to believe in
> monotheism, that there is this insecurity in many people concerning the
> "absolute" and "reality", and questions of truth and falseness, like
> questions of good and evil, should be knowable to some form of completion.
> I know that is certainly a controversial opinion in some circles, but I
> wanted to throw it out there to give a better view of where I come from
and
> perhaps to stimulate discussion on the third topic.  Paradoxically, I have
> found that although I am drawn to multivalent logics and find monotheism
> anathema (ironic considering the words origins), I also enjoy studying the
> realist interpretations of quantum mechanics, which I suspect are guided
by
> very similar desires, so perhaps I just like to be contrary...
>
> In philosophy, epistemics, cognition, linguistics, formal models,
> computation, and the possible structure of our world, there are unifying
> principles of expressability that I find more and more useful.  It
confuses
> me that I find them still poorly understood in crowds where, at least to
me,
> it has always seemed they should be more well known.  So I thought I'd try
> to bring some of the more relevant communities together and see if I could
> start some discussion on broadening education along these important lines,
> for I feel that such is urgently needed to prevent a lot of "wheel
grinding"
> and repition of already known results in the separate fields.  I really
> believe that such a consolidation of logical education is needed in all of
> our fields to place more focus on our respective advances.
>

Historically, all of the sciences were once united under the rubric of
"natural science." Over time, they became fragmented and specialized.
Nevertheless, Wilson argues that there is a genetic and neurological basis
for knowledge and that all subjects of human inquiry can be reunited under
the umbrella of "consilience." ["a jumping together," of the many branches
of human knowledge]

....a wonderfully broad study that encourages scholars to bridge the many
gaps that yawn between and within the cultures of science and the arts. No
such gaps should exist, Wilson maintains, for the sciences, humanities, and
arts have a common goal: to give understanding a purpose, to lend to us all
"a conviction, far deeper than a mere working proposition, that the world is
orderly and can be explained by a small number of natural laws."

He shows how and why our explosive rise in intellectual mastery of the
truths of our universe has its roots in the ancient Greek concept of an
intrinsic orderliness that governs our cosmos and the human species--a
vision that found its apogee in the Age of Enlightenment, then gradually was
lost in the increasing fragmentation and specialization of knowledge in the
last two centuries. Drawing on the physical sciences and biology,
anthropology, psychology, religion, philosophy, and the arts, Professor
Wilson shows why the goals of the original Enlightenment are surging back to
life, why they are reappearing on the very frontiers of science and
humanistic scholarship, and how they are beginning to sketch themselves as
the blueprint of our world as it most profoundly, elegantly, and excitingly
is.

Consilience : The Unity of Knowledge
by Edward O. Wilson
http://www.amazon.com/exec/obidos/tg/detail/-/0679450777/

>
> -- 
> -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
>
> galathaea: prankster, fablist, magician, liar
>
>
>



0
2/6/2004 8:56:01 PM
mitch wrote:
: galathaea wrote:
: >
: > In case you didn't read it, my post is about education, something I feel
is
: > very important.
: >
:
: Unfortunately, I think many people are somewhat cynical about this
particular
: topic.  If they perceive fortunate circumstance because of education, they
have
: no reason to question its value.  If they are ambivalent there is nothing
to be
: concerned about except, perhaps, the skeptical question concerning the
agenda
: behind a reformer's motivation.

That's one of the nicest explanations I have seen in quite a while!  I am
aware of the difficulties that present themselves concerning reforming
education, but these concerns are why I chose to pick such a large
crossposting and focus on the many useful area my topic arises in.  I though
it would be nice for various communities to come together and share their
work's foundations in Heyting algebras, so that everyone could see that its
teaching was really worthwhile.

I see it somewhat like quantum mechanics.  When QM was first introduced, it
was a research topic and found mostly in the journals.  As the results
became established, which was very quickly done, it moved into graduate
programs.  Now it is an undergraduate topic that gets introduced even to
high school students in their basic chemistry and physics courses.

: On sci.logic, George Greene observed that constructive mathematics was
: difficult.  So what you are describing would increase a burden already
: perceived as onerous for many.

And this is why my suggestion was in particular to introduce the topic prior
to classical logic.  By introduce, I don't mean a complete exposition of
everything in the field.  I intend only that the basic structure of the
logic is taught along with practice of the rules and an overview of the
semantic interpretations.  I just believe that understanding that structure,
by itself, is important to all people interested in modern research in any
of the fields I mention.  But I don't intend to constrain education to only
constructive mathematics, and think afterwards adding axioms of bivalence
and choice and teaching their use is fine.  In other words, I'm not looking
to education forcing students to do constructive mathematics, I just believe
that it is important for students to understand the logical structure, and
personally feel that the best place to do this is while the formal system is
first being developed.

: Galathaea, I have several journal articles on things like constructive
e-sets
: and solvable Boolean algebras.  But I do not have the background to read
them
: directly.  Do you know of any expository texts that would help introduce
me to
: the methodologies for constructive mathematics?

Some classics in the field include Errett Bishop's "Foundations of
Constructive Analysis" and Per Martin-Lof's "Notes on Constructive
Analysis".  A. A. Markov also has a good book about the foundations of
algorithmics and recursive function theory in which the constructive form is
made explicit.

: You might also wish to visit the pages,
:
:  http://plato.stanford.edu/entries/logic-paraconsistent/
:
:  http://plato.stanford.edu/entries/mathematics-inconsistent/
:
: although you are probably aware of them.
:
: I find the fact that these concepts are contrasted with consistency
somewhat
: amusing.  Since my background concerning these questions is closely
associated
: with Kantian epistemology, I am still waiting for someone to convince me
that
: what is taught as "logic" is anything but the fixed delusion of certain
: influential narcissists and those who mistakenly investigated their
program.

I find your comment on what is taught particularly true in those schools
where logic is taught as a part of the philosophy department and not the
mathematics or computer science departments, where there is often quite a
focus on the names.

Although I've looked around plato on the stanford many times before, I don't
believe I have read those two pages.  Particularly the page on inconsistent
mathematics seemed rather odd, and its mention of dualities existing between
formally consistent and formally inconsistent models was intriguing.  I will
have to follow that trail one of these weeks.

: Here is one other site that you might find more interesting.  The Polish
school
: of mathematics (along with Paul Halmos and a few others) pursued algebraic
: semantics along the lines of Tarski's cylindrical algebras.  Jacek
Malinowski
: has a number of interesting papers.  Algebraic semantics allows for a
natural
: distinction between equivalential and non-equivalential logics in contrast
to
: the kind of investigation begun by Heyting.
:
:  http://www.uni.torun.pl/~jacekm/publications.htm

I like the variety of topics covered by the papers listed.  I really thank
you for this one, as I have at various times followed several member of the
Polish school's line of thought.

: Still, I would like to see someone discussing the details of Heyting
algebras
: with you.  I am now aware that many of my own former computer tasks were
based
: on the structure of Brouwerian semilattices.  Had I been aware of that at
the
: time, I probably could have done a number of things far more effectively.

On one of my jobs, we required certain proofs on modules in our programs
concerning maintaining invariants and other routine programming checks such
as algorithmic correctness and completeness.  Although most coders could do
the proofs by hand, when we decided to automate, several other coders became
frustrated with the propositional logic needed, and it was eventually handed
over to me to do.  I also was the only one with training in functional
languages, which also netted me some jobs no one else would take.  Sometimes
being efficient doesn't mean less work!

=)

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/6/2004 9:35:20 PM
galathaea wrote:
> mitch wrote:
> : galathaea wrote:
> : >
> : > In case you didn't read it, my post is about education, something I feel
> is
> : > very important.
> : >
> :
> : Unfortunately, I think many people are somewhat cynical about this
> particular
> : topic.  If they perceive fortunate circumstance because of education, they
> have
> : no reason to question its value.  If they are ambivalent there is nothing
> to be
> : concerned about except, perhaps, the skeptical question concerning the
> agenda
> : behind a reformer's motivation.
> 
> That's one of the nicest explanations I have seen in quite a while!

Just to beg inclusion into some other bucket of the classification, I myself 
am of the opinion that education reform in mathematics counts as the most 
efficient intergalactic space drive we can have !

0
borcis (46)
2/6/2004 10:22:01 PM
galathaea wrote:
> 
> Sokol's little prank

I believe the name is Sokal, and that the accurate name for his device was 
trojan horse.

0
borcis (46)
2/6/2004 11:04:38 PM
galathaea wrote:
> 
> "Steve Schafer" wrote:
> : On Fri, 6 Feb 2004 09:10:06 -0800, "galathaea" <galathaea@excite.com>
> : wrote:
> :
> : >Can you please explain why I get such responses, when I have taken time
> : >to carefully write my post?
> :
> : It has been said that unless you are able to explain an idea in such a
> : way that a three-year-old can understand it, you don't truly understand
> : it yourself. I wouldn't go quite that far, but the thought does have
> : some merit.
> 
> I actually felt that what I wrote was dumbing things down quite a bit.  I am
> getting the feeling that is more a problem of attention defecit and the
> length of the post more than anything else.  All of the comments so far have
> made it quite clear that the negativity was due to having not read any
> furthur than the first few paragraphs.
> 
> : A couple of specific criticisms:
> :
> : You haven't laid any framework for your discussion. You launch right
> : into elaboration without even stating the topic, and so your readers are
> : guaranteed to be lost from the very beginning. _You_ may know what
> : you're talking about, but nobody else does. It's a bit like the three
> : rules of thumb for a scientific paper or presentation: (1) Tell them
> : what you're going to tell them. (2) Tell them. (3) Tell them what you
> : just told them.
> 
> I rarely see the abstract/paper/conclusion format on these groups, but if
> you think it would help, maybe I will try that approach.  It does seem
> apparent that some people are having a difficult time reading far enough to
> see any of the points made.
> 
> : Your long-winded prose is so meandering (and occasionally convoluted)
> : that it's difficult to figure out what the hell you're trying to say,
> : sometimes even within a single paragraph. On the surface, it begins to
> : sound like the meaningless drivel that so often passes for literary
> : criticism these days, and which Alan Sokol so successfully parodied a
> : few years back. (Note that I'm not saying that your writing _is_
> : meaningless drivel, only that it _looks_ like meaningless drivel.)
> 
> I don't find it too meandering.  It has a fairly linear outline.  It first
> introduces the point that Heyting algebras are currently considered very

How many readers of sci.lang do you think know what Heyting algebras
are?
-- 
Peter T. Daniels                       grammatim@att.net
0
grammatim (38)
2/7/2004 1:09:29 AM
in article <40243ac9.34dd@worldnet.att.net>,
peter t. daniels <grammatim@worldnet.att.net> wrote:

|How many readers of sci.lang do you think know what Heyting algebras
|are?

a fair number of them, but probably fewer than the number who think
that your attempts to narrow the focus of the newsgroup are motivated
by your personal insecurities about your vast ignorance.


-- 


[e-mail address jdolan@math.ucr.edu]

0
jdolan1 (1)
2/7/2004 2:11:13 AM
"Peter T. Daniels" wrote:
: How many readers of sci.lang do you think know what Heyting algebras
: are?

Well, from the discussions I've read lately, admittedly not many.  But they
should!  When you are approaching an analysis of natural languages inside
logical classification systems, one is lead to topics like Dynamic Predicate
Logic where you begin to model the natural languages in induction and
implication logics.  When these elements are combined with theoretical or
semi-empirical metrics on phoneme space and between logical structures, one
gets an approach to linguistic taxonomy that is numerically testable.  It,
in fact, is the same basic mathematical structure useful in building a logic
of biological phylogeny.  It is the logic on trees or more general graphs,
and it is known from logic programming that this is Heyting.

In other words, linguists have the capability to build scientific theories
of the same quantitative essence as any other "hard" science.  More
information can be collected about language groups which could lead, in some
theories, to better understandings of population migration patterns and
could represent indicators for archaeological prospecting.  I know that
there are many on sci.lang that just like languages and their history from a
non mathematical perspective, but I thought that one or two might actually
hold some interest in foundational issues for a mathematical science of
linguistics.  That wass actually a strong incentive for me to cross post in
general, because there are usually only the rare few in any of these groups
that hold an interest in mathematical foundations of their respective
disciplines in the abstractness that is the realm of Heyting algebras and
logical semantics, but I do see some.  My style of post was hoping to draw
those types out, since I find that they are usually much more interested in
the abstraction process that I tried to portray.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/7/2004 2:13:32 AM
"Morris Carr�" wrote:
: Just to beg inclusion into some other bucket of the classification,
: I myself am of the opinion that education reform in mathematics
: counts as the most efficient intergalactic space drive we can have !

Aha!  I knew there'd be some agreement coming out of this!

....unless... you're not against efficient intergalactic space drives, are
you?

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/7/2004 2:17:31 AM
"Peter T. Daniels" wrote:
: How many readers of sci.lang do you think know what Heyting algebras
: are?

Well, from the discussions I've read lately, admittedly not many.  But they
should!  When you are approaching an analysis of natural languages inside
logical classification systems, one is lead to topics like Dynamic Predicate
Logic where you begin to model the natural languages in induction and
implication logics.  When these elements are combined with theoretical or
semi-empirical metrics on phoneme space and between logical structures, one
gets an approach to linguistic taxonomy that is numerically testable.  It,
in fact, is the same basic mathematical structure useful in building a logic
of biological phylogeny.  It is the logic on trees or more general graphs,
and it is known from logic programming that this is Heyting.

In other words, linguists have the capability to build scientific theories
of the same quantitative essence as any other "hard" science.  More
information can be collected about language groups which could lead, in some
theories, to better understandings of population migration patterns and
could represent indicators for archaeological prospecting.  I know that
there are many on sci.lang that just like languages and their history from a
non mathematical perspective, but I thought that one or two might actually
hold some interest in foundational issues for a mathematical science of
linguistics.  That wass actually a strong incentive for me to cross post in
general, because there are usually only the rare few in any of these groups
that hold an interest in mathematical foundations of their respective
disciplines in the abstractness that is the realm of Heyting algebras and
logical semantics, but I do see some.  My style of post was hoping to draw
those types out, since I find that they are usually much more interested in
the abstraction process that I tried to portray.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar



0
galathaea1 (62)
2/7/2004 2:54:28 AM
galathaea <galathaea@excite.com> wrote:

> "Peter T. Daniels" wrote:
> : How many readers of sci.lang do you think know what Heyting algebras
> : are?
> 
> Well, from the discussions I've read lately, admittedly not many.  But they
> should!  When you are approaching an analysis of natural languages inside
> logical classification systems, one is lead to topics like Dynamic Predicate
> Logic where you begin to model the natural languages in induction and
> implication logics.  When these elements are combined with theoretical or
> semi-empirical metrics on phoneme space and between logical structures, one
> gets an approach to linguistic taxonomy that is numerically testable.  It,
> in fact, is the same basic mathematical structure useful in building a logic
> of biological phylogeny.  It is the logic on trees or more general graphs,
> and it is known from logic programming that this is Heyting.
> 
....
Can you recommend an introductory text for the terminally immatherate? I
am coming from the biological phylogeny and philosophical logic side of
things...
-- 
John Wilkins
wilkins.id.au
"Men mark it when they hit, but do not mark it when they miss" 
                                               - Francis Bacon
0
2/7/2004 3:11:45 AM

Morris Carr� wrote:

> mitch wrote:
> >
> > Morris Carr� wrote:
> >
> >
> >>A distributed cosmos-wide
> >>anti-computer, democratically as capable as the swarm of the real computers,
> >>to provide intelligence service to us by its influence over the evolution of
> >>computation.
> >
> >
> > You overestimate your ability with the part that reads "as capable as."
> >
> > Carnegie-Mellon University began the development of Capability Maturity Models because
> > the swarm to which you refer had been undependable, unreliable, and costly.  The
> > paradigm of Extreme Programming is an ad hoc implementation of certain parts of the
> > Capability Maturity Models for people who cannot read technical documentation for lack
> > of illustrations.
>
> Did they try to do something for people who can't read illustrations for lack
> of technical documentation ?
>

:-)


>
> >
> > I suspect, however, that the companies for which you worked depended on the very
> > religious faith that you have so willfully disrespected.It is likely that they
> > failed to demonstrate any productivity from their computer investments until recession
> > forced them to institute sound business practices once again--that is, if they
> > survived.
>
> Well, last I worked seriously for somebody it was a school of psychology and
> indeed the most spectacular thing was how computer displays got the majority
> of attention of paid workers, an evolution that I think in the case of
> psychology allows reading as a recession, if not financial.
>

Indeed.  If I am interpreting your description here correctly, it is quite like taking care
of business matters--say a mortgage payment to a bank--in person and waiting as bank
representative puts one on hold while answering telephone calls.

It seems as if workplaces have become so regimented. I guess they always have been.
Minesweeper and solitaire on the desktop CHANGED EVERYTHING--at least for a short time.

:-)

mitch



0
mitchs (45)
2/7/2004 6:31:57 AM

Morris Carr� wrote:

> galathaea wrote:
> > mitch wrote:
> > : galathaea wrote:
> > : >
> > : > In case you didn't read it, my post is about education, something I feel
> > is
> > : > very important.
> > : >
> > :
> > : Unfortunately, I think many people are somewhat cynical about this
> > particular
> > : topic.  If they perceive fortunate circumstance because of education, they
> > have
> > : no reason to question its value.  If they are ambivalent there is nothing
> > to be
> > : concerned about except, perhaps, the skeptical question concerning the
> > agenda
> > : behind a reformer's motivation.
> >
> > That's one of the nicest explanations I have seen in quite a while!
>
> Just to beg inclusion into some other bucket of the classification, I myself
> am of the opinion that education reform in mathematics counts as the most
> efficient intergalactic space drive we can have !

Quite so.

It would be difficult to explain just how much delusional nonsense with which this
question has presented me through life.  There is little doubt in my mind that the
battle between mathematicians and other members of society has raged from the
earliest days of civilization.  In order for our language skills to keep us alive,
certain words must have "magical" properties.  Undoubtedly, the same men (and
women [that is said respectfully although probably vacuous]) who figured out when
to plant and harvest were also responsible for taxes and levies.  There are
fragments of Linear A from Crete complaining about the Egyptian scribes.

In modern times, the advocacy of Russell's logicism has created presentations of
mathematics that are totally disconnected from the idiomatic needs of other
subjects.

I have a degree in mathematics.  The reason I have a degree in mathematics is
because I was going to fail out of college.  I had never had problems until
calculus in college.  All of a sudden, my grades depended on the ability to write
proofs.  I dropped out of school in my second year.  When I returned, I took a
course on intermediate logic followed by a course on Kant's "Critique of Pure
Reason."  with the addition of one more extracurricular topic--namely, topology--I
suddenly became quite good.  Although I was unable to recover from the poor
performance in my first year, I still ended up with the highest GPA among
mathematics graduates at my school.

One of the reasons I have an interest in what Galathaea is doing is because I
realize that the history of this situation is simply perverse.  Of course, there
may simply be no way to decide how to treat the subject.  Their is a sense in
which we have obsfucated all of our unanswerable questions with an impenetrable
language.  :-)

:-)

mitch



0
mitchs (45)
2/7/2004 7:02:56 AM

Steve Schafer wrote:

> On Fri, 6 Feb 2004 09:10:06 -0800, "galathaea" <galathaea@excite.com>
> wrote:
>
> >Can you please explain why I get such responses, when I have taken time
> >to carefully write my post?
>
> It has been said that unless you are able to explain an idea in such a
> way that a three-year-old can understand it, you don't truly understand
> it yourself. I wouldn't go quite that far, but the thought does have
> some merit.
>

I had similar problems recently on sci.logic.

I had had many years of experience explaining the basic sense of the matter
to all sorts of people--construction workers, waitresses, administrative
assistants, etc.  The only people who had ever had difficulty with the basic
sense of my claims were people with formal training.

Go figure.


>
> A couple of specific criticisms:
>
> You haven't laid any framework for your discussion. You launch right
> into elaboration without even stating the topic, and so your readers are
> guaranteed to be lost from the very beginning.

To the extent that my problems had been comparable, let me make the
following comparison:  I would be quite confused if another man kissed my
cheeks if I were expecting a handshake.



> _You_ may know what
> you're talking about, but nobody else does. It's a bit like the three
> rules of thumb for a scientific paper or presentation: (1) Tell them
> what you're going to tell them. (2) Tell them. (3) Tell them what you
> just told them.
>

With any luck, the discussions will lead to something that can follow that
kind of format.



>
> Your long-winded prose is so meandering (and occasionally convoluted)
> that it's difficult to figure out what the hell you're trying to say,
> sometimes even within a single paragraph. On the surface, it begins to
> sound like the meaningless drivel that so often passes for literary
> criticism these days, and which Alan Sokol so successfully parodied a
> few years back. (Note that I'm not saying that your writing _is_
> meaningless drivel, only that it _looks_ like meaningless drivel.)
>

The issues associated with Heyting algebras go back to the debates about the
foundations of mathematics in the late nineteenth and early twentieth
centuries.  At present, there are two axioms in set theory that reflect
mathematics not available at the time Zermelo-Fraenkel set theory was
formulated (namely, the axiom of determinacy and the axiom of projective
determinacy).  I bring these up because they relate to certain specific
concepts.  The problem with "meaningless drivel" arises because of these
concepts.

You will need to recall that these matters were being debated during the
rise of nationalism in Europe.  The traditions of British empiricists and
German idealists were not entirely compatible with one another.

In 1781 Jeremy Bentham published "The Principles of Morals and
Legislation."  This book introduced a notion of utility that was
fundamentally Epicurean.  That is, Bentham writes,

"Nature has placed mankind under the governance
of two sovereign masters, pain and pleasure.  It is
for them alone to point out what we ought to do, as
well as to determine what we shall do."

In modern terms, this would be related to formulations of deontic logic.
Deontic logic is a subclassical logic from which one can discern a
consequence relation as per Malinowski's analysis in

 http://www.uni.torun.pl/~jacekm/bimatrix.pdf

Bentham's idea of utility is important here because it is the political
concept that leads to game theory.  The axiom of determinacy is a
game-thoeretic assertion.

On the other hand, the axiom of determinacy also conveys the topological
properties important to descriptive set theory.  This is much more along the
lines corresponding to Kant's distinction between mathematics and logic
according to aesthetic principles.  For a modern discussion of the
"descriptive ability of mathematics" you might look at Mark Steiner's "The
Applicability of Mathematics as a Philosophical Problem."

The reason Kant's distinctions get involved have to do with temporal logics
and tense logics.  Like deontic logic, these are subclassical logics from
which a consequence relation can be discerned.

So, what I am trying to say is that you are attempting to impose a criterion
that would require an immense amount of complexity because of the
philosophical detail involved.  There is a real sense in which Galathaea is
simply looking to get some discussion started in order to see what
directions must be pursued.

It may be thought of as an exploratory rather than an expository.


>
> You may very well have some worthwhile ideas, but until you learn to
> organize your thoughts more carefully and express them more clearly and
> concisely, no one else is going to be able to tell.
>

And, the difficulty is that one requires questions and feedback in order to
make clarifications.

:-)

mitch





0
mitchs (45)
2/7/2004 7:57:51 AM
"galathaea" <galathaea@excite.com> wrote in message
news:1027ij4728kqfd0@corp.supernews.com...
> "Franz Heymann" wrote:
> : You waffled too long before coming to anything substantive, so I snipped
> all
> : without reading further.
> : Verbal diarrhoea is curable.  See a doctor.
>
> This is the second comment on bowel movements associated to my post.  Yet
I
> do not see any "waffling" when I read it.

All the more reason why you should see a doctor.

>  Can you please explain why I get
> such responses, when I have taken time to carefully write my post?

Because you emit a continuous stream of cowpee.

>  I have
> followed many of your posts on the sci.physics forum and do respect your
> opinion, but do not understand from where you are coming.
>
> In case you didn't read it, my post is about education, something I feel
is
> very important.

Education might be important.  Your views on it are not.  The firstthing you
should be educated about is to divide your total number of words per posting
by about ten or so.

> In fact, I am getting the impression that many don't read the post,
perhaps
> because reading hurts their head.

Your posts largely remain unread because folk can only stomach so much crap
in one session.

Franz


0
2/7/2004 7:58:51 AM
"galathaea" <galathaea@excite.com> wrote in message
news:1027r437rbok275@corp.supernews.com...
> "Steve Schafer" wrote:
> : On Fri, 6 Feb 2004 09:10:06 -0800, "galathaea" <galathaea@excite.com>
> : wrote:
> :
> : >Can you please explain why I get such responses, when I have taken time
> : >to carefully write my post?
> :
> : It has been said that unless you are able to explain an idea in such a
> : way that a three-year-old can understand it, you don't truly understand
> : it yourself. I wouldn't go quite that far, but the thought does have
> : some merit.
>
> I actually felt that what I wrote was dumbing things down quite a bit.

Then the original version must have been real supershit.
>  I am
> getting the feeling that is more a problem of attention defecit

deficit.

 and the
> length of the post more than anything else.  All of the comments so far
have
> made it quite clear that the negativity was due to having not read any
> furthur than the first few paragraphs.

Yes.  You did not succeed in hiding the crap well enough.
>

>
> I don't find it too meandering.

I did.  Intensely so.
I suggest you stop posting until you have learnt how to communicate.

[snip the apologia]

Franz


0
2/7/2004 7:58:52 AM
"galathaea" <galathaea@excite.com> wrote in message
news:1027k0d2l5g5l43@corp.supernews.com...
> "Franz Heymann" wrote
> : You waffled too long before coming to anything substantive, so I snipped
> all
> : without reading further.
> : Verbal diarrhoea is curable.  See a doctor.
>
> In fact, I find it difficult to see how I can broach my topic amongst all
> groups without taking the path I chose.

That is one enormous mistake you made.  Do you think any scientist is going
to be interested in the waffling that philosophers and psychologists might
contribute?

Franz




0
2/7/2004 7:58:53 AM

Franz Heymann wrote:

>
> That is one enormous mistake you made.  Do you think any scientist is going
> to be interested in the waffling that philosophers and psychologists might
> contribute?
>

Hmm...  Have you read the nonsense that Scientific American has been publishing
recently?

Perhaps you mean bureaucrat or assistant.

Since you certainly do not intend that interpretation of the word "scientist,"
could you direct me to some discursive treatment that will explain your use?
Most people associate science with informationally incomplete models, and, that
is closely related to Galathaea's posts.  The tenor of your remark suggests that
you do not see scientific investigation in these terms.  So, clarification of
your usage would be greatly appreciated.

Or, perhaps, you would simply like me to accept the fact that some knowledgeable
university bureaucrat gave you that assignment according to some organizational
chart prepared by a business school graduate.

:-)

mitch


P.S.  I am not as familiar with Hilbert spaces as a practicing physicist, but I
will gladly take you up on any invitation along those lines.




0
mitchs (45)
2/7/2004 9:02:48 AM

Franz Heymann wrote:

>
> Then the original version must have been real supershit.

Let's see...  How did that GRE analogy question go?

Franz Heymann:supershit =

:-)

mitch



0
mitchs (45)
2/7/2004 9:05:46 AM

Franz Heymann wrote:

>
> Your posts largely remain unread because folk can only stomach so much crap
> in one session.
>

I will have take your word on this.  You seem rather knowledgeable about SCAT.

:-)

mitch



0
mitchs (45)
2/7/2004 9:08:29 AM

galathaea wrote:

> mitch wrote:
>
> : On sci.logic, George Greene observed that constructive mathematics was
> : difficult.  So what you are describing would increase a burden already
> : perceived as onerous for many.
>
> And this is why my suggestion was in particular to introduce the topic prior
> to classical logic.  By introduce, I don't mean a complete exposition of
> everything in the field.  I intend only that the basic structure of the
> logic is taught along with practice of the rules and an overview of the
> semantic interpretations.  I just believe that understanding that structure,
> by itself, is important to all people interested in modern research in any
> of the fields I mention.

Part of the problem is the bureaucratic structure of the education system.
Development in mathematics departments is independent of the needs of other
disciplines.  So, when other departments impose curriculum requirements without
clearly understanding what is not being taught, they are not always giving their
own students what they need.

I think that a lot of physics students may actually experience this.  The
mathematics of physics uses different symbol sets from the same basic
presentations in mathematics departments.  I seem to remember a complex analysis
class...



>  But I don't intend to constrain education to only
> constructive mathematics, and think afterwards adding axioms of bivalence
> and choice and teaching their use is fine.  In other words, I'm not looking
> to education forcing students to do constructive mathematics, I just believe
> that it is important for students to understand the logical structure, and
> personally feel that the best place to do this is while the formal system is
> first being developed.
>

It would take about 2 class sessions, right?  That is far less than the changes
I would like to see.  In the case of mathematics, the entire issue of algebraic
semantics arises.  Goodness--it was TARSKI who introduced cylindrical algebras.
Try to find a class where it is discussed.



>
> : Galathaea, I have several journal articles on things like constructive
> e-sets
> : and solvable Boolean algebras.  But I do not have the background to read
> them
> : directly.  Do you know of any expository texts that would help introduce
> me to
> : the methodologies for constructive mathematics?
>
> Some classics in the field include Errett Bishop's "Foundations of
> Constructive Analysis" and Per Martin-Lof's "Notes on Constructive
> Analysis".  A. A. Markov also has a good book about the foundations of
> algorithmics and recursive function theory in which the constructive form is
> made explicit.
>

I noticed citations to Markov.  I had been surprised.  I think of Markov in
terms of classical mathematics.  It must be that great education for I *paid.*



>
> : You might also wish to visit the pages,
> :
> :  http://plato.stanford.edu/entries/logic-paraconsistent/
> :
> :  http://plato.stanford.edu/entries/mathematics-inconsistent/
> :
> : although you are probably aware of them.
> :
> : I find the fact that these concepts are contrasted with consistency
> somewhat
> : amusing.  Since my background concerning these questions is closely
> associated
> : with Kantian epistemology, I am still waiting for someone to convince me
> that
> : what is taught as "logic" is anything but the fixed delusion of certain
> : influential narcissists and those who mistakenly investigated their
> program.
>
> I find your comment on what is taught particularly true in those schools
> where logic is taught as a part of the philosophy department and not the
> mathematics or computer science departments, where there is often quite a
> focus on the names.
>
> Although I've looked around plato on the stanford many times before, I don't
> believe I have read those two pages.  Particularly the page on inconsistent
> mathematics seemed rather odd, and its mention of dualities existing between
> formally consistent and formally inconsistent models was intriguing.  I will
> have to follow that trail one of these weeks.
>

If you can find a copy of Halmos' "Algebraic Logic" it would be helpful.  It
turns out that the characterization of the existential quantifier in algebraic
semantics corresponds with Kuratowski's closure axioms.

With regard to set theory, I can also say that the transitive classes (implied
by the axiom of foundation) also satisfy Kuratowski's closure axioms.  Moreover,
those axioms make no explicit reference to a universe.  Of course, the axiom of
foundation provides for a description of models as cumulative hierarchies.

Also, for the people who are aware of dynamical truth or the use of transitive
derivations in formal language, the axiom of foundation precludes each set from
having infinite descending membership chains.


>
> : Here is one other site that you might find more interesting.  The Polish
> school
> : of mathematics (along with Paul Halmos and a few others) pursued algebraic
> : semantics along the lines of Tarski's cylindrical algebras.  Jacek
> Malinowski
> : has a number of interesting papers.  Algebraic semantics allows for a
> natural
> : distinction between equivalential and non-equivalential logics in contrast
> to
> : the kind of investigation begun by Heyting.
> :
> :  http://www.uni.torun.pl/~jacekm/publications.htm
>
> I like the variety of topics covered by the papers listed.  I really thank
> you for this one, as I have at various times followed several member of the
> Polish school's line of thought.
>

Well, if it is worth your investment, you might look for Czelakowski's
"Protoalgebraic Logics."  It is cited in Malinowski's papers. What I have read
in it is pretty good.

<snip>

:-)

mitch



0
mitchs (45)
2/7/2004 9:30:34 AM
"James Dolan" <jdolan@math-lw-n01.math.ucr.edu> wrote in message
news:c01hg1$8sr$1@glue.ucr.edu...
> in article <40243ac9.34dd@worldnet.att.net>,
> peter t. daniels <grammatim@worldnet.att.net> wrote:
>
> |How many readers of sci.lang do you think know what Heyting algebras
> |are?
>
> a fair number of them, but probably fewer than the number who think
> that your attempts to narrow the focus of the newsgroup are motivated
> by your personal insecurities about your vast ignorance.

The content of this thread does indeed require one hell of a lot of
narrowing of its focus.  In fact, to precisely zero.  This is a physics
newsgroup and there is no physics in the thread whatsoever.

Franz


0
2/7/2004 11:23:04 AM
"galathaea" <galathaea@excite.com> wrote in message
news:1028ie2lace0b0@corp.supernews.com...
> "Peter T. Daniels" wrote:
> : How many readers of sci.lang do you think know what Heyting algebras
> : are?
>
> Well, from the discussions I've read lately, admittedly not many.  But
they
> should!

Bollocks.  I have lived a long life and have followed a successful career
and until now I have never come across this idea.

[snip the usual long splurge]

Franz.


0
2/7/2004 11:23:04 AM
"galathaea" <galathaea@excite.com> wrote in message
news:102824fqo6c616e@corp.supernews.com...
> mitch wrote:
> : galathaea wrote:
> : >
> : > In case you didn't read it, my post is about education, something I
feel
> is
> : > very important.
> : >
> :
> : Unfortunately, I think many people are somewhat cynical about this
> particular
> : topic.  If they perceive fortunate circumstance because of education,
they
> have
> : no reason to question its value.  If they are ambivalent there is
nothing
> to be
> : concerned about except, perhaps, the skeptical question concerning the
> agenda
> : behind a reformer's motivation.
>
> That's one of the nicest explanations I have seen in quite a while!

Then you must be as much of a kook as the person to whom you are replying
Where the hell is the physics in this thread?
If you do not remove sci.physics from your spam list, I willcontinue to tell
you what an idiot you are.

Franz

>  I am
> aware of the difficulties that present themselves concerning reforming
> education, but these concerns are why I chose to pick such a large
> crossposting and focus on the many useful area my topic arises in.  I
though
> it would be nice for various communities to come together and share their
> work's foundations in Heyting algebras, so that everyone could see that
its
> teaching was really worthwhile.
>
> I see it somewhat like quantum mechanics.  When QM was first introduced,
it
> was a research topic and found mostly in the journals.  As the results
> became established, which was very quickly done, it moved into graduate
> programs.  Now it is an undergraduate topic that gets introduced even to
> high school students in their basic chemistry and physics courses.
>
> : On sci.logic, George Greene observed that constructive mathematics was
> : difficult.  So what you are describing would increase a burden already
> : perceived as onerous for many.
>
> And this is why my suggestion was in particular to introduce the topic
prior
> to classical logic.  By introduce, I don't mean a complete exposition of
> everything in the field.  I intend only that the basic structure of the
> logic is taught along with practice of the rules and an overview of the
> semantic interpretations.  I just believe that understanding that
structure,
> by itself, is important to all people interested in modern research in any
> of the fields I mention.  But I don't intend to constrain education to
only
> constructive mathematics, and think afterwards adding axioms of bivalence
> and choice and teaching their use is fine.  In other words, I'm not
looking
> to education forcing students to do constructive mathematics, I just
believe
> that it is important for students to understand the logical structure, and
> personally feel that the best place to do this is while the formal system
is
> first being developed.
>
> : Galathaea, I have several journal articles on things like constructive
> e-sets
> : and solvable Boolean algebras.  But I do not have the background to read
> them
> : directly.  Do you know of any expository texts that would help introduce
> me to
> : the methodologies for constructive mathematics?
>
> Some classics in the field include Errett Bishop's "Foundations of
> Constructive Analysis" and Per Martin-Lof's "Notes on Constructive
> Analysis".  A. A. Markov also has a good book about the foundations of
> algorithmics and recursive function theory in which the constructive form
is
> made explicit.
>
> : You might also wish to visit the pages,
> :
> :  http://plato.stanford.edu/entries/logic-paraconsistent/
> :
> :  http://plato.stanford.edu/entries/mathematics-inconsistent/
> :
> : although you are probably aware of them.
> :
> : I find the fact that these concepts are contrasted with consistency
> somewhat
> : amusing.  Since my background concerning these questions is closely
> associated
> : with Kantian epistemology, I am still waiting for someone to convince me
> that
> : what is taught as "logic" is anything but the fixed delusion of certain
> : influential narcissists and those who mistakenly investigated their
> program.
>
> I find your comment on what is taught particularly true in those schools
> where logic is taught as a part of the philosophy department and not the
> mathematics or computer science departments, where there is often quite a
> focus on the names.
>
> Although I've looked around plato on the stanford many times before, I
don't
> believe I have read those two pages.  Particularly the page on
inconsistent
> mathematics seemed rather odd, and its mention of dualities existing
between
> formally consistent and formally inconsistent models was intriguing.  I
will
> have to follow that trail one of these weeks.
>
> : Here is one other site that you might find more interesting.  The Polish
> school
> : of mathematics (along with Paul Halmos and a few others) pursued
algebraic
> : semantics along the lines of Tarski's cylindrical algebras.  Jacek
> Malinowski
> : has a number of interesting papers.  Algebraic semantics allows for a
> natural
> : distinction between equivalential and non-equivalential logics in
contrast
> to
> : the kind of investigation begun by Heyting.
> :
> :  http://www.uni.torun.pl/~jacekm/publications.htm
>
> I like the variety of topics covered by the papers listed.  I really thank
> you for this one, as I have at various times followed several member of
the
> Polish school's line of thought.
>
> : Still, I would like to see someone discussing the details of Heyting
> algebras
> : with you.  I am now aware that many of my own former computer tasks were
> based
> : on the structure of Brouwerian semilattices.  Had I been aware of that
at
> the
> : time, I probably could have done a number of things far more
effectively.
>
> On one of my jobs, we required certain proofs on modules in our programs
> concerning maintaining invariants and other routine programming checks
such
> as algorithmic correctness and completeness.  Although most coders could
do
> the proofs by hand, when we decided to automate, several other coders
became
> frustrated with the propositional logic needed, and it was eventually
handed
> over to me to do.  I also was the only one with training in functional
> languages, which also netted me some jobs no one else would take.
Sometimes
> being efficient doesn't mean less work!
>
> =)
>
> -- 
> -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
>
> galathaea: prankster, fablist, magician, liar
>
>


0
2/7/2004 11:23:06 AM
"Immortalist" <Reanimater_2000@yahoo.com> wrote in message
news:1028014681hg516@corp.supernews.com...

[snip]

> I was providing setup for the notion of ongoing patterns interacting.
> Interference and resulting changes and all that.

You have just strung together a number of words into a sequence of one
sentence followed by a group of words failing to be a sentence.  Neither of
these fragments displayed any signs of having been produced by a being
endowed with any intellectual abilities.

 Surely you cannot be as stupid as you come across.  I guess you must be
trying to mimic those other contributors of bullshit to this thread.  You
are eminently successful.

[snip reams of cack]

Franz


0
2/7/2004 11:23:07 AM
James Dolan wrote:
> 
> in article <40243ac9.34dd@worldnet.att.net>,
> peter t. daniels <grammatim@worldnet.att.net> wrote:
> 
> |How many readers of sci.lang do you think know what Heyting algebras
> |are?
> 
> a fair number of them, but probably fewer than the number who think
> that your attempts to narrow the focus of the newsgroup are motivated
> by your personal insecurities about your vast ignorance.

So where's _your_ constructive discussion of Miss Galathaea's essay?
-- 
Peter T. Daniels                       grammatim@att.net
0
grammatim (38)
2/7/2004 12:23:02 PM
galathaea wrote:
> 
> "Peter T. Daniels" wrote:
> : How many readers of sci.lang do you think know what Heyting algebras
> : are?
> 
> Well, from the discussions I've read lately, admittedly not many.  But they
> should!  When you are approaching an analysis of natural languages inside
> logical classification systems, one is lead to topics like Dynamic Predicate

Why would one be doing such a thing?

> Logic where you begin to model the natural languages in induction and
> implication logics.  When these elements are combined with theoretical or
> semi-empirical metrics on phoneme space and between logical structures, one
> gets an approach to linguistic taxonomy that is numerically testable.  It,
> in fact, is the same basic mathematical structure useful in building a logic
> of biological phylogeny.  It is the logic on trees or more general graphs,
> and it is known from logic programming that this is Heyting.

All of a sudden, a whole bunch of biologists have suddenly hit on the
notion that they have something to say about "trees or ... graphs," and
it turns out they haven't bothered to consult either facts or what has
already been learned about such topics.

> In other words, linguists have the capability to build scientific theories
> of the same quantitative essence as any other "hard" science.  More
> information can be collected about language groups which could lead, in some
> theories, to better understandings of population migration patterns and
> could represent indicators for archaeological prospecting.  I know that

Ah. If that's what you're after, then you're utterly misguided. As you
would know if you'd actually learned something about human languages,
there's no necessary connection between languages and populations;
moreover, there's nothing particularly "logical" about human language.

> there are many on sci.lang that just like languages and their history from a
> non mathematical perspective, but I thought that one or two might actually
> hold some interest in foundational issues for a mathematical science of
> linguistics.  That wass actually a strong incentive for me to cross post in
> general, because there are usually only the rare few in any of these groups
> that hold an interest in mathematical foundations of their respective
> disciplines in the abstractness that is the realm of Heyting algebras and
> logical semantics, but I do see some.  My style of post was hoping to draw
> those types out, since I find that they are usually much more interested in
> the abstraction process that I tried to portray.

Have you tried looking at the _existing_ work in "mathematical
linguistics"?

> --
> -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
> 
> galathaea: prankster, fablist, magician, liar

No argument there.
-- 
Peter T. Daniels                       grammatim@att.net
0
grammatim (38)
2/7/2004 12:29:06 PM
galathaea wrote:
> and call on recollections of known forms of full words.  We've learned
> to attach meanings to utterances and visual shapes, and while you are
> reading this you are building structures of meaning to the words which
> can assist in the recognition, determining patterns of abstractions

The important effect where you skip over whole paragraphs looking
for something interesting preparatory to skipping the article has been
left out.

Even an interesting title has little effect, eg.

  Subject: Hand Turning Black, Medical Reasons?

if it begins

  First a little history.  I was born in 1971 in East Lansing MI, and
  my father ...

gets skipped.  It's hopeless to find the interesting part, if any, is
the judgment.  To hell with it.
-- 
Ron Hardin
rhhardin@mindspring.com

On the internet, nobody knows you're a jerk.
0
rhhardin (172)
2/7/2004 12:38:40 PM
On Thu, 5 Feb 2004 20:10:50 -0800 "galathaea"
<galathaea@excite.com> wrote in
<news:10264u282mchk23@corp.supernews.com> in
alt.philosophy,comp.lang.functional,sci.lang,sci.physics,sc
i.psychology.theory:

[...]

> In these communities I am
> speaking to, I expect some reasonable understanding of the concepts I
> mentioned.  [...]

Then you have wildly unrealistic expectations.  You are
assuming a very high degree of mathematical sophistication
in a couple of specific areas, one that you can't reasonably
expect to find in more than a smallish minority even in
sci.math.  (And this fact alone should tell you something
about the program that you suggest.)

[...]

Brian
0
b.scott (18)
2/7/2004 3:09:42 PM
"Steve Schafer" <see@reply.to.header> wrote in message
news:0an720hr5ca5dntgf9rhghv79qikh4fa90@4ax.com...
> On Fri, 6 Feb 2004 09:10:06 -0800, "galathaea" <galathaea@excite.com>

[snip]

> It has been said that unless you are able to explain an idea in such a
> way that a three-year-old can understand it, you don't truly understand
> it yourself.

Whoever said that had the intellect of the 3 year old he was talking about..

[snip]

Franz


0
2/7/2004 3:27:30 PM
"mitch" <mitchs@rcnNOSPAM.com> wrote in message
news:4024B03A.81F8C5@rcnNOSPAM.com...
>
>
> galathaea wrote:
>
> > mitch wrote:
> >
> > : On sci.logic, George Greene observed that constructive mathematics was
> > : difficult.  So what you are describing would increase a burden already
> > : perceived as onerous for many.
> >
> > And this is why my suggestion was in particular to introduce the topic
prior
> > to classical logic.  By introduce, I don't mean a complete exposition of
> > everything in the field.  I intend only that the basic structure of the
> > logic is taught along with practice of the rules and an overview of the
> > semantic interpretations.  I just believe that understanding that
structure,
> > by itself, is important to all people interested in modern research in
any
> > of the fields I mention.
>
> Part of the problem is the bureaucratic structure of the education system.
> Development in mathematics departments is independent of the needs of
other
> disciplines.

In that case you must be talking of singularly bum Universities.
I have taught at 3, in 3 different continents, and I have examined in
approximately 20.  In none of those Universities did your statement hold
true as far as either Physics or Electrical Engineering are concerned.

>  So, when other departments impose curriculum requirements without
> clearly understanding what is not being taught, they are not always giving
their
> own students what they need.

I discussed the mathematics requirements in my department quite regularly
with my colleagues in the mathematics department.  So did my colleagues in
chemistry and in the engineering faculty

Franz


0
2/7/2004 3:27:31 PM
"mitch" <mitchs@rcnNOSPAM.com> wrote in message
news:4024A9B8.128FE209@rcnNOSPAM.com...
>
>
> Franz Heymann wrote:
>
> >
> > That is one enormous mistake you made.  Do you think any scientist is
going
> > to be interested in the waffling that philosophers and psychologists
might
> > contribute?
> >
>
> Hmm...  Have you read the nonsense that Scientific American has been
publishing
> recently?

I agree entirely with you that the Scientific American, which used to be a
very highly respected journal with a very positive pedagogical content is
now as near as dammit part of the gutter press.
>
> Perhaps you mean bureaucrat or assistant.

No.  I really did mean philosophers and psychologists.
The former have not advanced their subject along a discernible direction
since Aristotle, who was in any case too stupid to realise that if one was
interested in comparing a teeth count between men and women, it pays to get
out and count them.
>
> Since you certainly do not intend that interpretation of the word
"scientist,"
> could you direct me to some discursive treatment that will explain your
use?

I did not offer you any interpretation of the word "scientist".
However, if you really do not know,  a scientist is one who pursues research
in science according to the tenets of the scientific method.

> Most people associate science with informationally incomplete models,
> and, that
> is closely related to Galathaea's posts.  The tenor of your remark
suggests that
> you do not see scientific investigation in these terms.  So, clarification
of
> your usage would be greatly appreciated.

You have waffled.  Any reference to Galathea's posts are bound to contain
only waffle, even if it is only derogatory waffle, like mine.  If you were
to put a specific question to me clearly and unambiguously, I will try to
answer it briefly.
>
> Or, perhaps, you would simply like me to accept the fact that some
knowledgeable
> university bureaucrat gave you that assignment

What asignment?


> according to some organizational
> chart prepared by a business school graduate.

I never allowed any business school graduate in my department.

> P.S.  I am not as familiar with Hilbert spaces as a practicing physicist,
but I
> will gladly take you up on any invitation along those lines.

That, too, was waffle.  I have no idea of what you want me to invite you yo
do.

Franz


0
2/7/2004 3:27:32 PM

Franz Heymann wrote:

> "James Dolan" <jdolan@math-lw-n01.math.ucr.edu> wrote in message
> news:c01hg1$8sr$1@glue.ucr.edu...
> > in article <40243ac9.34dd@worldnet.att.net>,
> > peter t. daniels <grammatim@worldnet.att.net> wrote:
> >
> > |How many readers of sci.lang do you think know what Heyting algebras
> > |are?
> >
> > a fair number of them, but probably fewer than the number who think
> > that your attempts to narrow the focus of the newsgroup are motivated
> > by your personal insecurities about your vast ignorance.
>
> The content of this thread does indeed require one hell of a lot of
> narrowing of its focus.  In fact, to precisely zero.  This is a physics
> newsgroup and there is no physics in the thread whatsoever.
>

imbecile...

"Kant anticipated that momentum-energy is the substantial
correlate of spacetime. Bypassing Newton, he caught up
with Einstein.[9] "

"In light of quantum geometry and its modern guises � superstring
and M-theories � this last remark might well have been Kant's most
far-sighted prediction. Despite suffering from insufficient scientific
training, the rejection by his advisor, the academic failure, and the
catastrophe in his family, Kant's philosophical debut in 1749 reveals
the mark of genius."

 http://www.seop.leeds.ac.uk/entries/kant-development/


Your own failure to seek an adequate education is not the fault of anyone
in this thread.

:-)

mitch




0
mitchs (45)
2/7/2004 6:13:53 PM
"Franz Heymann" wrote:
: The content of this thread does indeed require one hell of a lot of
: narrowing of its focus.  In fact, to precisely zero.  This is a physics
: newsgroup and there is no physics in the thread whatsoever.

There is physics in my post, and there would be more if you or others in the
physics group started discussing them.  I specifically mention things like
quantum logic and its Heyting structure, and I've seen this discussed _many_
times in sci.physics.research.  Or take a look at the arXiv's:
gr-qc/9811053.

Franz,
I now count over 11 posts of yours for some reason opposed to me and my
post.  You use descriptions of bowel movements and urination to describe my
post.  You cry that it is ten times longer than required for your complete
reading.

Don't you think in the time it took you to write 11 responses, you could
have read my article once through?

Because seriously you are drawing conclusions like my article being mainly
associated with philosophy and lack of rigour that are entirely untrue and
would, I hope, become more apparent after reading the piece.  I am
discussing a formal, mathematical structure which has appeared in a lot of
diverse research.  It is found in dynamic systems theories.  It is found in
quantum mechanics.  It is found in the theory of computation.

I still do not understand how that could elicit such a flurry of negativity.
What I have learned is that some objected to my format, and that is fine.  I
thought I'd introduce the topic starting from the vision research crowd in
what I thought at the time to be a clever or creative way.  And as with all
creative efforts, that opens one up for a whole new line of criticism from
the aesthetic side.  Maybe I failed in my approach, but the topic is still
glaring right out of the monitor if you took the time to read the piece.  I
repeat it over and over, in each new context.

So maybe I am a failed artist here, Franz, but that in no way devalues the
discussion my post was concerning.  And you won't find me cowering away
because you can throw scatology around like an angry primate.  I still
believe that the ubiquity of the Heyting algebraic structure across all of
the disciplines I covered, and others, is indicative of a deeper
computational structure to our models, both foundational and practical, and
feel that if this was just taught during that time when the more specific
Boolean algebras (which are also Heyting) are taught, maybe there would be a
lot less recapitulation of results across disciplines, which is wheel
spinning that is counter productive.

What you've shown, however, is that you are someone who will post negative
responses to something you admit you haven't read.  What you've shown,
Franz, is that a piece no longer than a simple preface is considered too
long for you to spend your time on, but attempting to ridicule people is an
activity you have plenty of time for.  If that's the personality you want
anyone glancing through these posts to pick up, that is your perogative.
But it is not a personality type I give much value to.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/7/2004 6:20:41 PM
"Brian M. Scott" wrote:
: "galathaea" wrote:
: [...]
:
: > In these communities I am
: > speaking to, I expect some reasonable understanding of the concepts I
: > mentioned.  [...]
:
: Then you have wildly unrealistic expectations.  You are
: assuming a very high degree of mathematical sophistication
: in a couple of specific areas, one that you can't reasonably
: expect to find in more than a smallish minority even in
: sci.math.  (And this fact alone should tell you something
: about the program that you suggest.)

I see constructivism talked about quite intelligently in sci.math from time
to time.  Some of the regular posters to sci.math, like David C. Ullrich and
Arturo Magidin, have contributed to the expositions.  Its not really that
obscure.  Alot of famous mathematicians have contributed, and I have dropped
some of their names in both my paper and several leafs in this thread.

But I am also trying something here.  I am trying to bring out those with
pieces of the puzzles in other disciplines.  Computational theory has a lot
of constructively trained theoreticians who understand Heyting algebras,
particularly in Europe and following topics brought up in the Russian
school.  Many books have been written exploring the Heyting algebras of
physics, on quantum logic and the like.  And so on through the disciplines
mentioned in my article.  Because, although I recognise that the numbers
working on the topic are small in each discipline, I felt that together they
could recognise the importance of my request to broaden education.

I don't believe that the estimates of those on these groups understanding
Boolean algebras would be anywhere as small, yet as I mention in my post, I
believe that these algebras are often less useful, at least in the areas I
mention.  And Boolean algebras are Heyting algebras, so there seems a
natural priority here.

And also I've had questions about the structures as well.  So the minority
population grows with exposure.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/7/2004 6:38:14 PM

Franz Heymann wrote:

> "mitch" <mitchs@rcnNOSPAM.com> wrote in message
> news:4024B03A.81F8C5@rcnNOSPAM.com...
> >
> >
> > galathaea wrote:
> >
> > > mitch wrote:
> > >
> > > : On sci.logic, George Greene observed that constructive mathematics was
> > > : difficult.  So what you are describing would increase a burden already
> > > : perceived as onerous for many.
> > >
> > > And this is why my suggestion was in particular to introduce the topic
> prior
> > > to classical logic.  By introduce, I don't mean a complete exposition of
> > > everything in the field.  I intend only that the basic structure of the
> > > logic is taught along with practice of the rules and an overview of the
> > > semantic interpretations.  I just believe that understanding that
> structure,
> > > by itself, is important to all people interested in modern research in
> any
> > > of the fields I mention.
> >
> > Part of the problem is the bureaucratic structure of the education system.
> > Development in mathematics departments is independent of the needs of
> other
> > disciplines.
>
> In that case you must be talking of singularly bum Universities.
> I have taught at 3, in 3 different continents, and I have examined in
> approximately 20.  In none of those Universities did your statement hold
> true as far as either Physics or Electrical Engineering are concerned.
>

Right.  In your experience with presentations of mathematics largely--and
uncritically--based upon "hand-waving".


>
> >  So, when other departments impose curriculum requirements without
> > clearly understanding what is not being taught, they are not always giving
> their
> > own students what they need.
>
> I discussed the mathematics requirements in my department quite regularly
> with my colleagues in the mathematics department.  So did my colleagues in
> chemistry and in the engineering faculty
>

Right.

Look.  I just managed to get a truce (uneasy rest) on sci.logic from a flame war
that lasted over a year.  So my own responses to vulgar language and summary
dismissals in this thread are a little too swift.  It is clear that you have an
excellent background and require some sense of why this thread might have
relevance in sci.physics.

What you are describing here is the "preaching to the choir" type of
collaboration.  In the postscript to this message I have copied parts of a
thread from sci.logic.  I will not claim that my response will be entirely
coherent--like Galathaea, I have no particular paradigm within which to discuss
these matters.  But, the question had been from a  physics student.  He seemed
to appreciate the responses.

:-)

mitch


----

Blake Winter wrote:

> Does Godel's incompleteness theorems apply to nonboolean logics such
> as quantum logic?

I am certainly not expert enough to give a definitive answer.  There is
a sense in which many philosophical questions would need to have answers
for someone to give an affirmative.

Usually, quantum logics are characterized in terms of a linear
combination of operators for Hilbert spaces and "questions" according to
the work of von Neumann, Birkhoff and Mackey.  The Stanford Encyclopedia
has a useful page,

 http://plato.stanford.edu/entries/qt-quantlog/#1

For other reasons, I happen to have a different formalization for how to
think about quantum logics available in ASCII,



----

"We recall that the orthomodular quantum
logic OML[|=] is defined semantically by the
class OML of orthomodular lattices with the
unit element 1 designated.  Thus:

   (a in OML[|=](X)) iff for every (A in OML)
   and every homomorphism h:S->A,

          h(X) subset {1} implies h(a)=1

OML[|=] is thus the assertional logic of the
class OML.


"Consider the following sentences of S in two
variables x and y:

p_0(x,y) := ~x \/ y

p_1(x,y) := (~x /\ y) \/ (~x /\ ~y) \/ (x /\ (~x \/ y))

p_2(x,y) := (~x /\ y) \/ (x /\ y) \/ ((~x \/ y) /\ ~y)

p_3(x,y) := ~x \/ (x /\ y)

p_4(x,y) := y \/ (~x /\ ~y)

p_5(x,y) := (~x /\ y) \/ (x /\ y) \/ (~x /\ ~y)


"Theorem 5.5.1.  Up to identity over OML, p_1,..., p_5
are the only formulas p in two variables having the
following property: for any algebra (A in OML) and all
(a, b in A), p(a,b)=1 iff a<=b."

"The proof of Theorem 5.5.1 is omitted.  The proof
makes use of the free algebra F_OML(2) on two
generators.  It has 96 elements and it is known to
be isomorphic with the direct product

MO2 x 2^4

of the "Chinese lantern" MO2 with the 16-element
Boolean algebra, denoted 2^4.

                           1
                         // \\
                      /  /   \  \
                   /    /     \    \
                /      /       \      \
  MO2          a     ~a         b     ~b
                \      \       /      /
                   \    \     /    /
                      \  \   /  /
                         \\ //
                           0


"F_OML(2) is finite but the free algebra F_OML(3)
is infinite.  Theorem 5.5.1 iimplies:

"Corollary 5.5.2  The logic OML[|=] is implicative
and each of the above (definable) connectives
p_i (i=1,...,5) is its implication.  Furthermore,
the class Mod*(OML[|=]) coincides with OML.

"It follows from the above corollary that each of the
sets {p_i(x,y),p_i(y,x)}, i=0,...,5 is an equivalence
for OML[|=].

"The consistent strengthenings of the logic OML[|=]
are called quantum logics.  Every quantum logic C is
thus regularly algebraizable and, if C is finitary,
its equivalent algebraic semantics coincides with the
quasivariety Mod*(C) which is clearly a quasivariety
of orthomodular lattices.  The classical consequence
K is a limit case - it is the strongest quantum logic.
The class BA of Boolean algebras is the smallest
non-trivial variety of orthomodular lattices.

"The consequence OML[|=] has been axiomatized by
Kalmbach [1974], [1981].  Let MP_i be the detachment
rule determined by the implication p_i, i.e., MP_i
is the rule

x, p_i(x,y)
-----------
y

for i=0,...,5.  Define the binary connective R by:

(a R b) := (a /\ b) \/ (~a /\ ~b)

for any a, b.  Then define the following axioms:

 A1     ~(p R q) \/ (~p \/ q)

 A2     p R p

 A3     ~(p R q) \/ (~(q R r) \/ (p R r))

 A4     ~(p R q) \/ (~p R ~q)

 A5     ~(p R q) \/ ((p R r) R (q R r))

 A6     (p /\ q) R (q /\ p)

 A7     (p /\ (q /\ r)) R ((p /\ q) /\ r)

 A8     (p /\ (p \/ q)) R p

 A9     (~p /\ p) R ((~p /\ p) /\ q)

A10     ~(p \/ q) R (~p /\ ~q)

A11     p R ~~p

A12     (p \/ (~p /\ (p \/ q))) R (p \/ q)

A13     (p R q) R (q R p)

A14     (~p \/ q) ->_1 (p ->_1 (p ->_1 q))

A15     ~(p ->_1 q) \/ (~p \/ q)

(In A14 and A15 we write (a ->_1 b) instead of p_1(a,b).)

"Theorem 5.5.3.  Each of the sysetems {A1,...,A13,MP_0}
and {A1,...,A15,MP_1} forms an inferential base for
OML[|=].

"The proof is omitted.

"The logics determined by the bases

OML[|=](emptyset) cup MP_i for i in {2,...,5}

are known to be weaker than OML[|=].  Quantum logics
give rise to many counterexamples to some metalogical
properties which hold for classical logic and for a
large class of weaker logics.  We mention here one
result:

Theorem 5.5.4.  If C is a logic such that
OML[|=]<=C<=K, and ~(C=K), then C does not admit the
parameter-free Local Deduction Theorem; in particular,
C does not admit the Deduction Theorem in the sense
of Section 2.6

"The above theorem has a simple algebraic interpretation:
under the hypotheses of the theorem, the class Mod*(C)
fails to have the C-filter extension property.  This result
implies that BA is the only variety of orthomodular lattices
with the congruence extension property."




There are several good reasons to think that classical "results" like
incompleteness do not apply here.  For example, this is what Halmos has
written concerning Goedel incompleteness in a context related to the
text from which I excerpted the material above,

"The Goedel theorem does not assert that every
Peano algebra is syntactically incomplete.  It
asserts, instead, that the definition of Peano
algebras is not a faithful algebraic transcription
of all intuitive facts about elementary arithmetic.
In algebraic terms, this means that while some
Peano algebras may be syntactically complete,
there definitely exist others that are not."


The original questions had to do with whether or not arithmetic could
ground the truths of geometry... or some such thing.  I am not the one
to state that precisely.  But, the interpretation of the incompleteness
theorem is mired in a great many questions that make your simple
question not so simple.

:-)

mitch



-----
Blake Winter wrote:

> Thank you very much; this was very helpful to me.  I am a physics
> major, so the connection to physics helps me understand these things,
> rather than a more abstract approach.  In connection with the question
> I have already asked, however, I would like to add: Does Tarski's
> theorem on the undefinability of truth apply to systems of quantum
> logic?

It is my personal opinion that almost nothing in classical logic is
relevant.  I have been subject to a great deal of appeal-to-ridicule on
sci.logic over the last year, but if you find my various posts (and sort
through the flame war) you will find some things of interest.

One of the reasons for the flame war is because I invoked the work of
Immanuel Kant as a foundation for my ideas.  If you were to read "Critique
of Pure Reason" (I am not recommending it) you would find that Kant's idea
of infinity is single-point compactification ("Thus, the concept of a
number (which belongs to the category of totality) is not always possible
simply upon the presence of concepts of plurality and unity (for instance,
in the representation of the infinite.") as opposed to the concept of
infinity as a transfinite number that can be extended with a successor
function.  So his concept of "number" in relation to infinity corresponds
with the fundamental theorem of algebra (closure of the complex numbers
relative to algebraic field extensions) and single-point compactification
(extended complex plane/Reimannian spherical coordinates).

You may be aware that the proponents of supersymmetry (string theory) are
looking at a number of substructures associated with the 26-dimensional
unimodular Lorentzian lattice Pi_(25,1).  In turn, the roots of this
lattice are given by MOG codes associated with the 24-dimensional Leech
lattice.  You can find a discussion of these things in "Sphere Packings,
Lattices, and Groups" by Conway and Sloane [ISBN: 0-38798-585-9].

The relationship here is the duality between classical sphere packing
problems and information-theoretic error correction codes.  I am not
expert, but in trying to understand the significance, I was able to
recognize that it involves spherical codes.  In pure information-theoretic
contexts, codes have "shapes" that distinguish between valid and invalid
codes.  You are more familiar with this in the common parlance of
"analog-to-digital quantization."  But, Conway and Sloane point out that
practical applications of this are only in 1 dimension.  In general, the
spherical codes transform classical integration to discrete summations.
That is how the spherical geometry presents.

I believe the significance is related to work in geometry done by Hilbert
and Dehn involving triangles and tetrahedra.  If you imagine a triangle in
the plane whose vertices are incident with lines passing through the
surface of a sphere to its "point at infinity," you end up with
correspondences between planar triangles and spherical triangles given by
a tetrahedral simplex.  Since Hilbert's actual work involved pairs of
congruent triangles you get a purely mathematical sense of "duality."
Alexandrov did classic work in combinatorial topology and triangulations
of manifolds.  If you combine that with Coxeter's later work in geometry,
you will be right back to the book I recommended above.

The reason all of this "collapses" away from classical logic (in the sense
of philosophical justifications) has to do with De Morgan conjugation.  If
you can make sense of the excerpts I put in the sci.logic post
"Strawsonian presupposition and subclassical logic" at

news:<400F27CB.7F6EC30C@rcnNOSPAM.com>

you will see that the formalization of logic makes no particular
difference for empirical studies so long as an "unknown" consequence
relation satisfies de Morgan's laws.

The particular statements involving de Morgan's laws are at the end of the
post and are made with respect to "presupposition via negation."  Let me
just say that Kant also has a discussion of infinity in relation to
negation.  The import of those remarks would correspond to Schmidt's
theorem for closure systems,

Schmidt's Theorem -

For a closure system C the following conditions
are equivalent:

  (i) C is finitary

 (ii) C is inductive

(iii) The union of every non-empty directed subset of C belongs to C.


Right now it appears that the people making most of the preliminary
investigations not based on the Hilbert space characterization are the
Polish logicians.  Here is one of their pages with online publications,

 http://www.uni.torun.pl/~jacekm/publications.htm

You should be able to trace through the reference pages for others.

Just so you get some sense of how you can circumvent the classical
philosophical logic, here are just a few things to consider.

First of all, if you were to apply de Morgan conjugation to the projection
connectives and their complements,

 A B |  A
----------
 T T |  T
 T F |  T
 F T |  F
 F F |  F


 A B | ~A
----------
 T T | F
 T F | F
 F T | T
 F F | T


 A B |  B
----------
 T T |  T
 T F |  F
 F T |  T
 F F |  F


 A B | ~B
----------
 T T | F
 T F | T
 F T | F
 F F | T


you would discover that these four connectives are "fixed" or
"invariant."  For example, B is the de Morgan conjugate of B, and, ~A is
the de Morgan conjugate of ~A.  The other 12 Boolean switching functions
map to a different connective just as we typically think of AND and OR as
being de Morgan conjugates of one another.

So, you need a way to characterize the invariant without the "semantic
interpretation" of the truth tables.  You should be able to recognize
numerous different ways of combining any two columns in the matrix

          a/1    b/5    c/3    d/4    e/2    f/6

{1,2,4}     0      1      1      0      0      1

{1,6,5}     0      0      1      1      1      0

{2,3,5}     1      0      0      1      0      1

{3,4,6}     1      1      0      0      1      0


to form truth tables with four distinct rows.  The labeling for this
matrix combines the incidence matrix for the trivial affine geometry with
a particular Steiner quasigroup quadrilateral (triple systems, algebraic
geometry).  But, its relation to the truth table columns should be
recognizable.

Whatever two columns are not used to form A, B, ~A, or ~B will end up
being logical equivalence or exclusive disjunction.  But, there will be
some ambiguity of interpretation (since I am not fixing semantics here).
If you were to look at the paper,

 http://citeseer.nj.nec.com/feigelson97forbidden.html

you would find that this ambiguity does express itself mathematically.
There is a particular characterization in Lemma 4 that fails precisely for
logical equivalence and exclusive disjunction.

For a good treatment of classical logic relative to combinatorial topology
(rather than philosophy) look at

Threshold Logic
Sze-Tsen Hu
University of California Press
Berkeley, CA (1965)
Library of Congress Catalog Number: 65-21982

For a good treatment of triple systems (note that two-fold triple systems
relate directly to combinatorial triangulations) look at

Triple Systems
Charles J. Colbourn & Alexander Rosa
Clarendon Press
Oxford (1999)
ISBN: 0-19-853576-7

Complex analysis rears its ugly head by virtue of linear fractional
transformations.  If you do look at the threshold logic reference, you
will see that there is a difference between a threshold function and an
arbitrary switching function.  Geometrically, a threshold function can
always separate the points mapping to 0 (or F) from the points mapping to
1 (or T) by a hyperplane.  In complex analysis, the modular linear
fractional transformations separate the plane according to whether
Im(z)>0, Im(z)<0, or Im(z)=0.  The elliptical modular function will get
you to temporal and information-theoretic relationships.

I should note that in the same post on subclassical logic, you will find
mention that tense logics are subclassical modal logics.  Tense logics
include temporality.  So you get the "physical temporality" and the
"philosophical temporality" converging to classical truth tables.

My reference on the complex analysis stuff here is

Normal Families
Joel L. Schiff
Springer-Verlag
New York (1993)
ISBN:0-387-97967-0

At this point, some of this gets a little more fuzzy.  In general, there
are degrees of freedom associated with the linear fractional
transformations.  The bounds that distinguish elliptical/hyperbolic from
parabolic appear to coorespond with the Peetre inequality discussed in

Calculus on Heisenberg Manifolds
Richard Beals and Peter Greiner
Annals of Mathematics Studies, Vol. 119
Princeton University Press
Princeton, NJ (1988)
ISBN:0-691-08501-3

But, the bound for the Peetre parabolic inequality escapes me.  I strongly
suspect that this has to do with some relationship between the remaining
linear fractional transformations that are loxodromic and  pseudoconvexity
in complex geometry.  I just do not know any complex geometry.  But, I
have found that pseudoconvexity has been generalized into some kind of
separating surface in real spaces.  By what is essentially a Weierstrass
approximation theorem these surfaces can probably be locally approximated
by the polynomial threshold functions investigated in the development of
artificial neural networks.

But, ignoring the things of which I am completely ignorant, you might look
at the discussion of model operators for the Heisenberg Manifolds.  The
definition given for its group structure yields a two-step nilpotent Lie
group or an abelian group.  So, we start getting back to simple
structures.  Once again, I am far beyond my abilities here, but I believe
the Lie group reflects a sense of "successor" (given that I have avoided
the philosophical treatment) relative to creation and annihilation
operators while the commutativity of the abelian group seems to get back
to the lattice structures by virtue of the work done by Boris Schein,

Pseudosemilattices and Pseudolattices
Boris Schein
American Mathematical Society Translations Vol. 119
1983

There is another reason I do not overly concern myself with the
significance of philosophical logic.  In "Set Theory" by Thomas Jech,
there is a discussion of cofinality on the ordinal numbers.  You can
probably find a definition of cofinality in any good topology book, but
for set theory it collapses a given ordinal number to the smallest ordinal
number that can be used to index a sequence terminating at the given
ordinal number.  So, for example,

cf(omega + omega) = cf(Aleph_omega) = omega

So, here is the deal.  While

cf(alpha) <= alpha,

cf(cf(alpha) = cf(alpha).

The guys doing algebraic logic have defined something called a structural
consequence relation on an algebra S,

X<=C(X)

if X<=Y then C(X)<=C(Y)

C(C(X))<=C(X)

e(C(X))<=C(e(X))

for all X, Y and every endomorphism e on S.

But,

cf(X)<=cf(cf(X))

if cf(X)<=cf(Y) then cf(cf(X))<=cf(cf(Y)

cf(cf(cf(X)))<=cf(cf(X))

and I am pretty certain that the axiom of regularity gives me the
substitutability embodied in the last statement.

What I am saying here is that the development of set theory in
philosophical logic and its association with an axiomatic successor
function may, in fact, collapse to a structural consequence from an
algebraic perspective.  It is one of those "cheap math tricks" everyone
hates, but logicians invoke the Principle of Excluded Middle circularly.
It is used causally to establish the "Fregean ontology" of sets (or
numbers) and then used evidentially to reject arguments opposing this
ontology.  If you read about the relationship of the orthologics to
classical logics in the papers on Malinowski's page, you will realize that
the classical logic cannot be divorced from the orthologics either.

The result is that classical logic justifies "interpretable" axiom sets
like set theory using infinitistic axiom schemas.  If you attempt to
formulate closure system like that described by Schmidt's theorem the only
way to capture the compactness while complying with the standard syntactic
rules of first-order logic will result in the use of circular reference.

It is an odd conundrum, but it was noted by Edmund Husserl in his
"Prolegomena to Pure Logic."

In any case, I hope you never have to worry about philosophical logic
again.  Just direct your attention to descriptive set theory and either
the axiom of determinacy or the axiom of projective determinacy (if you
thing the full strength of the axiom of choice should be kept).

Good luck with your studies.

:-)

mitch




0
mitchs (45)
2/7/2004 6:52:31 PM

"Peter T. Daniels" wrote:

> galathaea wrote:
> >
> > "Peter T. Daniels" wrote:
> > : How many readers of sci.lang do you think know what Heyting algebras
> > : are?
> >
> > Well, from the discussions I've read lately, admittedly not many.  But they
> > should!  When you are approaching an analysis of natural languages inside
> > logical classification systems, one is lead to topics like Dynamic Predicate
>
> Why would one be doing such a thing?
>

That is what people in philosophical logic departments do.  You would be
surprised.


>
> > Logic where you begin to model the natural languages in induction and
> > implication logics.  When these elements are combined with theoretical or
> > semi-empirical metrics on phoneme space and between logical structures, one
> > gets an approach to linguistic taxonomy that is numerically testable.  It,
> > in fact, is the same basic mathematical structure useful in building a logic
> > of biological phylogeny.  It is the logic on trees or more general graphs,
> > and it is known from logic programming that this is Heyting.
>
> All of a sudden, a whole bunch of biologists have suddenly hit on the
> notion that they have something to say about "trees or ... graphs," and
> it turns out they haven't bothered to consult either facts or what has
> already been learned about such topics.
>

Strangely, the most famous logician in all of history was quite interested in the
taxonomy of living organisms.  To some extent, you have this backwards.  :-)

Clearly, Galathaea is trying to bring the kind of problem of which you speak to
people's attention.



>
> > In other words, linguists have the capability to build scientific theories
> > of the same quantitative essence as any other "hard" science.  More
> > information can be collected about language groups which could lead, in some
> > theories, to better understandings of population migration patterns and
> > could represent indicators for archaeological prospecting.  I know that
>
> Ah. If that's what you're after, then you're utterly misguided. As you
> would know if you'd actually learned something about human languages,
> there's no necessary connection between languages and populations;
> moreover, there's nothing particularly "logical" about human language.
>

There are statistically described regularities.  That is something discussed in
the original papers founding information theory.

It is true that neither Aristotelian nor Russellian logic has the correlations
that were once believed.

But, what Galathaea is discussing happens to coincide with the men who disagreed
with those beliefs.  Brouwer and Heyting find justification for their work in
topological frameworks.  I do not know where your particular interests lie.
However, Barry Smith has been looking at mereotopology as a possible framework for
cognitive linguistics.  Peter Gardenfors has been investigating semantics based on
geometric and topological principles.

The last chapter of "The Blackwell Guide to Philosophical Logic" is dedicated to
logic and natural language.  I have not read it yet.  It's author is Alice ter
Meulen.  I ran a Google search.  She works in English departments.



>
> > there are many on sci.lang that just like languages and their history from a
> > non mathematical perspective, but I thought that one or two might actually
> > hold some interest in foundational issues for a mathematical science of
> > linguistics.  That wass actually a strong incentive for me to cross post in
> > general, because there are usually only the rare few in any of these groups
> > that hold an interest in mathematical foundations of their respective
> > disciplines in the abstractness that is the realm of Heyting algebras and
> > logical semantics, but I do see some.  My style of post was hoping to draw
> > those types out, since I find that they are usually much more interested in
> > the abstraction process that I tried to portray.
>
> Have you tried looking at the _existing_ work in "mathematical
> linguistics"?
>

Have you any good online references?

:-)

mitch


0
mitchs (45)
2/7/2004 7:08:35 PM
"John Wilkins" wrote:
: Can you recommend an introductory text for the terminally immatherate? I
: am coming from the biological phylogeny and philosophical logic side of
: things...

From the philosophical logic side, I have always liked the book "Topoi: The
Categorial Analysis of Logic" by R. Goldblatt as being a clear introduction
to some of the topics.  Also nice is Heyting's book on Intuitionism.
However, these books do have math in them.  They are only more elementary
introductions than other sources.  There are many more involved texts which
explore the various aspects that arise, such as madal logics, Kripke
semantics, and the development of the various logics.  There are also
constructive developments of mathematics that, although including logic, go
into analysis, topology, and other areas.

From the biological phylogenetic side, I can't really give any good
introductory texts, because I am not aware of any.  There have been some
research papers in the various related areas of evolutionary topoi, logic
programming on trees and graphs, and analyses of the related recognition
problem on trees.  The field is slowly organising itself, but I am not aware
of any nice introductory text on bioinformatics that explores the issues,
which is one of the indicators to me that there is a need for more education
in this area.  What I do have to offer are things like math.LO/0203113 found
in the arXiv's and related work on tree and graph thoeries from a more
mathematically involved approach.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/7/2004 7:14:14 PM

Franz Heymann wrote:

> mitch wrote:

> > Since you certainly do not intend that interpretation of the word
> "scientist,"
> > could you direct me to some discursive treatment that will explain your
> use?
>
> I did not offer you any interpretation of the word "scientist".
> However, if you really do not know,  a scientist is one who pursues research
> in science according to the tenets of the scientific method.
>

That is very circular.  But, I have no problem with it.

How does this description relate to ordinary people?  Why should they believe
what scientists claim to be true?

I have no particular problem accepting scientific evidence.  But, many other
disciplines have modeled their presentation of facts along similar lines.  When
you do the reduction to mathematics and logic, it becomes easy for people with
other claims to impose legitimate doubts.

In information theory, the problem breaks up into an engineering problem, a
semantics problem, and an effectiveness problem.  Modern logicians and
philosophers spend a great deal of time framing systems of syntax and
semantics.  This is the result of formalisms introduced by Frege and popularized
by Russell.  They can frame a defense against almost any claim of effectiveness.

Given that, you get back to why ordinary people should believe scientists.

It is not just Scientific American.  I understand Kip Thorne and some of his
colleagues are actually getting journal articles printed about how time travel
might work given a supply of negative energy.  Superstrings and membranes cannot
be tested.  Doubly-special relativity appears to be a crass mathematical
device--once one fixes both the speed of light and the Planck constant, you
simply get an extremely complicated "outer representation of time" a la Kant.
Worse yet, once one has two fixed constants, Abraham Robinson's note on
threshold functions comes into play.  Hence, one risks an inability to
distinguish relativity from artificial neural networks.


There had been a time when I was a little disdainful toward engineers.  I regret
that now.  Testing reality to see what works with respect to specific problems
is faithful to the scientific method.  In general, however, science and
scientists have much more at stake than empirical procedure.

:-)

mitch



0
mitchs (45)
2/7/2004 7:51:15 PM
"Peter T. Daniels" wrote:
: All of a sudden, a whole bunch of biologists have suddenly hit on the
: notion that they have something to say about "trees or ... graphs," and
: it turns out they haven't bothered to consult either facts or what has
: already been learned about such topics.

Yes!  I mention this in my post, that there is a lot of recapitulation
because of a lack in education.  That is my point!  Combinatorics is well
developed, yet bioinformatics is a new science.  But their overlap is
tremendous.

: Ah. If that's what you're after, then you're utterly misguided. As you
: would know if you'd actually learned something about human languages,
: there's no necessary connection between languages and populations;
: moreover, there's nothing particularly "logical" about human language.

So it is acceptable for other linguists to speak of dialect chains, but when
I do, I haven't learned something of human languages?  That's just silly.
Of course human languages have a geographic character, but there are
diffusive factors which have given a much more intricate structure than that
portrayed by simple distribution maps.  But when linguists look to
connections between the Amerind and Afroasiatic linguistic phyla, and speak
of organisations like a Nostratic superphylum, it does lend actual
supporting information to the migration of asiatic peoples into the
americas, and can even provide, albeit not precise, measures on when such a
migration could have occurred.  Evidence from languages can also give
information concerning other theories of migration.  In fact, such research
extends over all human symbolic evolution.

As to logic, we can drop that term if you object or strongly associate it
with Boolen algebras and move to "grammar".  There are rules, many implicit,
for conveying information in a language.  When collections of people perform
their utterances, there are many collective goals that are intended.  From
acknowledged agreement of perceptions, to task specifications, to
predictions, etc. there is always quite a lot of actual information content
distributed.  The dynamics of such situations can be studied in a formal
manner.  Even contradictions can be modeled.  Yes, most of these logics are
not Boolean, but yes that is my point.

: Have you tried looking at the _existing_ work in "mathematical
: linguistics"?

Of course I have.  I spent a year under a professor of linguistics and the
philosophy of science.  He guided me through a lot of the material, from the
Chomskian developments and similar string and tree based approaches, to the
connectionists and neural net based approaches.  I have studied the
recognition problem in the mathematics department.  In my job, I have had to
use many algorithms developed in mathematical linguistics for data mining
programs and various other operations on natural languages.

I also love languages and the history of human interaction.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/7/2004 7:59:07 PM

"Brian M. Scott" wrote:

> On Thu, 5 Feb 2004 20:10:50 -0800 "galathaea"
> <galathaea@excite.com> wrote in
> <news:10264u282mchk23@corp.supernews.com> in
> alt.philosophy,comp.lang.functional,sci.lang,sci.physics,sc
> i.psychology.theory:
>
> [...]
>
> > In these communities I am
> > speaking to, I expect some reasonable understanding of the concepts I
> > mentioned.  [...]
>
> Then you have wildly unrealistic expectations.  You are
> assuming a very high degree of mathematical sophistication
> in a couple of specific areas, one that you can't reasonably
> expect to find in more than a smallish minority even in
> sci.math.  (And this fact alone should tell you something
> about the program that you suggest.)
>
> [...]
>

Quite.

And that is part of the problem.  Galathaea is attempting to point out some
relatively simple changes to curriculum that would be of benefit to many
people in their day-to-day careers.  Understanding that this is the case
does require mathematical sophisitication.  But, the changes would not.

There is a documented history of enmity by philosophical logicians toward
mathematicians.  With formal languages and information theory being so
important now, these historical academic rivalries are counterproductive
for the many students who actually *pay tuition* for *useful* educations.

That is not to say that the higher philosophical questions are
unimportant.  But, to the extent that what is involved here constitutes
opinion that has been subject to constant challenge for the last century,
these biases and prejudices should not be a matter of indoctrination from
one's first formal logic class.

:-)

mitch



0
mitchs (45)
2/7/2004 8:04:59 PM
On Sat, 07 Feb 2004 14:04:59 -0600 mitch
<mitchs@rcnNOSPAM.com> wrote in
<news:402544EB.BCE63A73@rcnNOSPAM.com> in
alt.philosophy,comp.lang.functional,sci.lang,sci.physics,sci
..psychology.theory: 

[...] 

> Galathaea is attempting to point out some relatively
> simple changes to curriculum that would be of benefit to
> many people in their day-to-day careers.  Understanding
> that this is the case does require mathematical
> sophisitication.  But, the changes would not.

The second statement is undoubtedly true.  The claim of
benefit is probably at least colorable, though the actual
magnitude of the 'many' is open to question.  The final
claim is far from self-evident.

[...]

Sci.lang removed from f'ups.
0
b.scott (18)
2/7/2004 8:46:08 PM
On Sat, 7 Feb 2004 10:38:14 -0800 "galathaea"
<galathaea@excite.com> wrote in
<news:102ac4di009r407@corp.supernews.com> in
alt.philosophy,comp.lang.functional,sci.lang,sci.physics,sci
..psychology.theory: 

> "Brian M. Scott" wrote:
>: "galathaea" wrote: [...]

>:> In these communities I am speaking to, I expect some
>:> reasonable understanding of the concepts I mentioned. 
>:> [...]

>: Then you have wildly unrealistic expectations.  You are
>: assuming a very high degree of mathematical
>: sophistication in a couple of specific areas, one that
>: you can't reasonably expect to find in more than a
>: smallish minority even in sci.math.  (And this fact
>: alone should tell you something about the program that
>: you suggest.)

> I see constructivism talked about quite intelligently in
> sci.math from time to time.  Some of the regular posters
> to sci.math, like David C. Ullrich and Arturo Magidin,
> have contributed to the expositions.  Its not really that
> obscure.

It's a minor specialist area of no interest to most working
mathematicians.  

The fact that you occasionally see discussions of it in
sci.math is no indication that more than a small minority
there have the appropriate background.  In any case, my
comment applied collectively to the entire body of
mathematics mentioned in your post (Heyting algebras,
Martin-L�f, category theory, etc.), not just to
constructivism.

[...]

I will add to my original observation: you also have wildly
unrealistic expectations of Usenet.  It is not the place to
try to conduct a high-level interdisciplinary academic
seminar.

Sci.lang removed from f'ups.
0
b.scott (18)
2/7/2004 8:46:49 PM
"mitch" <mitchs@rcnNOSPAM.com> wrote in message
news:40252AE1.563DB82B@rcnNOSPAM.com...
>
>
> Franz Heymann wrote:
>
> > "James Dolan" <jdolan@math-lw-n01.math.ucr.edu> wrote in message
> > news:c01hg1$8sr$1@glue.ucr.edu...
> > > in article <40243ac9.34dd@worldnet.att.net>,
> > > peter t. daniels <grammatim@worldnet.att.net> wrote:
> > >
> > > |How many readers of sci.lang do you think know what Heyting algebras
> > > |are?
> > >
> > > a fair number of them, but probably fewer than the number who think
> > > that your attempts to narrow the focus of the newsgroup are motivated
> > > by your personal insecurities about your vast ignorance.
> >
> > The content of this thread does indeed require one hell of a lot of
> > narrowing of its focus.  In fact, to precisely zero.  This is a physics
> > newsgroup and there is no physics in the thread whatsoever.
> >
>
> imbecile...
>
> "Kant anticipated that momentum-energy is the substantial
> correlate of spacetime. Bypassing Newton, he caught up
> with Einstein.[9] "
>
> "In light of quantum geometry and its modern guises - superstring
> and M-theories - this last remark might well have been Kant's most
> far-sighted prediction. Despite suffering from insufficient scientific
> training, the rejection by his advisor, the academic failure, and the
> catastrophe in his family, Kant's philosophical debut in 1749 reveals
> the mark of genius."
>
>  http://www.seop.leeds.ac.uk/entries/kant-development/
>
>
> Your own failure to seek an adequate education is not the fault of anyone
> in this thread.

My education served me magnificently through a long and successful career.

Franz


0
2/7/2004 10:25:45 PM
"galathaea" <galathaea@excite.com> wrote in message
news:102ab5rmbek8fa9@corp.supernews.com...
> "Franz Heymann" wrote:
> : The content of this thread does indeed require one hell of a lot of
> : narrowing of its focus.  In fact, to precisely zero.  This is a physics
> : newsgroup and there is no physics in the thread whatsoever.
>
> There is physics in my post, and there would be more if you or others in
the
> physics group started discussing them.  I specifically mention things like
> quantum logic and its Heyting structure, and I've seen this discussed
_many_
> times in sci.physics.research.  Or take a look at the arXiv's:
> gr-qc/9811053.
>
> Franz,
> I now count over 11 posts of yours for some reason opposed to me and my
> post.  You use descriptions of bowel movements and urination to describe
my
> post.  You cry that it is ten times longer than required for your complete
> reading.

It is indeed so.  Just have a look at the length below here which you filled
with nonsense which need not have occupied more than two lines.
Why not just slate me and be done if that is what you wanted to do?

>
> Don't you think in the time it took you to write 11 responses, you could
> have read my article once through?

No.  I saw that you were too verbose by an order of magnitude.
>
> Because seriously you are drawing conclusions like my article being mainly
> associated with philosophy and lack of rigour that are entirely untrue and
> would, I hope, become more apparent after reading the piece.  I am
> discussing a formal, mathematical structure which has appeared in a lot of
> diverse research.  It is found in dynamic systems theories.  It is found
in
> quantum mechanics.  It is found in the theory of computation.
>
> I still do not understand how that could elicit such a flurry of
negativity.
> What I have learned is that some objected to my format, and that is fine.
I
> thought I'd introduce the topic starting from the vision research crowd in
> what I thought at the time to be a clever or creative way.  And as with
all
> creative efforts, that opens one up for a whole new line of criticism from
> the aesthetic side.  Maybe I failed in my approach, but the topic is still
> glaring right out of the monitor if you took the time to read the piece.
I
> repeat it over and over, in each new context.
>
> So maybe I am a failed artist here, Franz, but that in no way devalues the
> discussion my post was concerning.  And you won't find me cowering away
> because you can throw scatology around like an angry primate.  I still
> believe that the ubiquity of the Heyting algebraic structure across all of
> the disciplines I covered, and others, is indicative of a deeper
> computational structure to our models, both foundational and practical,
and
> feel that if this was just taught during that time when the more specific
> Boolean algebras (which are also Heyting) are taught, maybe there would be
a
> lot less recapitulation of results across disciplines, which is wheel
> spinning that is counter productive.
>
> What you've shown, however, is that you are someone who will post negative
> responses to something you admit you haven't read.

Verbosity is not a virtue, and neither is association with philosophers and
psychologists.

>  What you've shown,
> Franz, is that a piece no longer than a simple preface is considered too
> long for you to spend your time on, but attempting to ridicule people is
an
> activity you have plenty of time for.  If that's the personality you want
> anyone glancing through these posts to pick up, that is your perogative.
> But it is not a personality type I give much value to.

None of that bothers me one jot.

Franz


0
2/7/2004 10:25:46 PM
"galathaea" <galathaea@excite.com> wrote in message
news:102ae84g3q2u444@corp.supernews.com...
> "John Wilkins" wrote:
> : Can you recommend an introductory text for the terminally immatherate? I
> : am coming from the biological phylogeny and philosophical logic side of
> : things...
>
> From the philosophical logic side, I have always liked the book "Topoi:
The
> Categorial Analysis of Logic" by R. Goldblatt as being a clear
introduction
> to some of the topics.  Also nice is Heyting's book on Intuitionism.

Isms and science do not make good bedfellows, so there is another book that
will not read.

Franz


0
2/7/2004 10:25:47 PM
"mitch" <mitchs@rcnNOSPAM.com> wrote in message
news:402533EE.63550C06@rcnNOSPAM.com...
>
>
> Franz Heymann wrote:
>
> > "mitch" <mitchs@rcnNOSPAM.com> wrote in message
> > news:4024B03A.81F8C5@rcnNOSPAM.com...
> > >
> > >
> > > galathaea wrote:
> > >
> > > > mitch wrote:
> > > >
> > > > : On sci.logic, George Greene observed that constructive mathematics
was
> > > > : difficult.  So what you are describing would increase a burden
already
> > > > : perceived as onerous for many.
> > > >
> > > > And this is why my suggestion was in particular to introduce the
topic
> > prior
> > > > to classical logic.  By introduce, I don't mean a complete
exposition of
> > > > everything in the field.  I intend only that the basic structure of
the
> > > > logic is taught along with practice of the rules and an overview of
the
> > > > semantic interpretations.  I just believe that understanding that
> > structure,
> > > > by itself, is important to all people interested in modern research
in
> > any
> > > > of the fields I mention.
> > >
> > > Part of the problem is the bureaucratic structure of the education
system.
> > > Development in mathematics departments is independent of the needs of
> > other
> > > disciplines.
> >
> > In that case you must be talking of singularly bum Universities.
> > I have taught at 3, in 3 different continents, and I have examined in
> > approximately 20.  In none of those Universities did your statement hold
> > true as far as either Physics or Electrical Engineering are concerned.
> >
>
> Right.  In your experience with presentations of mathematics largely--and
> uncritically--based upon "hand-waving".

You are not in  a position to judge anything whatsoever about my experience
other than what I said above.  What I said there does not provide you with
the evidence on which to base your assertion.

> >
> > >  So, when other departments impose curriculum requirements without
> > > clearly understanding what is not being taught, they are not always
giving
> > their
> > > own students what they need.
> >
> > I discussed the mathematics requirements in my department quite
regularly
> > with my colleagues in the mathematics department.  So did my colleagues
in
> > chemistry and in the engineering faculty
> >
>
> Right.
>
> Look.  I just managed to get a truce (uneasy rest) on sci.logic from a
flame war
> that lasted over a year.  So my own responses to vulgar language and
summary
> dismissals in this thread are a little too swift.  It is clear that you
have an
> excellent background and require some sense of why this thread might have
> relevance in sci.physics.
>
> What you are describing here is the "preaching to the choir" type of
> collaboration.

Neither you nor I have any understanding of what that was supposed to mean.

>  In the postscript to this message I have copied parts of a
> thread from sci.logic.  I will not claim that my response will be entirely
> coherent--like Galathaea, I have no particular paradigm within which to
discuss
> these matters.  But, the question had been from a  physics student.  He
seemed
> to appreciate the responses.

Good for him

[snip]

Franz


0
2/7/2004 10:25:48 PM
"mitch" <mitchs@rcnNOSPAM.com> wrote in message
news:402541B3.21AB1BEB@rcnNOSPAM.com...
>
>
> Franz Heymann wrote:
>
> > mitch wrote:
>
> > > Since you certainly do not intend that interpretation of the word
> > "scientist,"
> > > could you direct me to some discursive treatment that will explain
your
> > use?
> >
> > I did not offer you any interpretation of the word "scientist".
> > However, if you really do not know,  a scientist is one who pursues
research
> > in science according to the tenets of the scientific method.
> >
>
> That is very circular.  But, I have no problem with it.

There is nothing circular about it.  It is a perfectly good definition.
>
> How does this description relate to ordinary people?

I have not the slightest idea.  Why should it relate to ordinary people?

>  Why should they believe
> what scientists claim to be true?

Does it matter?
>
> I have no particular problem accepting scientific evidence.  But, many
other
> disciplines have modeled their presentation of facts along similar lines.
When
> you do the reduction to mathematics and logic, it becomes easy for people
with
> other claims to impose legitimate doubts.

That would be their problem.

From here onwards, you presented us with a word salad, so I snipped it.

[snip]

Franz


0
2/7/2004 10:25:49 PM
"Brian M. Scott" wrote:
: "galathaea" wrote:
: > I see constructivism talked about quite intelligently in
: > sci.math from time to time.  Some of the regular posters
: > to sci.math, like David C. Ullrich and Arturo Magidin,
: > have contributed to the expositions.  Its not really that
: > obscure.
:
: It's a minor specialist area of no interest to most working
: mathematicians.
:
: The fact that you occasionally see discussions of it in
: sci.math is no indication that more than a small minority
: there have the appropriate background.  In any case, my
: comment applied collectively to the entire body of
: mathematics mentioned in your post (Heyting algebras,
: Martin-L�f, category theory, etc.), not just to
: constructivism.

My original post was to detail why I believe that opinion of its
significance should be updated.  And I've mentioned on other leafs of this
thread that I'm not expecting everyone reading the post to be familiar with
all of its contents.  This was why I removed all the distraction of symbolic
justifications, logical formalisms, equations, etc.  I wanted those who did
have some familiarity from one of the many different directions to come to
discuss the importance (or lack) of Heyting structures in the education of
their field.

: [...]
:
: I will add to my original observation: you also have wildly
: unrealistic expectations of Usenet.  It is not the place to
: try to conduct a high-level interdisciplinary academic
: seminar.

I have some people telling me in this thread that my post is baseless and
ignorant, and others saying my expectations of others are unrealistic.  I
try to take a path more median to these extremes, and believe that there are
people on the usenet that can contribute to the discussion.  Unfortunately,
I don't have the type of investor funding secured to put a seminar together,
and find the usenet a fair alternative.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/7/2004 10:36:49 PM
So, no actual contribution?

You even snipped mitch's nice piece on quantum logic elsewhere and ignored.

But you still seem to think this is something it is not.

Nice avoidance reaction there.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/7/2004 10:46:30 PM
"Ron Hardin" wrote:
: galathaea wrote:
: > and call on recollections of known forms of full words.  We've learned
: > to attach meanings to utterances and visual shapes, and while you are
: > reading this you are building structures of meaning to the words which
: > can assist in the recognition, determining patterns of abstractions
:
: The important effect where you skip over whole paragraphs looking
: for something interesting preparatory to skipping the article has been
: left out.
:
: Even an interesting title has little effect, eg.
:
:   Subject: Hand Turning Black, Medical Reasons?
:
: if it begins
:
:   First a little history.  I was born in 1971 in East Lansing MI, and
:   my father ...
:
: gets skipped.  It's hopeless to find the interesting part, if any, is
: the judgment.  To hell with it.

That is certainly an important part of reading.  Normally I will skip
through a piece to get a layout of the various topics mentioned if it is too
large for one sitting, and then build my understanding of various sections
that concern what I am interested in with rereadings of those sections.

However, I do not quite see the relevance to Heyting algebras.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/7/2004 11:01:26 PM
galathaea wrote:
> : Even an interesting title has little effect, eg.
> :
> :   Subject: Hand Turning Black, Medical Reasons?
> :
> : if it begins
> :
> :   First a little history.  I was born in 1971 in East Lansing MI, and
> :   my father ...
> :
> : gets skipped.  It's hopeless to find the interesting part, if any, is
> : the judgment.  To hell with it.
> 
> That is certainly an important part of reading.  Normally I will skip
> through a piece to get a layout of the various topics mentioned if it is too
> large for one sitting, and then build my understanding of various sections
> that concern what I am interested in with rereadings of those sections.
> 
> However, I do not quite see the relevance to Heyting algebras.

Have you ever read ``Thomas Mann and Eighteenth Century Comic Fiction'' by Wayne Booth?

The author wrote a thesis on _Tristram Shandy_ and then traces its influence on everything.
-- 
Ron Hardin
rhhardin@mindspring.com

On the internet, nobody knows you're a jerk.
0
rhhardin (172)
2/8/2004 12:15:53 AM
galathaea <galathaea@excite.com> wrote:

> "John Wilkins" wrote:
> : Can you recommend an introductory text for the terminally immatherate? I
> : am coming from the biological phylogeny and philosophical logic side of
> : things...
> 
> From the philosophical logic side, I have always liked the book "Topoi: The
> Categorial Analysis of Logic" by R. Goldblatt as being a clear introduction
> to some of the topics.  Also nice is Heyting's book on Intuitionism.
> However, these books do have math in them.  They are only more elementary
> introductions than other sources.  There are many more involved texts which
> explore the various aspects that arise, such as madal logics, Kripke
> semantics, and the development of the various logics.  There are also
> constructive developments of mathematics that, although including logic, go
> into analysis, topology, and other areas.

I have enough math to understand basic equations. I just can't prove a
theorem :-)

Modal logics and directed graphs? Interesting juxtaposition. Here's
where I come from:

The concept of "species" (= eidos = form = sort) in logic from the
Categories onwards is understood traditionally as a tree diagram (the
famous Tree of Porphyry). Several phylogeneticists, including Nelson and
Platnick, have pointed out the topological identity of P's Tree with a
cladogram, so I went alooking. I found that the biological notion of
species is formed indirectly from a logical notion of species beginning
with Aristotle and the late neo-Platonists, but that when Linnaeus and
John Ray introduced a specifically biological notion in the 17th and
18th centuries, they dropped the idea of a tree, with infimae (lowest)
species being a fixed level instead of merely the terminal nodes in a
tree of an indefinite number of branches as in the older logic.

Modern phylogenetics has rediscovered the tree of Porphyry. But under
set theory, there are no terminal sets implicit in the way things are -
a phylogenetic tree is just the collection of proper sets and subsets
over the range of data - no partial intersections permitted, and no
exclusion sets either - what Aristotle would have called a privative
class.

So this mathematical field is critical to understanding how the older
logic of division (or diairesis) is formally related to modern logic. I
was hoping for a Dummies Guide. I have a graduate degree in philosophy
(but not in logic) and just completed my PhD on the above topic.
> 
> From the biological phylogenetic side, I can't really give any good
> introductory texts, because I am not aware of any.  There have been some
> research papers in the various related areas of evolutionary topoi, logic
> programming on trees and graphs, and analyses of the related recognition
> problem on trees.  The field is slowly organising itself, but I am not
> aware of any nice introductory text on bioinformatics that explores the
> issues, which is one of the indicators to me that there is a need for more
> education in this area.  What I do have to offer are things like
> math.LO/0203113 found in the arXiv's and related work on tree and graph
> thoeries from a more mathematically involved approach.

Thanks. I shall check it out. The bioinformatics I am familiar with
tends to be based on statistical analysis - there is no apparent
connection with phylogenetic trees except to rehearse the old and now
generally discredited phenetics - Cartesian cluster analysis in a
mulitvariate space. But I work at a medical research institute, so I
guess that's to be expected.
-- 
John Wilkins
wilkins.id.au
"Men mark it when they hit, but do not mark it when they miss" 
                                               - Francis Bacon
0
2/8/2004 12:51:33 AM
Franz Heymann <notfranz.heymann@btopenworld.com> wrote:

> "galathaea" <galathaea@excite.com> wrote in message
> news:102ae84g3q2u444@corp.supernews.com...
> > "John Wilkins" wrote:
> > : Can you recommend an introductory text for the terminally immatherate? I
> > : am coming from the biological phylogeny and philosophical logic side of
> > : things...
> >
> > From the philosophical logic side, I have always liked the book "Topoi:
> The
> > Categorial Analysis of Logic" by R. Goldblatt as being a clear
> introduction
> > to some of the topics.  Also nice is Heyting's book on Intuitionism.
> 
> Isms and science do not make good bedfellows, so there is another book that
> will not read.
> 
> Franz

It's not an ideology. Intuitionism is a position in the metaphysics of
mathematics, usually contrasted to Platonism (the idea that numbers and
other mathematical entities have some kind of mind-independent reality).
Think of it as a similar dispute to the one in statistics, between
Bayesians and frequentists.
-- 
John Wilkins
wilkins.id.au
"Men mark it when they hit, but do not mark it when they miss" 
                                               - Francis Bacon
0
2/8/2004 12:51:35 AM
John Wilkins <john.wilkins@bigpond.com> wrote:

> The concept of "species" (= eidos = form = sort) in logic from the
> Categories onwards is understood traditionally as a tree diagram (the
> famous Tree of Porphyry). 

Oops. I mistyped. "...is understood traditionally as a terminal node
in..."
-- 
John Wilkins
wilkins.id.au
"Men mark it when they hit, but do not mark it when they miss" 
                                               - Francis Bacon
0
2/8/2004 1:03:47 AM
galathaea  escribi� (5 Feb 2004 16:06:39 -0800):
 
    galathaea> In  philosophy,   epistemics,  cognition,  linguistics,
    galathaea> formal models, computation,  and the possible structure
    galathaea> of  our   world,  there  are   unifying  principles  of
    galathaea> expressability that  I find  more and more  useful.  It
    galathaea> confuses me that I find them still poorly understood in
    galathaea> crowds where, at least to me, it has always seemed they
    galathaea> should be  more well  known.  So I  thought I'd  try to
    galathaea> bring  some of the  more relevant  communities together
    galathaea> and see if I  could start some discussion on broadening
    galathaea> education along these important  lines, for I feel that
    galathaea> such  is urgently  needed to  prevent a  lot  of "wheel
    galathaea> grinding" and repition of  already known results in the
    galathaea> separate  fields.    I  really  believe   that  such  a
    galathaea> consolidation of logical education  is needed in all of
    galathaea> our  fields  to  place  more focus  on  our  respective
    galathaea> advances.

May you  give some bibliography about constructivism  in cognition and
linguistics? I am interested. Thanks in advance.

    galathaea> -=-=-=--=-=-=--==-=-=-=-=-=-=-=-=-=-=-=-=-=-=

-- 
Sergio Roa Ovalle
Key fingerprint = 5427 E535 8E18 8B3B C38B  ADB5 9DF5 89DE FBF4 738C
0
s.roa (6)
2/8/2004 1:15:16 AM
"galathaea" <galathaea@excite.com> wrote in message news:<1027ij4728kqfd0@corp.supernews.com>...
> "Franz Heymann" wrote:
> : You waffled too long before coming to anything substantive, so I snipped
>  all
> : without reading further.
> : Verbal diarrhoea is curable.  See a doctor.
> 
> This is the second comment on bowel movements associated to my post. 

The grown up term is "feces", or perhaps "scatology".

There are fecal obsessed posters, but Franz is not one; he was merely
commenting on your long-windedness.

> Yet I
> do not see any "waffling" when I read it.  Can you please explain why I get
> such responses, when I have taken time to carefully write my post?  I have
> followed many of your posts on the sci.physics forum and do respect your
> opinion, but do not understand from where you are coming.

Perhaps you spent _too much_ time carefully writing your post.  Or at
least, too much time was spent grafting rather than pruning.
 
> In case you didn't read it, my post is about education, something I feel is
> very important.
> 
> In fact, I am getting the impression that many don't read the post, perhaps
> because reading hurts their head.

You failed to get and keep their attention.  A number of people
_started_ to read your post ... after that, it's your job to keep them
reading.
0
nulldev00 (40)
2/8/2004 2:11:26 AM
galathaea@excite.com (galathaea) wrote in message news:<b22ffac3.0402051606.f6de9b1@posting.google.com>...

You asked how you had waffled.  To begin with ...

> I posted this earlier this week, but discovered that many news servers
> (and Google) would not carry it, due to the number of newsgroups
> posted to, and this also prevented some who could access it from
> replying.  I feel this is an important topic to discuss in an
> interdisciplinary style, and I still believe that there is much
> benefit to all newsgroups and their respective professions which I
> posted to, but have broken the linking up in order to expose this to a
> wider audience of news servers.  I appologise if you received both
> postings on your news server, and I hope that you do not consider it
> spam.  I have read all charters and FAQs I could find and the only
> thing that is troubling is the double post, as the content applies to
> all fields in a quite straightforward way.

is 142 words where you haven't even _begun_ to fail to come to the point.

I don't think I've had sufficient sympathy for profs who must read term papers.
0
nulldev00 (40)
2/8/2004 2:24:15 AM
galathaea wrote:
> 
> "Peter T. Daniels" wrote:
> : All of a sudden, a whole bunch of biologists have suddenly hit on the
> : notion that they have something to say about "trees or ... graphs," and
> : it turns out they haven't bothered to consult either facts or what has
> : already been learned about such topics.
> 
> Yes!  I mention this in my post, that there is a lot of recapitulation
> because of a lack in education.  That is my point!  Combinatorics is well
> developed, yet bioinformatics is a new science.  But their overlap is
> tremendous.

And they're not relevant to language history, because language history
is quite unlike biological history.

> : Ah. If that's what you're after, then you're utterly misguided. As you
> : would know if you'd actually learned something about human languages,
> : there's no necessary connection between languages and populations;
> : moreover, there's nothing particularly "logical" about human language.
> 
> So it is acceptable for other linguists to speak of dialect chains, but when
> I do, I haven't learned something of human languages?  That's just silly.

If you spoke somewhere of dialect chains, and I'm certainly one of those
who found your earlier postings impenetrable, it's likely you weren't
referring to the same phenomena as receive that name within linguistics.

> Of course human languages have a geographic character, but there are
> diffusive factors which have given a much more intricate structure than that
> portrayed by simple distribution maps.  But when linguists look to
> connections between the Amerind and Afroasiatic linguistic phyla, and speak

First of all, there's no such thing as "the Amerind linguistic phylum,"
and second of all, no one has suggested linking it with Afroasiatic.

> of organisations like a Nostratic superphylum, it does lend actual
> supporting information to the migration of asiatic peoples into the
> americas, and can even provide, albeit not precise, measures on when such a

The Nostratic hypothesis doesn't touch on the Americas.

> migration could have occurred.  Evidence from languages can also give
> information concerning other theories of migration.  In fact, such research
> extends over all human symbolic evolution.
> 
> As to logic, we can drop that term if you object or strongly associate it
> with Boolen algebras and move to "grammar".  There are rules, many implicit,
> for conveying information in a language.  When collections of people perform

The rules of grammar (in the Chomskyan sense) don't deal with conveying
information; they deal with the arrangement of words, i.e. syntax.

The greatest of Chomskyism's many failings is its disregard of
semantics, and over the past half century there have been many attempts
at rigorous studies of semantics, and none has prevailed over any of the
others.

> their utterances, there are many collective goals that are intended.  From
> acknowledged agreement of perceptions, to task specifications, to
> predictions, etc. there is always quite a lot of actual information content
> distributed.  The dynamics of such situations can be studied in a formal
> manner.  Even contradictions can be modeled.  Yes, most of these logics are
> not Boolean, but yes that is my point.
> 
> : Have you tried looking at the _existing_ work in "mathematical
> : linguistics"?
> 
> Of course I have.  I spent a year under a professor of linguistics and the
> philosophy of science.  He guided me through a lot of the material, from the
> Chomskian developments and similar string and tree based approaches, to the

Those who do mathematical linguistics aren't particularly working within
the Chomskyan framework. Others at sci.lang are better able to point you
in relevant directions.

> connectionists and neural net based approaches.  I have studied the

"Connectionist and neural net based approaches" have already been shown
to be woefully inadequate for understanding language, which suggests
also that they're also not of much help for describing, as opposed to
modeling, what human brains actually do in general.

> recognition problem in the mathematics department.  In my job, I have had to
> use many algorithms developed in mathematical linguistics for data mining
> programs and various other operations on natural languages.
> 
> I also love languages and the history of human interaction.
> 
> --
> -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
> 
> galathaea: prankster, fablist, magician, liar

No argument there.
-- 
Peter T. Daniels                       grammatim@att.net
0
grammatim (38)
2/8/2004 2:26:50 AM

Franz Heymann wrote:

> "mitch" <mitchs@rcnNOSPAM.com> wrote in message
> news:40252AE1.563DB82B@rcnNOSPAM.com...
> >
> >
> > Franz Heymann wrote:
> >
> > > "James Dolan" <jdolan@math-lw-n01.math.ucr.edu> wrote in message
> > > news:c01hg1$8sr$1@glue.ucr.edu...
> > > > in article <40243ac9.34dd@worldnet.att.net>,
> > > > peter t. daniels <grammatim@worldnet.att.net> wrote:
> > > >
> > > > |How many readers of sci.lang do you think know what Heyting algebras
> > > > |are?
> > > >
> > > > a fair number of them, but probably fewer than the number who think
> > > > that your attempts to narrow the focus of the newsgroup are motivated
> > > > by your personal insecurities about your vast ignorance.
> > >
> > > The content of this thread does indeed require one hell of a lot of
> > > narrowing of its focus.  In fact, to precisely zero.  This is a physics
> > > newsgroup and there is no physics in the thread whatsoever.
> > >
> >
> > imbecile...
> >
> > "Kant anticipated that momentum-energy is the substantial
> > correlate of spacetime. Bypassing Newton, he caught up
> > with Einstein.[9] "
> >
> > "In light of quantum geometry and its modern guises - superstring
> > and M-theories - this last remark might well have been Kant's most
> > far-sighted prediction. Despite suffering from insufficient scientific
> > training, the rejection by his advisor, the academic failure, and the
> > catastrophe in his family, Kant's philosophical debut in 1749 reveals
> > the mark of genius."
> >
> >  http://www.seop.leeds.ac.uk/entries/kant-development/
> >
> >
> > Your own failure to seek an adequate education is not the fault of anyone
> > in this thread.
>
> My education served me magnificently through a long and successful career.
>

I realize that.  Please accept my apologies.  I was not clear about your
initial objections.

:-)

mitch



0
mitchs (45)
2/8/2004 4:22:08 AM

Franz Heymann wrote:

>
> Isms and science do not make good bedfellows, so there is another book that
> will not read.
>

Indeed.

Apparently, whomever invested in the education that has served you so well
wasted their money.  What makes it that much more unfortunate are the current
students and their families investing hard-earned money to be taught by a bigot
such as yourself.

:-)

mitch



0
mitchs (45)
2/8/2004 4:28:56 AM

Ron Hardin wrote:

>
> Have you ever read ``Thomas Mann and Eighteenth Century Comic Fiction'' by Wayne Booth?
>
> The author wrote a thesis on _Tristram Shandy_ and then traces its influence on everything.

Exactly.

You might try looking into the history of logic in the late nineteenth and early twentieth
centuries.

Frege wrote a nice paper on a deductive calculus that everyone ignored.  In order to advertise
it, he wrote "Foundations of Arithmetic."

Russell took that as an opportunity to attempt a Theory of Everything.

:-)

mitch



0
mitchs (45)
2/8/2004 4:39:54 AM

Edward Green wrote:

>
> I don't think I've had sufficient sympathy for profs who must read term papers.

Or mathematics homework.  You would be amazed at what passes for education.

:-)

mitch



0
mitchs (45)
2/8/2004 4:41:20 AM

"Brian M. Scott" wrote:

> On Sat, 07 Feb 2004 14:04:59 -0600 mitch
> <mitchs@rcnNOSPAM.com> wrote in
> <news:402544EB.BCE63A73@rcnNOSPAM.com> in
> alt.philosophy,comp.lang.functional,sci.lang,sci.physics,sci
> .psychology.theory:
>
> [...]
>
> > Galathaea is attempting to point out some relatively
> > simple changes to curriculum that would be of benefit to
> > many people in their day-to-day careers.  Understanding
> > that this is the case does require mathematical
> > sophisitication.  But, the changes would not.
>
> The second statement is undoubtedly true.  The claim of
> benefit is probably at least colorable, though the actual
> magnitude of the 'many' is open to question.  The final
> claim is far from self-evident.
>
> [...]
>

I think that is a fair evaluation.  Thanks.

But, I believe I would have to contest expectation of self-evident
claims.  :-)

:-)

mitch



0
mitchs (45)
2/8/2004 4:58:42 AM

John Wilkins wrote:

>
> So this mathematical field is critical to understanding how the older
> logic of division (or diairesis) is formally related to modern logic. I
> was hoping for a Dummies Guide. I have a graduate degree in philosophy
> (but not in logic) and just completed my PhD on the above topic.

I just discovered that Dover has published a copy of Kant's "Logic."  Hegel
accused Kant of returning to Aristotelian traditions, and, since learning that, I
have been able to trace some of Kant's remarks to specific passages.  That might
give you some sense of an intermediate modern stage.

One of the things with modern logic is the recursive definition of truth used for
the semantics of universal quantification.  I have seen this attributed to
Tarski.  But, I am not certain about the correctness of this.  However, this
would not appear in Kant.

Kant distinguishes between universality, induction, and analogy.  He points out
that the three are different.  So, the use of recursive definitions interpreting
quantifiers would be something distinctly different between modern logic and
Aristotelian logic.

The sense of analogy from Kant's work seems to be captured in descriptive set
theory.  I recently found a good book discussing these matters,

The Applicability of Mathematics as a Philosophical Problem
Mark Steiner
Harvard Press (1998)
ISBN 0-674-00970-3

Steiner refers to this as "Pythagoreanism," thereby bring a new (unneeded) term
into the fray.  Naturally, he is discussing these matters mostly in terms of
quantum mechanics.  But once you put the pieces together, it is descriptive set
theory.  There are two axioms to Zermelo-Fraenkel set theory that introduce its
consequences (the axiom of determinacy and the axiom of projective determinacy),
although they are rarely discussed.

What you might really want to be looking at are mereological discussions.  Here
is a useful Plato page,

 http://plato.stanford.edu/entries/mereology/

Varzi has several good papers on the internet as do others.

But, mereology becomes really complicated as one tries to make it more useful.
The issue is one of individuation.  You will find a number of papers discussing a
region connection calculus.  You can trace something similar to this back at
least to the discussion of extensive connection appearing in "Process and
Reality" by Whitehead and actually much earlier in the work of the Polish
logicians.  I have no direct familiarity with Lesniewski, however.

Naturally, resolving these issues goes back to Aristotle's discussion of
individuals, Kant's discussion of partitions of a universe, and the partition
characteristics associated with the large cardinal numbers that are associated
with the axioms mentioned above.

I'm sorry there is no Dummies guide.  I wish there were.  My head hurts with all
of this.  I started out with a love of biology and someone said that I would not
be permitted to study science unless I could write a proof.

:-)

mitch





0
mitchs (45)
2/8/2004 5:35:09 AM

"Brian M. Scott" wrote:

<snip>

>
> I will add to my original observation: you also have wildly
> unrealistic expectations of Usenet.  It is not the place to
> try to conduct a high-level interdisciplinary academic
> seminar.
>

<snip>

There is a difference between expectations and hopes.  You appear to
have access to an academic environment where one can have high-level
discussions with others.

If, in fact, that is the case, you should try to imagine being in China
during the Cultural Revolution when you next arrive at work.  Imagine
people telling you that you can no longer participate in intellectual
activity.  After all, those activities are not appropriate for people
who should just be teachers--and it is precisely that for which they are
paying taxes and tuitions.

As for the "correct" place...  if I recall correctly, the University of
Chicago had difficulties getting professors and staff to participate in
interdisciplinary programs.  So, if you cannot do it at universities and
you cannot do it at places of employment and you cannot do it in public
forums....

Why should the politics of Usenet be the politics of faculties?

:-)

mitch





0
mitchs (45)
2/8/2004 5:55:50 AM
mitch <mitchs@rcnNOSPAM.com> wrote:

> John Wilkins wrote:
> 
> >
> > So this mathematical field is critical to understanding how the older
> > logic of division (or diairesis) is formally related to modern logic. I
> > was hoping for a Dummies Guide. I have a graduate degree in philosophy
> > (but not in logic) and just completed my PhD on the above topic.
> 
> I just discovered that Dover has published a copy of Kant's "Logic."
> Hegel accused Kant of returning to Aristotelian traditions, and, since
> learning that, I have been able to trace some of Kant's remarks to
> specific passages.  That might give you some sense of an intermediate
> modern stage.
> 
> One of the things with modern logic is the recursive definition of truth
> used for the semantics of universal quantification.  I have seen this
> attributed to Tarski.  But, I am not certain about the correctness of
> this.  However, this would not appear in Kant.
> 
> Kant distinguishes between universality, induction, and analogy.  He
> points out that the three are different.  So, the use of recursive
> definitions interpreting quantifiers would be something distinctly
> different between modern logic and Aristotelian logic.

You want to be careful about that. The syllogistic logics of the late
medievals had four "moods" - Universal affirmation (A), universal
negation (E), Particular affirmation (I) and Particular negation (O),
which are very close to ForAll, Not-ForAll, ThereIs, and Not-ThereIs in
the QL. This is why the mnemonics bAbArA, cElArEnt, and so on - the
three step syllogisms could be taught as sequences of propositions of
universal quantifiers and existential quantifiers in the premises and
conclusion. [Whatley's Elements of Logic of 1836 is the best guide - I
was lucky to find a copy for $5AUS. More recently, you can find Joseph's
1906/1916 Introduction to Logic, which covers this territory well.]

Kant did not "return" to Aristotelian traditions - they had never left
in logic. It wasn't until the late nineteenth century that it faded
away, under the development (out of Aristotelian traditions) by Boole
and Venn and successors of symbolic logic and set theory. Even then,
Aristotelian logic is a special case of that logic. 

Kant's comments on species and genera are straight out of the
syllogistic tradition, particularly in the Critique of Pure Reason. I
can send you the section of my thesis on Kant by email if you like.
> 
> The sense of analogy from Kant's work seems to be captured in descriptive
> set theory.  I recently found a good book discussing these matters,
> 
> The Applicability of Mathematics as a Philosophical Problem
> Mark Steiner
> Harvard Press (1998)
> ISBN 0-674-00970-3
> 
> Steiner refers to this as "Pythagoreanism," thereby bring a new (unneeded)
> term into the fray.  Naturally, he is discussing these matters mostly in
> terms of quantum mechanics.  But once you put the pieces together, it is
> descriptive set theory.  There are two axioms to Zermelo-Fraenkel set
> theory that introduce its consequences (the axiom of determinacy and the
> axiom of projective determinacy), although they are rarely discussed.
> 
> What you might really want to be looking at are mereological discussions.
> Here is a useful Plato page,
> 
>  http://plato.stanford.edu/entries/mereology/
> 
> Varzi has several good papers on the internet as do others.

I know Barry Smith, and corresponded with one of his students at one
point. I was impressed at how little mereological approaches help with
species in biology. In particular I was impressed at how badly the
"intuitions" on mereologists capture actual biology - Aristotle was way
ahead of these guys in some respects. One tried to claim that if we wore
a suit of our DNA we would have extended boundaries. I had to point out
that this no more extended our boundaries than wearing a shirt made of
our own hair...
> 
> But, mereology becomes really complicated as one tries to make it more
> useful. The issue is one of individuation.  You will find a number of
> papers discussing a region connection calculus.  You can trace something
> similar to this back at least to the discussion of extensive connection
> appearing in "Process and Reality" by Whitehead and actually much earlier
> in the work of the Polish logicians.  I have no direct familiarity with
> Lesniewski, however.
> 
> Naturally, resolving these issues goes back to Aristotle's discussion of
> individuals, Kant's discussion of partitions of a universe, and the
> partition characteristics associated with the large cardinal numbers that
> are associated with the axioms mentioned above.
> 
> I'm sorry there is no Dummies guide.  I wish there were.  My head hurts
> with all of this.  I started out with a love of biology and someone said
> that I would not be permitted to study science unless I could write a
> proof.
> 
> :-)
> 
And you believed them?

I gave an ill-fated talk at an Australasian Association of Philosophy
conference on species and set theory. I was totally nonplussed by the
reactions - one respondent said that the sets I was discussing were such
*little* sets. I think he wanted to talk about Cantor sets and Lewisian
Big sets. But biology has no nondenumerable lists or ordered series.
It's all local, limited and finite. The logic is only relevant to the
extent that it deals with such objects, so far as biology goes. But
directed acyclic graphs (or cyclic, in the case of reticulating trees)
*do* have a purchase here, and so I wanted to follow it up.

Incidentally, I too believe this is indicative of more wide applications
of such matters. I don't know (yet) if Heyting algebras apply across the
board, but the tree-like logics do, wherever there is a lineage over
time or formal state space generated by some operators. It applies in
the case of culture, of biology, of ecology in general, whether
biological or not. Classification is my key focus. We classify either
natural kinds (which are sets intensionally defined by some physical
law, according to most) or natural groups (which are those groups
related by a common causal history). In phylogenetics, the former are
not identical to the latter, because history is a contingent process,
and causal processes such as ancestry-descent occupy only a very sparse
region of the possible state space, while intensionally defined sets
occupy, ex definitio, all of it so marked out.

By the way, an early attempt to apply set theory and QL to
classification was done by J H Woodger and revised by Gregg. Woodger
began by defining a successor relation to generate his sets. This
influenced Hennig and the cladists extensively.

Gregg, J. R. (1954). The language of taxonomy: an application of
symbolic logic to the study of classificatory systems. New York,
Columbia University Press.

Woodger, J. H. (1937). The axiomatic method in biology. Cambridge UK,
Cambridge University Press.
        
Woodger, J. H. (1952). "From biology to mathematics." British Journal
for the Philosophy of Science 3: 1-21.

Tarski wrote the technical appendix for Woodger 1937...
-- 
John Wilkins
wilkins.id.au
"Men mark it when they hit, but do not mark it when they miss" 
                                               - Francis Bacon
0
2/8/2004 6:38:06 AM
"Sergio Roa Ovalle" wrote:
: May you  give some bibliography about constructivism  in cognition and
: linguistics? I am interested. Thanks in advance.

I would love to! =)

This is actually where I find that most of my desire for the field comes
from.  The first part of the bibliography.  It starts with the field of
logics, where you find that they really are studying conceptual patterns and
the structure of our models.  The patterns may have properties that show
they are a collection with indexing, a string to build a language upon
(since our utterances are strings).  You can use these strings to construct
models, and models allowed us as early humans the self-reflexive ability to
build our utterances into an information system by playing games.

So a bibliography would have to include many works by Frege, Russel, Tarski,
Goedel, Kripke, a book by A. Robinson called "Introduction to model theory
and to the metamathematics of algebra", Kleene's "Mathematical logic", as
well as an introduction to Chwistek, Lesniewski, Lukasiewicz, Kotarbinsky,
Ajdukiewicz, and Jaskowski.  There are some good compendiums out there that
select papers or survey various fields in the logical theory of today, but I
normally have had to copy papers from the library and can't remember any
spectacular ones.  Mitch mentions Blackwell's, I believe, and although I
haven't seen it yet, if it is anything like their Companion to the
Philosophy of Mind, it should be quite informative.  Logics define model
objects and their properties of transformation, they define the freedom of
our ontologies for conceptual models, and several of the Polish logicians
certainly make explicit that it is an affirmation of the freedom of the mind
(over, for example, the Nazi agression). This was also illustrated in the
works of people like Lawvere who described much of the process of models in
the beautiful visual language of category theory (see also Grothendieck,
Eilenberg, Maclane, and Steenrod) which has the ability to also model set
theory.  There are these pretty constructions in category theory known as
topoi, and these obey many of the properties logicians study.  And they have
the benefit that many known mathematical structures, like topologies,
lattices, and algebras, have categories that are topoi.  A good book on this
is Robert Goldblatt's "Topoi: The categorial analysis of logic".  And there
is a nice connection between categories and computer science demonstrated in
works like Alfio Martini's paper "Category theory and the simply typed
lambda calculus".  And computing over a category's objects follows the logic
of the model.  There is this theorem known as the "Curry-Howard isomorphism"
that makes the connection explicit, and a good explanation of this is found
at http://www.folli.uva.nl/CD/1999/library/pdf/curry-howard.pdf.  See also
the works of Martin-Lof and Markov.  The connection is constructivist
interpretations, and it was found that computation describes very much the
same process that Kolmogorov, Brouwer, Heyting, and others describe as
constructive mathematics.

So we have these connections here showing that there are many different
logics in which we can build conceptual models of the world, over categories
of many different mathematical objects, and make computations with them.
That's the basis of science.  Thats how we predict, or in other ways, model
usefully.  They bring real world benefits.  Thats the cognitive revolution
of linguistics that gave humanity such its privileged position on the food
digraph.  A particularly good survey book on the study of this development
is "Handbook of human symbolic evolution" edited by Andrew Lock and Charles
Peters.

Let me stress that our natural languages are computable in order to convey
Shannon information.  That is meaning.  Identifiable options for
manipulations of concepts.  Papers like de Jong's "Attractors in the
development of communication" or the connectionist models like those found
in the works of Churchland, Smolensky, Goldsmith, etc. suggest that the
notion of dynamical attractors may underlie the notion of concepts in brain
modeling.  And attractors determine regions in state space corresponding to
the basins of attraction.  "The algebraic structure of sets of regions" by
Stell and Worboys describes a natural Heyting structure on such basins.

Our models of the brain, for instance those found in "Neural organisation:
structure, function, and dynamics" by Arbib, Erdi, and Szentogathai are
showing that as we learn more about the receptor response, cell
communication, and ion channels in neurons, we can still keep much of the
foundational neural net structures of connectionist and related models, so
this gives us good evidence that these models may be quite effective in
large scale brain simulations.

So, constructivist structures model both the process of abstraction /
conceptualisation, and the linguistic computations that are models.  They
are useful models on which to build theories of cognition.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/8/2004 10:32:29 AM
galathaea <galathaea@excite.com> wrote, inter alia:

> Let me stress that our natural languages are computable in order to convey
> Shannon information.  That is meaning.

This is not the case - meaning is determined by the ways in which
symbols are employed by a linguistic community (arguably including
referential employment), but Shannon information is merely the
probability that the sequence of symbols at the receiver are identical
to the sequence of symbols at the sender, irrespective of meaning.
Shannon himself noted this in his classic 1948 paper.
-- 
John Wilkins
wilkins.id.au
"Men mark it when they hit, but do not mark it when they miss" 
                                               - Francis Bacon
0
2/8/2004 12:46:27 PM
On Sat, 07 Feb 2004 23:35:09 -0600 mitch
<mitchs@rcnNOSPAM.com> wrote in
<news:4025CA8D.536315D1@rcnNOSPAM.com> in
sci.lang: 

[...] 

> There are two axioms to Zermelo-Fraenkel set theory that
> introduce its consequences (the axiom of determinacy and
> the axiom of projective determinacy), although they are
> rarely discussed.

Aren't part of ZF, either.

[...]

F'ups set.

Brian
0
b.scott (18)
2/8/2004 1:15:57 PM
"Brian M. Scott" <b.scott@csuohio.edu> wrote in message
news:bz1l8aysggg6$.199ehw3bozqj9.dlg@40tude.net...

There is no physics whatsoever in this thread.  Not even wrong physics.

Franz


0
2/8/2004 3:56:21 PM
"galathaea" <galathaea@excite.com> wrote in message
news:102aqlpsu231k3d@corp.supernews.com...
> So, no actual contribution?
>
> You even snipped mitch's nice piece on quantum logic elsewhere and
ignored.
>
> But you still seem to think this is something it is not.
>
> Nice avoidance reaction there.

There is no such thing as quantum logic.  Full stop.  I did not think it
necessary to state such an obvious fact, but since you insist.........

Franz


0
2/8/2004 3:56:22 PM
"John Wilkins" <john.wilkins@bigpond.com> wrote in message
news:1g8u5g9.agirq01sdr2nzN%john.wilkins@bigpond.com...
> Franz Heymann <notfranz.heymann@btopenworld.com> wrote:
>
> > "galathaea" <galathaea@excite.com> wrote in message
> > news:102ae84g3q2u444@corp.supernews.com...
> > > "John Wilkins" wrote:
> > > : Can you recommend an introductory text for the terminally
immatherate? I
> > > : am coming from the biological phylogeny and philosophical logic side
of
> > > : things...
> > >
> > > From the philosophical logic side, I have always liked the book
"Topoi:
> > The
> > > Categorial Analysis of Logic" by R. Goldblatt as being a clear
> > introduction
> > > to some of the topics.  Also nice is Heyting's book on Intuitionism.
> >
> > Isms and science do not make good bedfellows, so there is another book
that
> > will not read.
> >
> > Franz
>
> It's not an ideology. Intuitionism is a position in the metaphysics of
> mathematics, usually contrasted to Platonism (the idea that numbers and
> other mathematical entities have some kind of mind-independent reality).
> Think of it as a similar dispute to the one in statistics, between
> Bayesians and frequentists.

Ians, ists and isms are equally detestable word endings in physics.  I stop
reading whenever I encounter an example.

Franz



0
2/8/2004 3:56:23 PM
"mitch" <mitchs@rcnNOSPAM.com> wrote in message
news:4025BB08.EE0AD88F@rcnNOSPAM.com...
>
>
> Franz Heymann wrote:
>
> >
> > Isms and science do not make good bedfellows, so there is another book
that
> > will not read.
> >
>
> Indeed.
>
> Apparently, whomever invested in the education that has served you so well
> wasted their money.  What makes it that much more unfortunate are the
current
> students and their families investing hard-earned money to be taught by a
bigot
> such as yourself.

You are wrong.  *I* invested well.  *I* paid every penny of my University
education.
And  yes,  I am quite seriously bigoted about the soft sciences and the
stuff stinking of philosophy.

Franz

Franz


0
2/8/2004 3:56:24 PM

John Wilkins wrote:

> mitch <mitchs@rcnNOSPAM.com> wrote:
>
> > John Wilkins wrote:
> >
> > >
> > > So this mathematical field is critical to understanding how the older
> > > logic of division (or diairesis) is formally related to modern logic. I
> > > was hoping for a Dummies Guide. I have a graduate degree in philosophy
> > > (but not in logic) and just completed my PhD on the above topic.
> >
> > I just discovered that Dover has published a copy of Kant's "Logic."
> > Hegel accused Kant of returning to Aristotelian traditions, and, since
> > learning that, I have been able to trace some of Kant's remarks to
> > specific passages.  That might give you some sense of an intermediate
> > modern stage.
> >
> > One of the things with modern logic is the recursive definition of truth
> > used for the semantics of universal quantification.  I have seen this
> > attributed to Tarski.  But, I am not certain about the correctness of
> > this.  However, this would not appear in Kant.
> >
> > Kant distinguishes between universality, induction, and analogy.  He
> > points out that the three are different.  So, the use of recursive
> > definitions interpreting quantifiers would be something distinctly
> > different between modern logic and Aristotelian logic.
>
> You want to be careful about that. The syllogistic logics of the late
> medievals had four "moods" - Universal affirmation (A), universal
> negation (E), Particular affirmation (I) and Particular negation (O),
> which are very close to ForAll, Not-ForAll, ThereIs, and Not-ThereIs in
> the QL. This is why the mnemonics bAbArA, cElArEnt, and so on - the
> three step syllogisms could be taught as sequences of propositions of
> universal quantifiers and existential quantifiers in the premises and
> conclusion. [Whatley's Elements of Logic of 1836 is the best guide - I
> was lucky to find a copy for $5AUS. More recently, you can find Joseph's
> 1906/1916 Introduction to Logic, which covers this territory well.]
>
> Kant did not "return" to Aristotelian traditions - they had never left
> in logic. It wasn't until the late nineteenth century that it faded
> away, under the development (out of Aristotelian traditions) by Boole
> and Venn and successors of symbolic logic and set theory. Even then,
> Aristotelian logic is a special case of that logic.
>
> Kant's comments on species and genera are straight out of the
> syllogistic tradition, particularly in the Critique of Pure Reason. I
> can send you the section of my thesis on Kant by email if you like.

It would be greatly appreciated, as are these comments.



>
> >
> > The sense of analogy from Kant's work seems to be captured in descriptive
> > set theory.  I recently found a good book discussing these matters,
> >
> > The Applicability of Mathematics as a Philosophical Problem
> > Mark Steiner
> > Harvard Press (1998)
> > ISBN 0-674-00970-3
> >
> > Steiner refers to this as "Pythagoreanism," thereby bring a new (unneeded)
> > term into the fray.  Naturally, he is discussing these matters mostly in
> > terms of quantum mechanics.  But once you put the pieces together, it is
> > descriptive set theory.  There are two axioms to Zermelo-Fraenkel set
> > theory that introduce its consequences (the axiom of determinacy and the
> > axiom of projective determinacy), although they are rarely discussed.
> >
> > What you might really want to be looking at are mereological discussions.
> > Here is a useful Plato page,
> >
> >  http://plato.stanford.edu/entries/mereology/
> >
> > Varzi has several good papers on the internet as do others.
>
> I know Barry Smith, and corresponded with one of his students at one
> point. I was impressed at how little mereological approaches help with
> species in biology. In particular I was impressed at how badly the
> "intuitions" on mereologists capture actual biology - Aristotle was way
> ahead of these guys in some respects. One tried to claim that if we wore
> a suit of our DNA we would have extended boundaries. I had to point out
> that this no more extended our boundaries than wearing a shirt made of
> our own hair...

That does not surprise me.  There are a number of interesting ideas coming out
of cognitive philosophy--Peter Gardenfors concept spaces--but they seem to want
to *replace* rather than *integrate with* the existing paradigms of logic and
set theory.

It sounds as if they are all inappropriate for the problems at which you are
looking.



>
> >
> > But, mereology becomes really complicated as one tries to make it more
> > useful. The issue is one of individuation.  You will find a number of
> > papers discussing a region connection calculus.  You can trace something
> > similar to this back at least to the discussion of extensive connection
> > appearing in "Process and Reality" by Whitehead and actually much earlier
> > in the work of the Polish logicians.  I have no direct familiarity with
> > Lesniewski, however.
> >
> > Naturally, resolving these issues goes back to Aristotle's discussion of
> > individuals, Kant's discussion of partitions of a universe, and the
> > partition characteristics associated with the large cardinal numbers that
> > are associated with the axioms mentioned above.
> >
> > I'm sorry there is no Dummies guide.  I wish there were.  My head hurts
> > with all of this.  I started out with a love of biology and someone said
> > that I would not be permitted to study science unless I could write a
> > proof.
> >
> > :-)
> >
> And you believed them?
>

lol

It was the University of Chicago wrapped in all of their conceit.  I had been
from a low-income family.  My parents did  not even complete their secondary
education.  I was failing in mathematics.  So, being at the mercy of expert
bureaucrats,...

:-)



>
> I gave an ill-fated talk at an Australasian Association of Philosophy
> conference on species and set theory. I was totally nonplussed by the
> reactions - one respondent said that the sets I was discussing were such
> *little* sets. I think he wanted to talk about Cantor sets and Lewisian
> Big sets. But biology has no nondenumerable lists or ordered series.
> It's all local, limited and finite. The logic is only relevant to the
> extent that it deals with such objects, so far as biology goes. But
> directed acyclic graphs (or cyclic, in the case of reticulating trees)
> *do* have a purchase here, and so I wanted to follow it up.
>

So, you should be able to avoid most of the "foundational" subjects all together
(thus, avoiding suits of DNA).

Graph theory, lattice theory, topology...


>
> Incidentally, I too believe this is indicative of more wide applications
> of such matters. I don't know (yet) if Heyting algebras apply across the
> board, but the tree-like logics do, wherever there is a lineage over
> time or formal state space generated by some operators.

Well, then I better let Galathaea discuss the Heyting algebras.  :-)

I could not have known your exact background, and I knew that ideas from modern
formal logic were probably inapplicable.  So, I thought I would offer you some
other alternatives.  But they seem to have been tried and rejected.



> It applies in
> the case of culture, of biology, of ecology in general, whether
> biological or not. Classification is my key focus. We classify either
> natural kinds (which are sets intensionally defined by some physical
> law, according to most) or natural groups (which are those groups
> related by a common causal history). In phylogenetics, the former are
> not identical to the latter, because history is a contingent process,
> and causal processes such as ancestry-descent occupy only a very sparse
> region of the possible state space, while intensionally defined sets
> occupy, ex definitio, all of it so marked out.
>



>
> By the way, an early attempt to apply set theory and QL to
> classification was done by J H Woodger and revised by Gregg. Woodger
> began by defining a successor relation to generate his sets. This
> influenced Hennig and the cladists extensively.
>
> Gregg, J. R. (1954). The language of taxonomy: an application of
> symbolic logic to the study of classificatory systems. New York,
> Columbia University Press.
>
> Woodger, J. H. (1937). The axiomatic method in biology. Cambridge UK,
> Cambridge University Press.
>
> Woodger, J. H. (1952). "From biology to mathematics." British Journal
> for the Philosophy of Science 3: 1-21.
>
> Tarski wrote the technical appendix for Woodger 1937...

Thanks.

:-)

mitch



0
mitchs (45)
2/8/2004 6:44:55 PM

"Brian M. Scott" wrote:

> On Sat, 07 Feb 2004 23:35:09 -0600 mitch
> <mitchs@rcnNOSPAM.com> wrote in
> <news:4025CA8D.536315D1@rcnNOSPAM.com> in
> sci.lang:
>
> [...]
>
> > There are two axioms to Zermelo-Fraenkel set theory that
> > introduce its consequences (the axiom of determinacy and
> > the axiom of projective determinacy), although they are
> > rarely discussed.
>
> Aren't part of ZF, either.
>

Right.

I should have said "...in the language of Zermelo-Fraenkel set
theory..." so that some little twit like you could start an argument
about "...there is no such thing as a language of a theory..." in which
case I would have had to expand to something like "...in the set of
symbols commonly used to express the theory introduced by Zermelo,
developed for nearly a century by men of great talents and now commonly
known by Zermelo-Fraenkel set theory because..." so that some little
twit like you could start some further argument...

Thank you for a pissant remark.  If you believe it to have been a
correction for benefit of other participants with less knowledge, you
should have included some legitimate statements explaining the facts of
the matter.

:-)

mitch



0
mitchs (45)
2/8/2004 6:55:30 PM

Franz Heymann wrote:

> "mitch" <mitchs@rcnNOSPAM.com> wrote in message
> news:4025BB08.EE0AD88F@rcnNOSPAM.com...
> >
> >
> > Franz Heymann wrote:
> >
> > >
> > > Isms and science do not make good bedfellows, so there is another book
> that
> > > will not read.
> > >
> >
> > Indeed.
> >
> > Apparently, whomever invested in the education that has served you so well
> > wasted their money.  What makes it that much more unfortunate are the
> current
> > students and their families investing hard-earned money to be taught by a
> bigot
> > such as yourself.
>
> You are wrong.  *I* invested well.  *I* paid every penny of my University
> education.
> And  yes,  I am quite seriously bigoted about the soft sciences and the
> stuff stinking of philosophy.
>

That is an affirmation on all counts.

:-)

mitch



0
mitchs (45)
2/8/2004 7:03:29 PM

Franz Heymann wrote:

> "galathaea" <galathaea@excite.com> wrote in message
> news:102aqlpsu231k3d@corp.supernews.com...
> > So, no actual contribution?
> >
> > You even snipped mitch's nice piece on quantum logic elsewhere and
> ignored.
> >
> > But you still seem to think this is something it is not.
> >
> > Nice avoidance reaction there.
>
> There is no such thing as quantum logic.  Full stop.  I did not think it
> necessary to state such an obvious fact, but since you insist.........
>

Please elaborate.

You seem to be contradicting history with this statement.

:-)

mitch



0
mitchs (45)
2/8/2004 7:08:05 PM

Franz Heymann wrote:

> "Brian M. Scott" <b.scott@csuohio.edu> wrote in message
> news:bz1l8aysggg6$.199ehw3bozqj9.dlg@40tude.net...
>
> There is no physics whatsoever in this thread.  Not even wrong physics.
>

lol

"I can't define obscenity... but I know it when I see it."

Mr. Heymann seems to be under the impression that his mathematics speaks
for itself.

At the end of the day the phrase, "it works" is not physics either.  It is
what a child says.

:-)

mitch



0
mitchs (45)
2/8/2004 7:54:55 PM

John Wilkins wrote:

> galathaea <galathaea@excite.com> wrote, inter alia:
>
> > Let me stress that our natural languages are computable in order to convey
> > Shannon information.  That is meaning.
>
> This is not the case - meaning is determined by the ways in which
> symbols are employed by a linguistic community (arguably including
> referential employment), but Shannon information is merely the
> probability that the sequence of symbols at the receiver are identical
> to the sequence of symbols at the sender, irrespective of meaning.
> Shannon himself noted this in his classic 1948 paper.

But this is one of the places where things seem to be confused by the different
historical treatments.

I have a copy of Shannon's paper with an introduction by Warren Weaver.  The
introduction discusses the fact that there are three problems involved here.
There is the technical problem which is the principle focus of Shannon's paper.
But, Weaver also refers to the semantic problem and to the effectiveness
problem.  Moreover, Weaver is very clear about the vagueness which exists in
delineating the problems from one another.

During the last year on sci.logic, the person with whom I had the most
interaction kept using Church's Thesis as indicative of a psychologistic
principle.  I would not go quite that far, but it does seem to at least convey
the sense in which an information provider encodes a message and an information
consumer decodes a message.  So, while the usage paradigm is crucial and
primary, there is an underlying formalism involved with message passing.

Galathaea probably should have said something more along the lines that Shannon
information imposes a limitation on expressiveness.  But, that would also be
vague.

I have a paper by Zaslavskii discussing Shannon pseudofunctions and complexity
pseudofunctions.  The Shannon pseudofunctions seem to be of interest because
they are defined by a form familiar from many different formalisms.  Moreover,
Zaslavskii develops his paper so that the Shannon pseudofunctions are involved
with manipulating congruences and equivalences with respect to interpretation.

Obviously, natural languages are far more complicated than the formal languages
involved here.  So, I do not want to make any particular claims there.

But, the analogy might be applicable to the notion of gestalts as might be used
in a psychologistic context.  Obviously, the ability of two language users to
have the appearance of communication will depend on how their own perspectives
cohere with respect to information passed between them.  I visualize this in
terms of topologies and partial homeomorphisms between topologies.

I do not know as much about constructive mathematics as I would like.  But, in
the bibliography of one of the papers I have in the subject, I noticed a
reference to minimal sets.  I had already realized the significance of this idea
from my own studies in set theory.  The problem is that topological dynamics is
commonly presented with respect to real number systems for physicists.  For
logical systems where the fragment "is true" has been emphasized, the ring
structures are Boolean.

That still does not get me to any reasonable justification of Galathaea's
statement.  But, the information-theoretic model does get to the geometric work
of Coxeter in the form of spherical codes.  Now through even more nonsensical
invocations of stray mathematical results, I can point to...

Ultimately, I believe meaning has to reside with the receiver's interpretation.
The effectiveness problem discussed by Weaver seems to be game-theoretic in
certain contexts.  It has to do with the sender's expectations with regard to
intended interpretation and actual outcomes.  So meaning within the context of a
community of language users is quite complex.  Not only is their the direct
behavioral interaction at issue, but the static structure of a language is
associated with information-theoretic statistics regarding usage.  I believe
that is mentioned in Shannon's paper.

Well, I am certainly out of my league here.  But, there is no reason to see the
two statements as contradicting one another.  Perhaps I am in error.

:-)

mitch




0
mitchs (45)
2/8/2004 8:43:07 PM
"mitch" <mitchs@rcnNOSPAM.com> wrote in message
news:40268914.F0DA0259@rcnNOSPAM.com...
>
>
> Franz Heymann wrote:
>
> > "galathaea" <galathaea@excite.com> wrote in message
> > news:102aqlpsu231k3d@corp.supernews.com...
> > > So, no actual contribution?
> > >
> > > You even snipped mitch's nice piece on quantum logic elsewhere and
> > ignored.
> > >
> > > But you still seem to think this is something it is not.
> > >
> > > Nice avoidance reaction there.
> >
> > There is no such thing as quantum logic.  Full stop.  I did not think it
> > necessary to state such an obvious fact, but since you insist.........
> >
>
> Please elaborate.
>
> You seem to be contradicting history with this statement.

You are drivelling.  There is only logic,m as summarised in the rules laid
down by Aristotle. (About his only useful achievement)
I repeat.  There is no such thing as quantum logic.  If there is,please
saywhat it might be.

Franz


0
2/8/2004 8:49:03 PM
On Fri, 6 Feb 2004 11:35:41 -0800, "galathaea" <galathaea@excite.com>
wrote:

>I actually felt that what I wrote was dumbing things down quite a bit.

It's not about dumbing down. It's about clear presentation and
straightforward exposition.

>I rarely see the abstract/paper/conclusion format on these groups

Most USENET posts aren't 300+ lines long, either.

>I don't find it too meandering.  It has a fairly linear outline.

From a topological point of view, "linear" and "meandering" are the same
thing. The point is that "linear" isn't enough; there has to be some
structure. Think "tree" rather than "line."

There's this sentence from your original post:

>The logic of propositions in the models on shape theory, the theory of
>the topological, metrical, and orientation-based classification
>calculus, the dynamical logic of the attractor spaces in neural net
>models, the region-connection calculus, all of these logics are
>Heyting.

That, sir, is a classic case of First Degree Meandering. Forty-one words
covering a half-dozen seemingly disconnected ideas before you get to the
one word that's supposed to tie them all together. Present your thesis
first; _then_ elaborate on it.

>It first introduces the point that Heyting algebras are currently
>considered very likely to be our logic of perception 

No, it doesn't. It first consumes 33 lines of USENET space with a
rambling discussion of visual perception and the like, offering utterly
no clue as to why the topic is even being raised.

-Steve

0
see94 (37)
2/8/2004 8:58:26 PM
"John Wilkins" wrote
: galathaea wrote:
:
: > Let me stress that our natural languages are computable in
: > order to convey Shannon information.  That is meaning.
:
: This is not the case - meaning is determined by the ways in which
: symbols are employed by a linguistic community (arguably including
: referential employment), but Shannon information is merely the
: probability that the sequence of symbols at the receiver are identical
: to the sequence of symbols at the sender, irrespective of meaning.
: Shannon himself noted this in his classic 1948 paper.

Information is much more useful as a model than found only in signal theory
and channel communication.  The definition of self-information of a pattern
(often decomposed into strings of more primitive patterns or found in other
cognitive structures) is made relative to a model which predicts it with
probability p.  So information content helps describe our ability to predict
a particular natural language structure within a model.  That model is built
socially through various speech games we participate in during our
development, as pointed out by many throughout the years (like the
qualitative descriptions of Quine, or the quantified games that fill so much
of modern logical analyses of natural language).  When one looks at work
like that of "On information-theoretic measures of attribute importance" by
Yao, Wang, and Butz and similar modern work, the connection between
information theory and the recognition problem is made explicit.  Works such
as "Measuring interference in PCF" by Clark, Hunt, and Malacaria or the
Abramsky, Jagadeesan, and Malacaria "Full abstraction for PCF", and others
relating PCF to computation and Kripke semantics demonstrate how information
and entropy arise in the analysis of type theories and abstraction.

So there does seem to be a natural usage for building information theory
into the models of computation and natural languages, but one also should
analyse organisational content in more structured definitions of
"information".  That is the type of programme, for example, found in Vincent
Simonet's "Fine-grained information flow analysis for a lambda-calculus with
sum types" following works of Moggi, Pottier, and Conchon.

The meaning as recognition school is very intimately related to the concepts
as dynamic attractors school.  And these programmes have numerous
foreshadowings in the Polish school of logic.  This is our ability to
structure our world, to identify features of it and use those features in
models which we can use.

Yang and Campbell even have a beautiful piece out called "Linking form to
meaning: the expression and recognition of emotions through prosody" that
follows this programme into our expressions of cognitive states that are
more limbically influenced.

And following Church-Turing, it appears at least possible, and many would
say likely, that all models of meaning we can possibly build, including many
of the very strange and beautiful logics studied in the Polish school or
modern research, can all be modeled in a framework of computability that has
a Heyting algebraic structure.

That's why I figure that at least that general structure should be taught.
I would love it if many other logics were taught as well, but that seems to
be a fundamental structure that may have universality properties.  And many,
many models these days seem to possess the structure in a non-Boolean way,
including models of concepts and meaning.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/8/2004 11:56:57 PM
"John Wilkins" wrote:
: galathaea wrote:
:
: > "John Wilkins" wrote:
: > : Can you recommend an introductory text for the terminally immatherate?
I
: > : am coming from the biological phylogeny and philosophical logic side
of
: > : things...
: >
: > From the philosophical logic side, I have always liked the book "Topoi:
The
: > Categorial Analysis of Logic" by R. Goldblatt as being a clear
introduction
: > to some of the topics.  Also nice is Heyting's book on Intuitionism.
: > However, these books do have math in them.  They are only more
elementary
: > introductions than other sources.  There are many more involved texts
which
: > explore the various aspects that arise, such as madal logics, Kripke
: > semantics, and the development of the various logics.  There are also
: > constructive developments of mathematics that, although including logic,
go
: > into analysis, topology, and other areas.
:
: I have enough math to understand basic equations. I just can't prove a
: theorem :-)
:
: Modal logics and directed graphs? Interesting juxtaposition. Here's
: where I come from:
:
: The concept of "species" (= eidos = form = sort) in logic from the
: Categories onwards is understood traditionally as a tree diagram (the
: famous Tree of Porphyry). Several phylogeneticists, including Nelson and
: Platnick, have pointed out the topological identity of P's Tree with a
: cladogram, so I went alooking. I found that the biological notion of
: species is formed indirectly from a logical notion of species beginning
: with Aristotle and the late neo-Platonists, but that when Linnaeus and
: John Ray introduced a specifically biological notion in the 17th and
: 18th centuries, they dropped the idea of a tree, with infimae (lowest)
: species being a fixed level instead of merely the terminal nodes in a
: tree of an indefinite number of branches as in the older logic.
:
: Modern phylogenetics has rediscovered the tree of Porphyry. But under
: set theory, there are no terminal sets implicit in the way things are -
: a phylogenetic tree is just the collection of proper sets and subsets
: over the range of data - no partial intersections permitted, and no
: exclusion sets either - what Aristotle would have called a privative
: class.
:
: So this mathematical field is critical to understanding how the older
: logic of division (or diairesis) is formally related to modern logic. I
: was hoping for a Dummies Guide. I have a graduate degree in philosophy
: (but not in logic) and just completed my PhD on the above topic.

I want to appologise first and say that my earlier suggestions for Goldblatt
and Heyting, although good introductions, may not be appropriate to your
education.  I am having some difficulty gauging at what level to hold the
conversations, and am being told many conflicting things.  But just from
this summary of yours, I think I may dumbed down the approach I feel you
should take too much, and I am sorry.

You see, I too am working in my own research programmes on the logics of
phylogentics and evolutionary structures, and this may have also contributed
to the undervaluation.  But there is certainly much more information out
there that could contribute to your studies.  I mention a lot of logicians
in a different leaf of this thread to Sergio Roa Ovalle on which you also
responded.  These logicians do give a good background for the philosophical
logic side, at least of the work in the more distant past.  But there is a
lot more work involving constructive logics occuring in recent times.  For
example, there is a great article "Bimodal logics for reasoning about
continuous dynamics" which stands as an important, in my opinion, landmark
in the study of this form of reasoning which underlies many of our physical
models.

And for your particular interest in biological evolutionary structures, the
first place I would guide you to is the work of Tarski and others on
topological logics, closure algebras, and their semantic analysis.  Whether
you are working in propositions on trees or subtree relationships, they are
all propositions on the topology of the tree, and the topological logicas
capture the form of these expressions.  But also, you are often working from
present information to build such tree structures, such as the cladogram
inference common in bioinformatics.  There are many evaluations of this, and
I like Peter Wagner's survey "Phylogeny and the fossil record" because it
cautions on many of the known hypothesis biasings that should be
acknowledged.  When you invert probabilistic mutation models on gene space
to infer these branching relationships, you find yourself in the realm of
fuzzy sets and the logic of their probabilistic analyses.  There is a nice
book out called "Non-classical logics and their applications to fuzzy
subsets: a handbook of mathematical foundations of fuzzy set theory" which
details much of the logical analyses of such work, and the intimate
relationships with Heyting algebras are shown.  And then there are many,
many papers out there about logics on trees from the study of proof theory
and similar domains (like the paper I mentioned in my first post, which just
happened to be the one on the top of my pile that day for studying).  So you
can start to see that this evolutionary reasoning is intimately tied to
these Heyting.  There is even much research detailing known Heyting
structures in causal sets and causal histories.

But unfortunately, there is not a book I know of that combines this all up
in review.  In fact, I am unaware of any acknowledged connection between
these fields except in minor comments in the papers.  This is why I find it
may be a very successful researche programme for myself, and I do hope that
others such as yourself also pursue it.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/9/2004 12:52:44 AM
mitch wrote:
> 
> Franz Heymann wrote:
> 
> > "mitch" <mitchs@rcnNOSPAM.com> wrote in message
> > news:4025BB08.EE0AD88F@rcnNOSPAM.com...
> > >
> > >
> > > Franz Heymann wrote:
> > >
> > > >
> > > > Isms and science do not make good bedfellows, so there is another book
> > that
> > > > will not read.
> > > >
> > >
> > > Indeed.
> > >
> > > Apparently, whomever invested in the education that has served you so well
> > > wasted their money.  What makes it that much more unfortunate are the
> > current
> > > students and their families investing hard-earned money to be taught by a
> > bigot
> > > such as yourself.
> >
> > You are wrong.  *I* invested well.  *I* paid every penny of my University
> > education.
> > And  yes,  I am quite seriously bigoted about the soft sciences and the
> > stuff stinking of philosophy.
> >
> 
> That is an affirmation on all counts.
> 
> :-)

Tell us again why this squabbling is being posted to sci.lang?
-- 
Peter T. Daniels                       grammatim@att.net
0
grammatim (38)
2/9/2004 1:37:05 AM
galathaea  escribi� (Sun, 8 Feb 2004 02:32:29 -0800):

    galathaea> Our models  of the brain,  for instance those  found in
    galathaea> "Neural   organisation:    structure,   function,   and
    galathaea> dynamics" by Arbib,  Erdi, and Szentogathai are showing
    galathaea> that as we learn more about the receptor response, cell
    galathaea> communication,  and  ion channels  in  neurons, we  can
    galathaea> still  keep   much  of  the   foundational  neural  net
    galathaea> structures of connectionist and related models, so this
    galathaea> gives us  good evidence that these models  may be quite
    galathaea> effective in large scale brain simulations.

    galathaea> So, constructivist structures model both the process of
    galathaea> abstraction  /  conceptualisation,  and the  linguistic
    galathaea> computations that  are models.  They  are useful models
    galathaea> on which to build theories of cognition.

I  have  not  studied  deeply  mathematical  constructivism.   How  is
constructivism  related   to  connectionist  approaches   like  neural
networks? I  have seen, for  example, some work  about neural-symbolic
integration in knowledge representation. How might that be seen? As an
hybrid  approach  or as  an  analogy  between  these approaches?   For
example,  connectionist   modal  logic...    Or  is  this   all  about
constructivist epistemology in general? Is mathematical constructivism
related to constructivist epistemology?

-- 
Sergio Roa Ovalle
Key fingerprint = 5427 E535 8E18 8B3B C38B  ADB5 9DF5 89DE FBF4 738C
0
s.roa (6)
2/9/2004 1:49:25 AM
galathaea  escribi� (Sun, 8 Feb 2004 02:32:29 -0800):

    galathaea> "Sergio Roa Ovalle" wrote:
    galathaea> : May you  give some bibliography  about constructivism
    galathaea> : in cognition and linguistics? I am interested. Thanks
    galathaea> : in advance.

    galathaea> [...]   concepts  in  brain modeling.   And  attractors
    galathaea> determine regions  in state space  corresponding to the
    galathaea> basins of attraction.  "The algebraic structure of sets
    galathaea> of regions"  by Stell  and Worboys describes  a natural
    galathaea> Heyting structure on such basins.

Oh! I had not  realized the point here :) Although, for  me, it is not
clear Heyting structures on basins of attractions. For now ;)

    galathaea> Our models  of the brain,  for instance those  found in
    galathaea> "Neural   organisation:    structure,   function,   and
    galathaea> dynamics" by Arbib,  Erdi, and Szentogathai are showing
    galathaea> that as we learn more about the receptor response, cell
    galathaea> communication,  and  ion channels  in  neurons, we  can
    galathaea> still  keep   much  of  the   foundational  neural  net
    galathaea> structures of connectionist and related models, so this
    galathaea> gives us  good evidence that these models  may be quite
    galathaea> effective in large scale brain simulations.


-- 
Sergio Roa Ovalle
Key fingerprint = 5427 E535 8E18 8B3B C38B  ADB5 9DF5 89DE FBF4 738C
0
s.roa (6)
2/9/2004 2:17:39 AM
"Franz Heymann" wrote:
: There is no such thing as quantum logic.  Full stop.  I did not think it
: necessary to state such an obvious fact, but since you insist.........

Since you dind't read about it, it must be false?

You know that your attitude is why the James Harrises and Matthew Ormans of
the world don't listen, even when their errors are explicitly pointed out,
don't you?  Do you understand that your inability to learn new topics and
your disdain of important areas of human knowledge is what provides the
"cranks" of the world the mental justification they need to keep coming
back?

Do you believe von Neumann was a nut case?  Birkhoff?  Or are those two
names you never needed in your long, fruitful career?

There are numerous books dedicated to the logic of propositions on the
Hilbert spaces of quantum systems.  Studying them allows one to make
consistent statements in quantum mechanics, avoiding all that garbage about
quantum mechanics being "strange" or "impossible to understand".  Its a
scientific subject, discussed by scientists.  But I guess not cranky old men
who like to pretend they are scientists by avoiding rational discussion at
all costs.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/9/2004 2:35:59 AM
mitch <mitchs@rcnNOSPAM.com> wrote:

> John Wilkins wrote:
> 
> > mitch <mitchs@rcnNOSPAM.com> wrote:
....
> > > I'm sorry there is no Dummies guide.  I wish there were.  My head hurts
> > > with all of this.  I started out with a love of biology and someone said
> > > that I would not be permitted to study science unless I could write a
> > > proof.
> > >
> > > :-)
> > >
> > And you believed them?
> >
> 
> lol
> 
> It was the University of Chicago wrapped in all of their conceit.  I had been
> from a low-income family.  My parents did  not even complete their secondary
> education.  I was failing in mathematics.  So, being at the mercy of expert
> bureaucrats,...
> 
> :-)

I stopped believing bureacrats when they told my parents I was too
stupid to stay in high school. I am also the only member of my family to
complete a university course. In a month or so I should have a PhD,
studying while working fulltime for 20 years. I'd like to meet some of
those morons again, if they are still around...
> 
> 
> 
> >
> > I gave an ill-fated talk at an Australasian Association of Philosophy
> > conference on species and set theory. I was totally nonplussed by the
> > reactions - one respondent said that the sets I was discussing were such
> > *little* sets. I think he wanted to talk about Cantor sets and Lewisian
> > Big sets. But biology has no nondenumerable lists or ordered series.
> > It's all local, limited and finite. The logic is only relevant to the
> > extent that it deals with such objects, so far as biology goes. But
> > directed acyclic graphs (or cyclic, in the case of reticulating trees)
> > *do* have a purchase here, and so I wanted to follow it up.
> >
> 
> So, you should be able to avoid most of the "foundational" subjects all
> together (thus, avoiding suits of DNA).
> 
> Graph theory, lattice theory, topology...

I need to know some graph theory - I found a nice online tutorial but at
this stage it is very basic. However, I know a topologist - he's
clinically insane, so I may avoid the topic.
> 
> 
> >
> > Incidentally, I too believe this is indicative of more wide applications
> > of such matters. I don't know (yet) if Heyting algebras apply across the
> > board, but the tree-like logics do, wherever there is a lineage over
> > time or formal state space generated by some operators.
> 
> Well, then I better let Galathaea discuss the Heyting algebras.  :-)
> 
> I could not have known your exact background, and I knew that ideas from
> modern formal logic were probably inapplicable.  So, I thought I would
> offer you some other alternatives.  But they seem to have been tried and
> rejected.

Thanks. I appreciate it anyway. I do not think they are inapplicable so
much as many of the larger conclusions about sets and classes etc. are
not applicable. But since we do deal with a sparse but mostly treelike
group of organisms in biology, a lot of the results of this area will
have some point to it in biology.
....

-- 
John Wilkins
wilkins.id.au
"Men mark it when they hit, but do not mark it when they miss" 
                                               - Francis Bacon
0
2/9/2004 2:44:20 AM
galathaea <galathaea@excite.com> wrote:

> "John Wilkins" wrote:
> : galathaea wrote:
> :
> : > "John Wilkins" wrote:
> : > : Can you recommend an introductory text for the terminally immatherate?
> I
> : > : am coming from the biological phylogeny and philosophical logic side
> of
> : > : things...
> : >
> : > From the philosophical logic side, I have always liked the book "Topoi:
> The
> : > Categorial Analysis of Logic" by R. Goldblatt as being a clear
> introduction
> : > to some of the topics.  Also nice is Heyting's book on Intuitionism.
> : > However, these books do have math in them.  They are only more
> elementary
> : > introductions than other sources.  There are many more involved texts
> which
> : > explore the various aspects that arise, such as madal logics, Kripke
> : > semantics, and the development of the various logics.  There are also
> : > constructive developments of mathematics that, although including logic,
> go
> : > into analysis, topology, and other areas.
> :
> : I have enough math to understand basic equations. I just can't prove a
> : theorem :-)
> :
> : Modal logics and directed graphs? Interesting juxtaposition. Here's
> : where I come from:
> :
> : The concept of "species" (= eidos = form = sort) in logic from the
> : Categories onwards is understood traditionally as a tree diagram (the
> : famous Tree of Porphyry). Several phylogeneticists, including Nelson and
> : Platnick, have pointed out the topological identity of P's Tree with a
> : cladogram, so I went alooking. I found that the biological notion of
> : species is formed indirectly from a logical notion of species beginning
> : with Aristotle and the late neo-Platonists, but that when Linnaeus and
> : John Ray introduced a specifically biological notion in the 17th and
> : 18th centuries, they dropped the idea of a tree, with infimae (lowest)
> : species being a fixed level instead of merely the terminal nodes in a
> : tree of an indefinite number of branches as in the older logic.
> :
> : Modern phylogenetics has rediscovered the tree of Porphyry. But under
> : set theory, there are no terminal sets implicit in the way things are -
> : a phylogenetic tree is just the collection of proper sets and subsets
> : over the range of data - no partial intersections permitted, and no
> : exclusion sets either - what Aristotle would have called a privative
> : class.
> :
> : So this mathematical field is critical to understanding how the older
> : logic of division (or diairesis) is formally related to modern logic. I
> : was hoping for a Dummies Guide. I have a graduate degree in philosophy
> : (but not in logic) and just completed my PhD on the above topic.
> 
> I want to appologise first and say that my earlier suggestions for Goldblatt
> and Heyting, although good introductions, may not be appropriate to your
> education.  I am having some difficulty gauging at what level to hold the
> conversations, and am being told many conflicting things.  But just from
> this summary of yours, I think I may dumbed down the approach I feel you
> should take too much, and I am sorry.

Do not apologise - it's not like I have my background tatooed on the
forehead, or anything. And I am much dumber than you may suspect.
> 
> You see, I too am working in my own research programmes on the logics of
> phylogentics and evolutionary structures, and this may have also contributed
> to the undervaluation.  But there is certainly much more information out
> there that could contribute to your studies.  I mention a lot of logicians
> in a different leaf of this thread to Sergio Roa Ovalle on which you also
> responded.  These logicians do give a good background for the philosophical
> logic side, at least of the work in the more distant past.  But there is a
> lot more work involving constructive logics occuring in recent times.  For
> example, there is a great article "Bimodal logics for reasoning about
> continuous dynamics" which stands as an important, in my opinion, landmark
> in the study of this form of reasoning which underlies many of our physical
> models.

Can you send me that ref on bimodal logics? My email to use is wilkins
at wehi dot edu dot au, not the bigpond.com address of this post (it's a
highly successful spam trap).

I think the problem with the older logics is not that they are bimodal
but that they are binary - modes are statistical while the older logic
is unable to deal with vague predicates and fuzzy sets.
> 
> ...There is even much research detailing known Heyting
> structures in causal sets and causal histories.

These too - this is almost exactly what I want.
> 
> But unfortunately, there is not a book I know of that combines this all up
> in review.  In fact, I am unaware of any acknowledged connection between
> these fields except in minor comments in the papers.  This is why I find it
> may be a very successful researche programme for myself, and I do hope that
> others such as yourself also pursue it.

You too. So far I have been more historical and generally philosophical
than formal. I may never fully comprehend the formalisms, but I want at
least to know they are there...
-- 
John Wilkins
wilkins.id.au
"Men mark it when they hit, but do not mark it when they miss" 
                                               - Francis Bacon
0
2/9/2004 2:44:22 AM
"Peter T. Daniels" wrote:
: And they're not relevant to language history, because language history
: is quite unlike biological history.

Have you noticed that in both fields, they use strings of symbols (utterance
types vs. gene sequences) to make inferences about past relationships?

: If you spoke somewhere of dialect chains, and I'm certainly one of those
: who found your earlier postings impenetrable, it's likely you weren't
: referring to the same phenomena as receive that name within linguistics.

Whay are you like this?  Why do you feel such a drive to demean me without
first trying to understand my point?  I am willing to make an effort to
understand you if you make comments concerning the topic, but much of your
post is this antirational alpha strutting.

In case you didn't notice, my post concerning the use of metrics to develop
language phylogenies was about developing such relationships as found in
dialect chains all the way up to larger group relationships.  I do
understand what I talk about more than the level of a three year old, so if
you'd like to stop presupposing that I wouldn't dare be talking a topic that
you understand as well, maybe, just maybe, communication can result.  I bet
thats how language started...

: First of all, there's no such thing as "the Amerind linguistic phylum,"
: and second of all, no one has suggested linking it with Afroasiatic.

First of all, I should have chosen a less controversial grouping since I
should have realised that there'd be those who pretend they don't understand
the point being made (the study of the relationships between languages
throught time) by avoiding conversing about it and instead focusing on an
unrelated controversy.  OK.  No Amerind.  Focus on Na-Dene.

Harold Flemming has some work on the Borean hypothesis.  Here's an abstract:

http://greenberg-conference.stanford.edu/Fleming_Abstract.htm

He specifically mentions Amerind or Na-Dene, so take your pick.  There are
others working on such a theory.

There is even work that details the taxonomy.  Start with "Finding families:
quantitative methods in language classification" by April and Robert
McMahon.  They even discuss the links I mention as one of those
controversies that could have evidence from mathematical models.

Yet you state that no one has made the suggestion.  That is telling on your
understanding off the field.

: The Nostratic hypothesis doesn't touch on the Americas.

Pedersen's original "Nostratian" hypothesis certainly included Eskimo-Aleut.
It has been expanded at various times in various directions, but there was
the American connection connection from very early on.

: The rules of grammar (in the Chomskyan sense) don't deal with conveying
: information; they deal with the arrangement of words, i.e. syntax.
:
: The greatest of Chomskyism's many failings is its disregard of
: semantics, and over the past half century there have been many attempts
: at rigorous studies of semantics, and none has prevailed over any of the
: others.

Absolutely no argument there.  That's pretty standard.

: Those who do mathematical linguistics aren't particularly working within
: the Chomskyan framework. Others at sci.lang are better able to point you
: in relevant directions.

Again, I agree.  That's not at all what I'm saying.  There was a time when
the connectionist's main opponent were from Chomskyan directions, but now I
would certainly agree that most mathematical linguistics is done in other
logical frameworks.

: "Connectionist and neural net based approaches" have already been shown
: to be woefully inadequate for understanding language, which suggests
: also that they're also not of much help for describing, as opposed to
: modeling, what human brains actually do in general.

Shown?  No, there were some bigots who never realised that generalised
neural nets (with various dynamics defined over digraphs) is sufficient to
form a lambda calculus, so we're looking at a complete computing language.
So obviously it can't be "woefully inadequate" until you disprove the
Church-Turing thesis.

Actually, particularly in the vision research, we are finding certain neural
net models to actually give great models of the actual pathway processing.
Architectonics is a huge field, and with the advent of new electrode and
chemical assay technology has been spilling out a huge amount of information
about our mental processes.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/9/2004 7:13:03 AM

John Wilkins wrote:

> In a month or so I should have a PhD,
> studying while working fulltime for 20 years. I'd like to meet some of
> those morons again, if they are still around...

Congratulations

:-)

mitch



0
mitchs (45)
2/9/2004 8:30:29 AM
Franz Heymann wrote:

> 
> My education served me magnificently through a long and successful career.
> 
> Franz

Would you mind, Sir, if I suggested politely that you continue it outside
our newsgroups?

Jerzy Karczmarczuk
Caen, France

0
karczma (331)
2/9/2004 9:34:56 AM
galathaea wrote:
> 
> "Peter T. Daniels" wrote:
> : And they're not relevant to language history, because language history
> : is quite unlike biological history.
> 
> Have you noticed that in both fields, they use strings of symbols (utterance
> types vs. gene sequences) to make inferences about past relationships?

No.

> : If you spoke somewhere of dialect chains, and I'm certainly one of those
> : who found your earlier postings impenetrable, it's likely you weren't
> : referring to the same phenomena as receive that name within linguistics.
> 
> Whay are you like this?  Why do you feel such a drive to demean me without
> first trying to understand my point?  I am willing to make an effort to
> understand you if you make comments concerning the topic, but much of your
> post is this antirational alpha strutting.

Ok, I'll leave you to the physicists, but I wish they'd quit
cross-posting to sci.lang.

> In case you didn't notice, my post concerning the use of metrics to develop
> language phylogenies was about developing such relationships as found in
> dialect chains all the way up to larger group relationships.  I do
> understand what I talk about more than the level of a three year old, so if
> you'd like to stop presupposing that I wouldn't dare be talking a topic that
> you understand as well, maybe, just maybe, communication can result.  I bet
> thats how language started...
> 
> : First of all, there's no such thing as "the Amerind linguistic phylum,"
> : and second of all, no one has suggested linking it with Afroasiatic.
> 
> First of all, I should have chosen a less controversial grouping since I
> should have realised that there'd be those who pretend they don't understand
> the point being made (the study of the relationships between languages
> throught time) by avoiding conversing about it and instead focusing on an
> unrelated controversy.  OK.  No Amerind.  Focus on Na-Dene.
> 
> Harold Flemming has some work on the Borean hypothesis.  Here's an abstract:
> 
> http://greenberg-conference.stanford.edu/Fleming_Abstract.htm
> 
> He specifically mentions Amerind or Na-Dene, so take your pick.  There are
> others working on such a theory.

Thank you, but I'm personally acquainted with Hal Fleming. A very nice
guy, with some very unsupported notions.

> There is even work that details the taxonomy.  Start with "Finding families:
> quantitative methods in language classification" by April and Robert
> McMahon.  They even discuss the links I mention as one of those
> controversies that could have evidence from mathematical models.

You offer an article name without the slightest hint of how to find it?
And you claim to write clearly??

> Yet you state that no one has made the suggestion.  That is telling on your
> understanding off the field.
> 
> : The Nostratic hypothesis doesn't touch on the Americas.
> 
> Pedersen's original "Nostratian" hypothesis certainly included Eskimo-Aleut.
> It has been expanded at various times in various directions, but there was
> the American connection connection from very early on.
> 
> : The rules of grammar (in the Chomskyan sense) don't deal with conveying
> : information; they deal with the arrangement of words, i.e. syntax.
> :
> : The greatest of Chomskyism's many failings is its disregard of
> : semantics, and over the past half century there have been many attempts
> : at rigorous studies of semantics, and none has prevailed over any of the
> : others.
> 
> Absolutely no argument there.  That's pretty standard.
> 
> : Those who do mathematical linguistics aren't particularly working within
> : the Chomskyan framework. Others at sci.lang are better able to point you
> : in relevant directions.
> 
> Again, I agree.  That's not at all what I'm saying.  There was a time when
> the connectionist's main opponent were from Chomskyan directions, but now I
> would certainly agree that most mathematical linguistics is done in other
> logical frameworks.
> 
> : "Connectionist and neural net based approaches" have already been shown
> : to be woefully inadequate for understanding language, which suggests
> : also that they're also not of much help for describing, as opposed to
> : modeling, what human brains actually do in general.
> 
> Shown?  No, there were some bigots who never realised that generalised
> neural nets (with various dynamics defined over digraphs) is sufficient to
> form a lambda calculus, so we're looking at a complete computing language.
> So obviously it can't be "woefully inadequate" until you disprove the
> Church-Turing thesis.
> 
> Actually, particularly in the vision research, we are finding certain neural
> net models to actually give great models of the actual pathway processing.
> Architectonics is a huge field, and with the advent of new electrode and
> chemical assay technology has been spilling out a huge amount of information
> about our mental processes.
> 
> --
> -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
> 
> galathaea: prankster, fablist, magician, liar

That's for sure.
-- 
Peter T. Daniels                       grammatim@att.net
0
grammatim (38)
2/9/2004 12:43:52 PM
galathaea wrote:
> 
> "Franz Heymann" wrote:
> : There is no such thing as quantum logic.  Full stop.  I did not think it
> : necessary to state such an obvious fact, but since you insist.........
> 
> Since you dind't read about it, it must be false?
> 
> You know that your attitude is why the James Harrises and Matthew Ormans of
> the world don't listen, even when their errors are explicitly pointed out,
> don't you?  Do you understand that your inability to learn new topics and
> your disdain of important areas of human knowledge is what provides the
> "cranks" of the world the mental justification they need to keep coming
> back?
> 
> Do you believe von Neumann was a nut case?  Birkhoff?  Or are those two
> names you never needed in your long, fruitful career?
> 
> There are numerous books dedicated to the logic of propositions on the
> Hilbert spaces of quantum systems.  Studying them allows one to make
> consistent statements in quantum mechanics, avoiding all that garbage about
> quantum mechanics being "strange" or "impossible to understand".  Its a
> scientific subject, discussed by scientists.  But I guess not cranky old men
> who like to pretend they are scientists by avoiding rational discussion at
> all costs.

Again, is there a reason this squabbling is being posted to sci.lang?

> --
> -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
> 
> galathaea: prankster, fablist, magician, liar

Yep.
-- 
Peter T. Daniels                       grammatim@att.net
0
grammatim (38)
2/9/2004 12:45:23 PM
In message <40278086.4F31@worldnet.att.net>, Peter T. Daniels 
<grammatim@worldnet.att.net> writes
>galathaea wrote:
>>
>> "Peter T. Daniels" wrote:
>> : And they're not relevant to language history, because language history
>> : is quite unlike biological history.
>>
>> Have you noticed that in both fields, they use strings of symbols (utterance
>> types vs. gene sequences) to make inferences about past relationships?
>
>No.
>
>> : If you spoke somewhere of dialect chains, and I'm certainly one of those
>> : who found your earlier postings impenetrable, it's likely you weren't
>> : referring to the same phenomena as receive that name within linguistics.
>>
>> Whay are you like this?  Why do you feel such a drive to demean me without
>> first trying to understand my point?  I am willing to make an effort to
>> understand you if you make comments concerning the topic, but much of your
>> post is this antirational alpha strutting.
>
>Ok, I'll leave you to the physicists, but I wish they'd quit
>cross-posting to sci.lang.

I think (I _hope_) you mean the philosophers or the psychologists. We 
physicists aren't too happy about the cross-posting to sci.physics, and 
I doubt if the functional-computer-langugage people are much less 
bewildered.

-- 
Richard Herring
0
Richard
2/9/2004 1:20:50 PM
In sci.lang galathaea <galathaea@excite.com> wrote:
....
> Shown?  No, there were some bigots who never realised that generalised
> neural nets (with various dynamics defined over digraphs) is sufficient to
> form a lambda calculus, so we're looking at a complete computing language.
> So obviously it can't be "woefully inadequate" until you disprove the
> Church-Turing thesis.

But it can be "woefully inadequate".   Most linguists, probably, follow
Chomsky in seeking a theory which is just sufficient to describe human
language, rather than one which is sufficient.  Most linguists' theory
making has concentrated on constraints found in human language.  Chomsky's
original formulation of transformational grammar is now agreed to be
wrong, because it was found to be a Turing machine equivalent.

So, you see, in reporting that generalized neural nets is sufficient to
form a lambda calculus, to a linguist, you've just shown this is an
incorrect theory of human language.

We're on totally different wavelengths.  It's true that some linguists
like to spin out formal systems whose goal is merely to describe language,
but the dominant goal in linguistics has been to find a correct theory,
not one that is sufficient.

....
-- 
Greg Lee <greg@ling.lll.hawaii.edu>
0
greg1021 (22)
2/9/2004 1:39:13 PM
Morris Carr� wrote:
> 
> Peter T. Daniels wrote:
> >>There is even work that details the taxonomy.  Start with "Finding families:
> >>quantitative methods in language classification" by April and Robert
> >>McMahon.  They even discuss the links I mention as one of those
> >>controversies that could have evidence from mathematical models.
> >
> > You offer an article name without the slightest hint of how to find it?
> > And you claim to write clearly??
> 
> Pasting
> 
> "quantitative methods in language classification April Robert McMahon"
> 
> into the search field of Google's main input form and clicking "I am lucky",
> brings you directly to a page ending on the precisions you complain are
> missing. Google, of course, is too obscure a tool to go without saying...

Ok, so it's not important enough to actually provide the information you
just found.
-- 
Peter T. Daniels                       grammatim@att.net
0
grammatim (38)
2/9/2004 2:54:26 PM
Peter T. Daniels wrote:
>>There is even work that details the taxonomy.  Start with "Finding families:
>>quantitative methods in language classification" by April and Robert
>>McMahon.  They even discuss the links I mention as one of those
>>controversies that could have evidence from mathematical models.
> 
> You offer an article name without the slightest hint of how to find it?
> And you claim to write clearly??

Pasting

"quantitative methods in language classification April Robert McMahon"

into the search field of Google's main input form and clicking "I am lucky", 
brings you directly to a page ending on the precisions you complain are 
missing. Google, of course, is too obscure a tool to go without saying...

0
borcis (46)
2/9/2004 2:57:54 PM
"Peter T. Daniels" wrote:
: Thank you, but I'm personally acquainted with Hal Fleming. A very nice
: guy, with some very unsupported notions.

So, in one post you deny that anyone at all has had the idea, and you follow
up with saying you know the guy I mention who has?

And there is certainly support for the notion that many languages of the
Americas derive from a language or languages of Asia.  Its the genetic
information which shows that many peoples of the Americas and certain Asian
peoples likely share a common ancestry, and that such a divergence likely
occurred long after human symbolics had been established.  There are tool
correlations.

: > There is even work that details the taxonomy.  Start with "Finding
families:
: > quantitative methods in language classification" by April and Robert
: > McMahon.  They even discuss the links I mention as one of those
: > controversies that could have evidence from mathematical models.
:
: You offer an article name without the slightest hint of how to find it?
: And you claim to write clearly??

Here's a hint on how to find it:

There is this great new technology out there known as "journal databases".
They allow me to save typing by giving the information of the author's name
and article title, and you can use that information at your local university
library to find the article.  You can even pick up the article in the same
visit.  Some databases even offer the article, and if you get a yearly
account with your local university library (or work at one of the schools or
study there), you can search and retrieve from home.  Then, the information
I offered actually saves both of us time.

However, if you do not have access to such technology, try the April 2003
copy of "Transactions of the Philological Society", Volume 101, Issue 1,
Pages 7 to 55.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/9/2004 3:17:34 PM
"Richard Herring" wrote:
: I think (I _hope_) you mean the philosophers or the psychologists. We
: physicists aren't too happy about the cross-posting to sci.physics, and
: I doubt if the functional-computer-langugage people are much less
: bewildered.

Why do you believe physicists "aren't too happy" to discuss quantum logic or
the logic of evolving causal sets?

Do you believe the "functional-computer-language people" don't like to
discuss the lambda calculus, or that the Curry-Howard isomorphism bewilders
them?

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/9/2004 3:29:24 PM
In message <102f9qnfgv3u5b2@corp.supernews.com>, galathaea 
<galathaea@excite.com> writes
>"Richard Herring" wrote:
>: I think (I _hope_) you mean the philosophers or the psychologists. We
>: physicists aren't too happy about the cross-posting to sci.physics, and
>: I doubt if the functional-computer-langugage people are much less
>: bewildered.
>
>Why do you believe physicists "aren't too happy" to discuss quantum logic or
>the logic of evolving causal sets?

I don't, and I recognise a strawman argument when I see it.  I'm talking 
about this oddly crossposted thread, which is neither of the things you 
mention.

>Do you believe the "functional-computer-language people" don't like to
>discuss the lambda calculus, or that the Curry-Howard isomorphism bewilders
>them?
>
Likewise.

-- 
Richard Herring
0
Richard
2/9/2004 4:02:42 PM
"Sergio Roa Ovalle" wrote:
: Oh! I had not  realized the point here :) Although, for  me, it is not
: clear Heyting structures on basins of attractions. For now ;)

There are more references concerning that particular issue I can offer.
Jochen Renz has an article "A canonical model of the region-connection
calculus" which I find to be a fairly good reference to the reasoning here.
There is also a very interesting paper by Duntsch, Wang, and McCloskey
titled "A relation-algebraic approach to the region-connection calculus"
which beautifully ties the theory to the relation-algebraic theories being
used by Carlos Leguizamon in his work on modelling antigen-antibody
interactions or deviating a cancer process.

Also, Peter Gardenfors has a great piece "How logic emerges from the
dynamics of information" that brilliantly ties some of the pieces I mention
together for cognitive studies.  And, from a more technical approach, there
are papers like the "Bimodal logics for reasoning about continuous dynamics"
by Davoren and Gore which is a beautiful formal piece.

None of this really depends on the connectionist approach, either.  These
apply to many models of the brain and thought.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/9/2004 4:57:38 PM
"Richard Herring" wrote:
: galathaea writes:
: >Why do you believe physicists "aren't too happy" to discuss
: >quantum logic or the logic of evolving causal sets?
:
: I don't, and I recognise a strawman argument when I see it.  I'm talking
: about this oddly crossposted thread, which is neither of the things you
: mention.
:
: >Do you believe the "functional-computer-language people" don't like to
: >discuss the lambda calculus, or that the Curry-Howard isomorphism
bewilders
: >them?
:
: Likewise.

My "argument" was not meant to be a straw man, but I do realise that this
thread did not develop the way I had hoped.  I was hoping that various
professionals from various communities could get together and talk about how
Heyting algebras underly many topics in their various fields.  I was hoping
that I could stimulate discussion as to the importance of the logics such
algebras represent, and perhaps look to building some kind of consensus as
to the need for education in the area.  I hoped people would share
experiences of how understanding these structures has helped them make
better progress, or prevented certain incorrect conclusions, or anything
like that as they have progressed through their careers.

So I had hoped that physicists would mention von Neumann and Birkhoff's
quantum logic, or the beautiful work of Fotini Markopoulou-Kalamara and her
papers on causal sets.  I had hoped that computer scientists would mention
the lambda calculus.  I had hoped mathematicians would mention how they
respect constructive proofs.

But instead I got a bunch of bs and alpha posturing from people who wouldn't
even read past the vision research section.

So I agree, this thread is not yet any of those things.  It has a few
constructive discussions starting, and maybe others will start more or maybe
it will die out.  But for the most part, this thread is full of sound and
fury, signifying little.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/9/2004 5:14:56 PM
"Greg Lee" wrote:
: galathaea wrote:
: ...
: > Shown?  No, there were some bigots who never realised that generalised
: > neural nets (with various dynamics defined over digraphs) is sufficient
to
: > form a lambda calculus, so we're looking at a complete computing
language.
: > So obviously it can't be "woefully inadequate" until you disprove the
: > Church-Turing thesis.
:
: But it can be "woefully inadequate".   Most linguists, probably, follow
: Chomsky in seeking a theory which is just sufficient to describe human
: language, rather than one which is sufficient.  Most linguists' theory
: making has concentrated on constraints found in human language.  Chomsky's
: original formulation of transformational grammar is now agreed to be
: wrong, because it was found to be a Turing machine equivalent.
:
: So, you see, in reporting that generalized neural nets is sufficient to
: form a lambda calculus, to a linguist, you've just shown this is an
: incorrect theory of human language.
:
: We're on totally different wavelengths.  It's true that some linguists
: like to spin out formal systems whose goal is merely to describe language,
: but the dominant goal in linguistics has been to find a correct theory,
: not one that is sufficient.

I agree with that, in much the same way I would agree with similar comments
about the works of Langacker or Lakatos lacking definitive constraints.

There is, however, a modeling framework which neural nets define.  And
inside that framework, specific theories can be proposed concerning actual
connections and dynamic laws, learning, etc where the association of
concepts with attractor spaces is quite general.  Every year, tons of new
data comes out of the neuroanatomy/physiology research concerning
connections between the neurons, pathways, neurotransmitter response, etc.
Models are being built with many of the characteristic we see in human
thought.  For one extreme example, King, Barchas, and Huberman have modelled
the central dopaminergic neuronal system and found chaotic dynamics in areas
of state space that show similarity to schizophrenic patterns.  We do quite
well at modelling the visuo-motor coordination in the toad and frog with
projects such as Rana computatrix.  As far as language goes, there are still
some technical difficulties with the large number of brain "modules" which
cooperate in its construction, but we are slowly getting there.

Those models _are_ testable.  They appear to be quite good at predicting
brain behavior in simple to moderate systems, and there is no evidence yet
for much concern.

However, I absolutely agree that until that starts making some predictions
about language, we need to look to other models.  Which is why I also
mention formal languages and the logical approach to language.  These too
have Heyting algebras in prominence.  As does reasoning about the history of
languages and the construction of relationships.

And that is the whole point of post.  To ask professionals to share any
thoughts on Heyting algebras in the foundations of their profession and
perhaps discuss broadening education on the topic.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/9/2004 5:49:02 PM
In sci.lang galathaea <galathaea@excite.com> wrote:
....
> However, I absolutely agree that until that starts making some predictions
> about language, we need to look to other models.  Which is why I also
> mention formal languages and the logical approach to language.  These too
> have Heyting algebras in prominence.  As does reasoning about the history of
> languages and the construction of relationships.

This "logical approach to language" is another problem for me.  What little
I know suggests to me that the logic of English, at least, is classical.
E.g., DeMorgan's laws work, but they don't hold in intuitionist logic.
I don't know what Heyting algebras are, but I gather from this discussion
that they are weakened sorts of Boolean algebra, as intuitionist logic
is a weakened sort of classical logic.  If that is roughly so, and if
the logic of natural language is classical, wouldn't you expect to "have
Heyting algebras in prominence"?  In other words, I don't see how finding
some reason for using Heyting algebra to describe human language is any
reason to believe that the logic of language is non-classical, nor any
reason to bother with Heyting algebras, for that matter.

-- 
Greg Lee <greg@ling.lll.hawaii.edu>
0
greg1021 (22)
2/9/2004 6:18:48 PM
Peter T. Daniels wrote:

>>>>There is even work that details the taxonomy.  Start with "Finding families:
>>>>quantitative methods in language classification" by April and Robert
>>>>McMahon.  They even discuss the links I mention as one of those
>>>>controversies that could have evidence from mathematical models.
>>>
>>>You offer an article name without the slightest hint of how to find it?
>>>And you claim to write clearly??
>>
>>Pasting "quantitative methods in language classification April Robert McMahon"
>>into the search field of Google's main input form and clicking "I am lucky",
>>brings you directly to a page ending on the precisions you complain are
>>missing. Google, of course, is too obscure a tool to go without saying...
> 
> 
> Ok, so it's not important enough to actually provide the information you
> just found.

The information I provided quite fits the bill of what you demanded. Please 
don't take this fit as a measure of my own judgement about it, and please 
don't take my judgment about it as a universal measure of importance.

Regards, MC

0
borcis (46)
2/9/2004 6:52:17 PM
Jacques Guy wrote:
> Every topology provides a complete Heyting algebra in form
> of its open set lattice. In this case, the element A&rArr;B
> is the interior of Ac&cup;B, where Ac denotes the complement
> of the open set A. Not all complete Heyting algebras are of
> this form. These issues are studied in pointless topology,
> where complete Heyting algebras are also called frames or
> locales.

When is a door not a door?  When it's ajar.

That's a Heyting algebra.  Notice the open set.
-- 
Ron Hardin
rhhardin@mindspring.com

On the internet, nobody knows you're a jerk.
0
rhhardin (172)
2/9/2004 7:02:26 PM
"Jacques Guy" wrote:
: galathaea wrote:
:
: > And that is the whole point of post.  To ask professionals to share any
: > thoughts on Heyting algebras in the foundations of their profession and
: > perhaps discuss broadening education on the topic.
:
: So I did a search for "Heyting algebra" (no idea what the bloody
: thing is).
:
: Found a definition at http://mathworld.wolfram.com/HeytingAlgebra.html
:
: "An algebra which is a special case of a logos."
:
: Looked up "logos":
:
: "A generalization of a Heyting algebra which replaces Boolean
: algebra in "intuitionistic" logic."
:
: Lovely. So far, I have found out that a Heyting algebra
: was a special case of a generalization of a Heyting
: algebra. I know Boolean algebra, I know what logic is,
: but I have no idea what quote-intuitionistic-unquote
: means. Terrific.

That is horrible!  I have no idea what type of information that is supposed
to convey, but it ends up just illustrating the existence of three phrases
without any meaning.

: Looked at http://en.wikipedia.org/wiki/Heyting_algebra
:
: Same stuff.
:
: Not one single straight example, like, you know,
: "two eggs added to three eggs make five eggs. Now
: look: three eggs and two eggs also add up to five
: eggs. The order doesn't matter. That's what we mean
: by [piece of jargon].
:
: Oh, sure there is a link "examples" in the Wikipedia.
: So you click on it, and what to you get?
:
: Examples
:
: Every topology provides a complete Heyting algebra in form
: of its open set lattice. In this case, the element A&rArr;B
: is the interior of Ac&cup;B, where Ac denotes the complement
: of the open set A. Not all complete Heyting algebras are of
: this form. These issues are studied in pointless topology,
: where complete Heyting algebras are also called frames or
: locales.
:
: At that stage it became topological for me to continue.

Wikipedia is a bit better in that it gives the formal definition in terms of
lattices, and includes a link to intuitionist logic with some descriptions
of reasoning in that system.

: You want to "ask professionals to share any thoughts on
: Heyting algebras in the foundations of their profession"
: you make clear what you're talking about first. (And I
: have no idea either what the "foundation of my profession"
: could possibly mean. Lovely words, though. They do
: sound grand.)
:
: Ce qui se con�oit clairement s'exprime clairement.

The formal definition is the most accurate I can think of, but if you do not
already understand the relationship between logics and lattices, it can be
confusing.  Perhaps a better understanding can be had from an approach
through Kripke semantics and modal logics, but I will try to not overload on
details.

Basically, the logical structure represented by Heyting algebras can be
interpreted as having a temporal structure.  "Truth" and "falsity" do not
apply in an absolute sense, as they do classically, but instead apply only
at certain times.  This is where the ideas of constructivism arise, that
there is no truth or falsity except what has been arrived at through a
process.  We construct our notions of truth.  Each moment of time is
associated with a particular state of knowledge, and sentences are evaluated
relative to a state of knowledge.  Truth has a persistence property that
once a sentence is true for a particular state, it is true for all later
states as well.

This temporal ordering, in the general case, is only what is known as a
partial order and is not necessarily linear (though it can be).  This is why
such logics can also model possibility and certain forms of
counterfactuality.

This can all be formalised in what is known as the S4 modal logic.  More on
modal logics can be found at http://plato.stanford.edu/entries/logic-modal/
and the particular relationship with constructivism and computability can be
found in a brilliant paper by Alechina, Mendler, de Paiva, and Ritter called
"Categorical and Kripke semantics for constructive S4 modal logic" which I
believe can still be found on the internet.

And this structure is found all over the place in the sciences.  In natural
language, for example, much communication is done in modalities where
Boolean logic is not an appropriate model.  Its found in reasoning about the
way we model our reality, or in dynamical systems, or in all of the topics I
mention in my original post.  All of those things are Heyting algebras.  All
of the things I have been talking about in followups are as well Heyting.
Not all logics are Heyting represented directly, but then the work on
computability shows that it is likely those other logics have no more
modeling capability than that found in the lambda calculus, so there is some
kind of universality possible here.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/9/2004 8:27:32 PM

Fred Mailhot wrote:

> On 2/10/04 5:22 AM, "Jacques Guy" <jguy@alphalink.com.au> wrote:
>
> > galathaea wrote:
> >
> >> And that is the whole point of post.  To ask professionals to share any
> >> thoughts on Heyting algebras in the foundations of their profession and
> >> perhaps discuss broadening education on the topic.
> >
> > So I did a search for "Heyting algebra" (no idea what the bloody
> > thing is).
> >
> > Found a definition at http://mathworld.wolfram.com/HeytingAlgebra.html
>
> Ah...I didn't think to check MathWorld, oddly enough (clearly that's to my
> benefit)...but I did do Wikipedia...
>
> [snip]
>
> > Looked at http://en.wikipedia.org/wiki/Heyting_algebra
> >
> > Same stuff.
>
> I think I got a bit further than that...as near as I can tell (and
> presumably galathea, with her dazzlingly concise rhetoric, will fail to let
> me know if I'm right or not), a Heyting algebra is just a boolean algebra
> (lattice w/ top & bottom) w/o "excluded middle" as an axiom...
>
> Now we can all chime in and tell galathea how our research bears just on the
> issues she claims are important in the context of educational reform.
>
> :-|
>

Such a sour face.

Greg Lee writes:

"What little I know suggests to me that the logic
of English, at least, is classical. E.g., DeMorgan's
laws work, but they don't hold in intuitionist logic."

That may well spell doom for Galathaea's attempts here.  On the other hand, if
Mr. Lee is correct about de Morgan's laws, the discussion of "presupposition via
negation" by Jacek Malinowski should have some bearing.  Unfortunately, the
paper is far from trivial.  It can be found at

 http://www.uni.torun.pl/~jacekm/bimatrix.pdf

Those of you who may be wondering about the legitimacy of Galathaea's remarks
might be pleased to find that Malinowski finishes the paper with

"It seems that a link between sentences and their
presuppositions cannot be determined via a logic.
Strawson seems to be conscious of it in the following
comment on historical approaches to presupposition
(Strawson [50]):

     'Neither Aristotelian nor Russelian rules give
      the exact logic of any expressions in ordinary
      language, for ordinary language has no exact
      logic.'"


But the concept of presupposition via negation *is* associated with logical
frameworks.  To be precise, it is associated with modal logics that satisfy a
condition Malinowski refers to as subclassical.  The examples he cites in the
paper are tense logics and deontic logics.

The reason "classical logic" shows up in natural language is because of
structure that can arguably be traced back to geometric and topological forms.
I would guess that this is why cognitive linguistics realizes some successes.

To see why I quoted Mr. Lee's comment concerning de Morgan's laws, observe that
Malinowski also writes:

"In general, there is no clear method of generalizing
(2) for presuppositions of the sets of sentences. This
results from the use of negation operation. If we do
not indicate the concrete logical entailment, we are
unable to determine what is the negation of the set of
sentences X even if X is finite. The case of an infinite
set X causes even more problems. If the logical
consequence in (2) satisfies de Morgan laws, then we
could identify the negation of (finite) set X with the
disjunction of the negations of its elements. However
this identification depends strictly on the underlying
consequence operation."


Through a bunch of hoops, I could connect these remarks to a finitary closure
space and Kant's epistemology.  I will save everyone the details.

Now like most of the people complaining here, I know very little about Heyting
algebras.

But, I am also *painfully aware* that large groups of academic professionals are
running around trying to implement models of natural language semantics in ways
that are questionable.  Apparently, *they* seem to *know* precisely what rules
of logical entailment are to be applied for modeling natural languages when
closely related branches of research that seem to contradict them are being
ignored.  Such is the lure of a successfully implemented Turing test.

One reason Galathaea recognizes the ubiquity of Heyting algebras stems from the
fact that they are "implementable."  They have been studied for some time and
are recognized.  But, it would be a mistake to account for Heyting algebras
simply on the basis of rejecting "excluded middle."

To the contrary, what follows is the tree of logics that arises from
investigation of "algebraic semantics."   At the base of the tree you will find
an immediate split distinguishing "equivalential logics" from "non-equivalential
logics."  This is much closer to the mathematical reasoning for the
philosophical arguments that led to Heyting algebras.

                            Fregean
                         Protoalgebraic
                             Logics

                               |
                               |
                               |
                               |

   Regularly               Regularly
     Weakly               Algebraizable
  Algebraizable  -------     Logics
     Logics
                               |
       |                       |
       |                       |
       |                       |

     Weakly               Algebraizable
  Algebraizable  -------     Logics
     Logics
                               |
       |                       |
       |                       |
       |                       |
       |
       |                  Equivalential
       |                     Logics

        \                     /
         \                   /
          \                 /
           \               /
            \             /
             \           /
              \         /
               \       /

            Protoalgebraic
                Logics



Now, I am simply too damn ignorant to relate any of this in ways that will be
"useful" to anyone.  But, I know enough about set theory,
modernist/post-modernist logic, and mathematics to reject the simplistic ideas
that are commonly presented with respect to intuitionism and Heyting algebras.

Algebraic semantics realizes "classical logic" without regard for the
interpretations of twentieth century logicians and analytical philosophers.  I
cannot say whether or not Heyting algebras will be of use to any of you.  But, I
can share a quote from my own subject of interest explaining the consequences of
letting "foundational thinkers" decide matters for themselves:

"The development of the foundations of physics
in the twentieth century has taught us a serious
lesson.  Creating and understanding these foundations
turned out to have very little to do with the
epistemological abstractions which were of such
importance to the twentieth century critics of the
foundations of mathematics: finiteness, consistency,
constructibility, and, in general, the Cartesian notion
of intuitive clarity.  Instead, completely unforeseen
principles moved into the spotlight: complementarity,
and the nonclassical, probabilistic truth function.
The electron is infinite, capricious, and free and does
not at all share our love for algorithms."


The apparent distinction between mathematics and physics in this quote does not
contradict my remarks.  It relates precisely to the prejudices you will find in
the literature concerning intuitionism as motivated by the advocates of
modernist/post-modernist logic.

Sorry for polluting your newsgroups.  But, as a matter of historical record, it
is unlikely that anyone looking for information on Heyting algebras from
generally available sources will have a sense of the debate to its full extent.

I would think that the most profound benefit of learning about Heyting algebras
comes from recognizing where they are *appropriately* applied for a given topic.

:-)

mitch



0
mitchs (45)
2/9/2004 9:31:43 PM
"Fred Mailhot" wrote:
: "Jacques Guy" wrote:
[...]
: > Found a definition at http://mathworld.wolfram.com/HeytingAlgebra.html
:
: Ah...I didn't think to check MathWorld, oddly enough (clearly that's to my
: benefit)...but I did do Wikipedia...
:
: [snip]
:
: > Looked at http://en.wikipedia.org/wiki/Heyting_algebra
: >
: > Same stuff.
:
: I think I got a bit further than that...as near as I can tell (and
: presumably galathea, with her dazzlingly concise rhetoric, will fail to
let
: me know if I'm right or not), a Heyting algebra is just a boolean algebra
: (lattice w/ top & bottom) w/o "excluded middle" as an axiom...

That is very much the case, with some minor details about expressing the
logical axioms correctly so as not to force bivalence some other way or not
ending up with some other system (there are other, more "wild" logics
without excluded middle).  In constructive interpretations, that middle can
be associated to states of knowledge where the veracity or modality of a
sentence is not known or known in some still evaluating way (and can be
applied to probabilities or similar mathematical structures).  And there are
many specific Heyting algebras where this middle will not evaluate to true
or false for any state on certain sentences.

(I've also been told that my rhetoric is neither dazzling nor concise, which
makes it very difficult for me to gauge how to structure my responses.)

: Now we can all chime in and tell galathea how our research bears just on
the
: issues she claims are important in the context of educational reform.

I hope so!

=)

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/9/2004 9:41:28 PM
galathaea wrote:
> 
> "Peter T. Daniels" wrote:
> : Thank you, but I'm personally acquainted with Hal Fleming. A very nice
> : guy, with some very unsupported notions.
> 
> So, in one post you deny that anyone at all has had the idea, and you follow
> up with saying you know the guy I mention who has?

I do not know what _specific_ proposal of Hal Fleming's you may be
referring to; he has rarely published anything at all. I do know that he
has some very unsupported notions.

> And there is certainly support for the notion that many languages of the
> Americas derive from a language or languages of Asia.  Its the genetic
> information which shows that many peoples of the Americas and certain Asian
> peoples likely share a common ancestry, and that such a divergence likely
> occurred long after human symbolics had been established.  There are tool
> correlations.

Genetic information tells you NOTHING about language relationships.

> : > There is even work that details the taxonomy.  Start with "Finding families:
> : > quantitative methods in language classification" by April and Robert
> : > McMahon.  They even discuss the links I mention as one of those
> : > controversies that could have evidence from mathematical models.
> :
> : You offer an article name without the slightest hint of how to find it?
> : And you claim to write clearly??
> 
> Here's a hint on how to find it:
> 
> There is this great new technology out there known as "journal databases".
> They allow me to save typing by giving the information of the author's name
> and article title, and you can use that information at your local university
> library to find the article.  You can even pick up the article in the same
> visit.  Some databases even offer the article, and if you get a yearly
> account with your local university library (or work at one of the schools or
> study there), you can search and retrieve from home.  Then, the information
> I offered actually saves both of us time.
> 
> However, if you do not have access to such technology, try the April 2003
> copy of "Transactions of the Philological Society", Volume 101, Issue 1,
> Pages 7 to 55.

I do not have access to such technology, and the only library I have
access to that probably holds that journal (NYPL) charges 25c per page
for photocopying.

> --
> -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
> 
> galathaea: prankster, fablist, magician, liar

-- 
Peter T. Daniels                       grammatim@att.net
0
grammatim (38)
2/9/2004 10:05:39 PM
galathaea wrote:
> 
> "Richard Herring" wrote:
> : galathaea writes:
> : >Why do you believe physicists "aren't too happy" to discuss
> : >quantum logic or the logic of evolving causal sets?
> :
> : I don't, and I recognise a strawman argument when I see it.  I'm talking
> : about this oddly crossposted thread, which is neither of the things you
> : mention.
> :
> : >Do you believe the "functional-computer-language people" don't like to
> : >discuss the lambda calculus, or that the Curry-Howard isomorphism
> bewilders
> : >them?
> :
> : Likewise.
> 
> My "argument" was not meant to be a straw man, but I do realise that this
> thread did not develop the way I had hoped.  I was hoping that various
> professionals from various communities could get together and talk about how
> Heyting algebras underly many topics in their various fields.  I was hoping
> that I could stimulate discussion as to the importance of the logics such
> algebras represent, and perhaps look to building some kind of consensus as
> to the need for education in the area.  I hoped people would share
> experiences of how understanding these structures has helped them make
> better progress, or prevented certain incorrect conclusions, or anything
> like that as they have progressed through their careers.
> 
> So I had hoped that physicists would mention von Neumann and Birkhoff's
> quantum logic, or the beautiful work of Fotini Markopoulou-Kalamara and her
> papers on causal sets.  I had hoped that computer scientists would mention
> the lambda calculus.  I had hoped mathematicians would mention how they
> respect constructive proofs.

So since you expected nothing of linguistics, you concede that your
approach is not relevant to natural language, which, being a product of
the vagaries of evolution, need not involve any sort of logic at all?

> But instead I got a bunch of bs and alpha posturing from people who wouldn't
> even read past the vision research section.
> 
> So I agree, this thread is not yet any of those things.  It has a few
> constructive discussions starting, and maybe others will start more or maybe
> it will die out.  But for the most part, this thread is full of sound and
> fury, signifying little.

> galathaea: prankster, fablist, magician, liar

At least she's clear about herself.
-- 
Peter T. Daniels                       grammatim@att.net
0
grammatim (38)
2/9/2004 10:08:07 PM
Jacques Guy wrote:
> 
> galathaea wrote:
> 
> > And that is the whole point of post.  To ask professionals to share any
> > thoughts on Heyting algebras in the foundations of their profession and
> > perhaps discuss broadening education on the topic.
> 
> So I did a search for "Heyting algebra" (no idea what the bloody
> thing is).

If I were going to bother to try to find out, I might start by looking
for a biography of Heyting, perhaps in an encyclopedia of mathematics.

> Found a definition at http://mathworld.wolfram.com/HeytingAlgebra.html
> 
> "An algebra which is a special case of a logos."
> 
> Looked up "logos":
> 
> "A generalization of a Heyting algebra which replaces Boolean
> algebra in "intuitionistic" logic."
> 
> Lovely. So far, I have found out that a Heyting algebra
> was a special case of a generalization of a Heyting
> algebra. I know Boolean algebra, I know what logic is,
> but I have no idea what quote-intuitionistic-unquote
> means. Terrific.
> 
> Looked at http://en.wikipedia.org/wiki/Heyting_algebra
> 
> Same stuff.
> 
> Not one single straight example, like, you know,
> "two eggs added to three eggs make five eggs. Now
> look: three eggs and two eggs also add up to five
> eggs. The order doesn't matter. That's what we mean
> by [piece of jargon].
> 
> Oh, sure there is a link "examples" in the Wikipedia.
> So you click on it, and what to you get?
> 
> Examples
> 
> Every topology provides a complete Heyting algebra in form
> of its open set lattice. In this case, the element A&rArr;B
> is the interior of Ac&cup;B, where Ac denotes the complement
> of the open set A. Not all complete Heyting algebras are of
> this form. These issues are studied in pointless topology,
> where complete Heyting algebras are also called frames or
> locales.
> 
> At that stage it became topological for me to continue.

Do you suppose practitioners of "pointless topology" even notice the
inconcinnity?

> You want to "ask professionals to share any thoughts on
> Heyting algebras in the foundations of their profession"
> you make clear what you're talking about first. (And I
> have no idea either what the "foundation of my profession"
> could possibly mean. Lovely words, though. They do
> sound grand.)
> 
> Ce qui se con�oit clairement s'exprime clairement.
-- 
Peter T. Daniels                       grammatim@att.net
0
grammatim (38)
2/9/2004 10:14:29 PM
"galathaea" <galathaea@excite.com> wrote in message
news:102dsgj3m2smgb6@corp.supernews.com...
> "Franz Heymann" wrote:
> : There is no such thing as quantum logic.  Full stop.  I did not think it
> : necessary to state such an obvious fact, but since you insist.........
>
> Since you dind't read about it, it must be false?
>
> You know that your attitude is why the James Harrises and Matthew Ormans
of
> the world don't listen, even when their errors are explicitly pointed out,
> don't you?  Do you understand that your inability to learn new topics and
> your disdain of important areas of human knowledge is what provides the
> "cranks" of the world the mental justification they need to keep coming
> back?
>
> Do you believe von Neumann was a nut case?  Birkhoff?  Or are those two
> names you never needed in your long, fruitful career?

Neither of them was a physicist.  The nearest von Neumann came to physics
was when he produced his proof that Quantum Mechanics does not allow the
existence of hidden veriables to remove the limitations imposed by the
statistical nature of its predictions.  He has been shown to be wrong in
that, insofar as Bohm and Hiley have produced a deterministic interpretation
of QM, and have explicitly shown what the hiden variable is which allows
this interpretation.

> There are numerous books dedicated to the logic of propositions on the
> Hilbert spaces of quantum systems.

Nonsense.  There is only one set of rules for conducting a logical argument,
namely the set propounded ny Aristotle.  Those are indeed the rules used in
using vectors in Hilbert space to make predictions of the behaviour of
quantum systems.

>  Studying them allows one to make
> consistent statements in quantum mechanics,

Studying what? A new fancy logic, or the use of vectors in Hilbert space?
I taught quantum mechanics for many years.  Inter alia I, of course,
introduced the students to the representation of the state of a system by a
vector in Hilbert space, but I have never had to use any fancy logic or
fancy footwork to do so.  The mathematiics involved was no more than the
stuff a second year maths student has behind his/her blades.

> avoiding all that garbage about
> quantum mechanics being "strange" or "impossible to understand".

I am not aware of encountering attitides exemplified by "all that
garbage........." at any time in my teaching or research career, and my
students were often more adept at doing QM calculations than classical
mechanics calculations.  Statistical physics in fact is a damn sight easier
when approached from the QM viepoint than by starting with classical
mechanics.

>  Its a
> scientific subject, discussed by scientists.  But I guess not cranky old
men
> who like to pretend they are scientists by avoiding rational discussion at
> all costs.

Yes you are right.  Are you perhaps such a cranky old person, or are you
just another dilletante when it comes to mechanics, of either the classical
or quantum kind?

Franz


0
2/9/2004 11:06:48 PM
"Peter T. Daniels" <grammatim@worldnet.att.net> wrote in message
news:4026E441.75E6@worldnet.att.net...

[snip]

> Tell us again why this squabbling is being posted to sci.lang?

And indeed why it is being posted to sci.physics.

Franz


0
2/9/2004 11:06:49 PM
"Jerzy Karczmarczuk" <karczma@info.unicaen.fr> wrote in message
news:40275440.8080304@info.unicaen.fr...
> Franz Heymann wrote:
>
> >
> > My education served me magnificently through a long and successful
career.
> >
> > Franz
>
> Would you mind, Sir, if I suggested politely that you continue it outside
> our newsgroups?

I have no career to continue.
And woould you, Sir, kindly ;earn not to snip context.

Some twerp, from I know not which group, has spammed this all over usenet,
including sci.physics, where I normally participate.  I  wish these
interlopers would get the hell out of here and restrict themselves to
whichever miserable gewsgroups they belong.

Franz


0
2/9/2004 11:06:53 PM
"Peter T. Daniels" <grammatim@worldnet.att.net> wrote in message
news:402780E2.5B33@worldnet.att.net...
> galathaea wrote:
> >
> > "Franz Heymann" wrote:
> > : There is no such thing as quantum logic.  Full stop.  I did not think
it
> > : necessary to state such an obvious fact, but since you insist.........
> >
> > Since you dind't read about it, it must be false?
> >
> > You know that your attitude is why the James Harrises and Matthew Ormans
of
> > the world don't listen, even when their errors are explicitly pointed
out,
> > don't you?  Do you understand that your inability to learn new topics
and
> > your disdain of important areas of human knowledge is what provides the
> > "cranks" of the world the mental justification they need to keep coming
> > back?
> >
> > Do you believe von Neumann was a nut case?  Birkhoff?  Or are those two
> > names you never needed in your long, fruitful career?
> >
> > There are numerous books dedicated to the logic of propositions on the
> > Hilbert spaces of quantum systems.  Studying them allows one to make
> > consistent statements in quantum mechanics, avoiding all that garbage
about
> > quantum mechanics being "strange" or "impossible to understand".  Its a
> > scientific subject, discussed by scientists.  But I guess not cranky old
men
> > who like to pretend they are scientists by avoiding rational discussion
at
> > all costs.
>
> Again, is there a reason this squabbling is being posted to sci.lang?

And what the hell is it doing in sci.physics?  I am squabbling to get the
perpetrator to address follow-ups only to the newsgroup in which he/she
participates, instead of spewing it over half of usenet.

> > galathaea: prankster, fablist, magician, liar
>
> Yep.
> -- 
> Peter T. Daniels

Franz

Franz


0
2/9/2004 11:06:54 PM
"galathaea" <galathaea@excite.com> wrote in message
news:102eco1363o020a@corp.supernews.com...

> In case you didn't notice, my post concerning the use of metrics to
develop
> language phylogenies was about developing such relationships as found in
> dialect chains all the way up to larger group relationships.

Mere word salad.

>  I do  understand what I talk about more than the level of a three year
old

Who do you think you are kidding?

Franz


0
2/9/2004 11:06:55 PM
"galathaea" <galathaea@excite.com> wrote in message
news:102f9qnfgv3u5b2@corp.supernews.com...
> "Richard Herring" wrote:
> : I think (I _hope_) you mean the philosophers or the psychologists. We
> : physicists aren't too happy about the cross-posting to sci.physics, and
> : I doubt if the functional-computer-langugage people are much less
> : bewildered.
>
> Why do you believe physicists "aren't too happy" to discuss quantum logic
or
> the logic of evolving causal sets?

Because, not to put too fine a point on it, you are emitting nothing but
crap.
Please get the hell out of sci.physics and redirect your miserable nonsense
elsewhere.

[snip]

> galathaea: prankster, fablist, magician, liar

Yes.

Franz


0
2/9/2004 11:06:56 PM
"Richard Herring" <junk@[127.0.0.1]> wrote in message
news:mcppO8Hi86JAFwWN@baesystems.com...
> In message <102f9qnfgv3u5b2@corp.supernews.com>, galathaea
> <galathaea@excite.com> writes
> >"Richard Herring" wrote:
> >: I think (I _hope_) you mean the philosophers or the psychologists. We
> >: physicists aren't too happy about the cross-posting to sci.physics, and
> >: I doubt if the functional-computer-langugage people are much less
> >: bewildered.
> >
> >Why do you believe physicists "aren't too happy" to discuss quantum logic
or
> >the logic of evolving causal sets?
>
> I don't, and I recognise a strawman argument when I see it.  I'm talking
> about this oddly crossposted thread, which is neither of the things you
> mention.
>
> >Do you believe the "functional-computer-language people" don't like to
> >discuss the lambda calculus, or that the Curry-Howard isomorphism
bewilders
> >them?
> >
> Likewise.

Richard, I fail to see why you are being polite to these interlopers.  There
are newsgroups where their inane word spinning and semantically based
nonsense might be discussed in greater comfort than in sci.physics, but they
appear to be too dumb to realise that.

Franz


0
2/9/2004 11:06:56 PM
"galathaea" <galathaea@excite.com> wrote in message
news:102fg0klm43u6a2@corp.supernews.com...
> "Richard Herring" wrote:
> : galathaea writes:
> : >Why do you believe physicists "aren't too happy" to discuss
> : >quantum logic or the logic of evolving causal sets?
> :
> : I don't, and I recognise a strawman argument when I see it.  I'm talking
> : about this oddly crossposted thread, which is neither of the things you
> : mention.
> :
> : >Do you believe the "functional-computer-language people" don't like to
> : >discuss the lambda calculus, or that the Curry-Howard isomorphism
> bewilders
> : >them?
> :
> : Likewise.
>
> My "argument" was not meant to be a straw man, but I do realise that this
> thread did not develop the way I had hoped.

Then you are devoid of common sense.  You may retrieve your position to some
extent by redirecting the thread to wherever you post from , and there ony,
every time you observe a note in sci.physics.
If you will tell me which is your home ng, I will start the redirection to
there, and there only when I notice contributions in sci'physics.

Crossposting to more than two ng's is a grossly annoying and puerile habit
which should be subject to a jail sentence.

Franz


0
2/9/2004 11:06:57 PM
"Jacques Guy" <jguy@alphalink.com.au> wrote in message
news:4028DB0D.7701@alphalink.com.au...
> galathaea wrote:
>
> > And that is the whole point of post.  To ask professionals to share any
> > thoughts on Heyting algebras in the foundations of their profession and
> > perhaps discuss broadening education on the topic.
>
> So I did a search for "Heyting algebra" (no idea what the bloody
> thing is).
>
> Found a definition at http://mathworld.wolfram.com/HeytingAlgebra.html
>
> "An algebra which is a special case of a logos."
>
> Looked up "logos":
>
> "A generalization of a Heyting algebra which replaces Boolean
> algebra in "intuitionistic" logic."
>
> Lovely. So far, I have found out that a Heyting algebra
> was a special case of a generalization of a Heyting
> algebra. I know Boolean algebra, I know what logic is,
> but I have no idea what quote-intuitionistic-unquote
> means. Terrific.

As soon as you encounter any word ending in "-ism" or "-istic" you may
safely assume that there are kooks around, and you may drop the subject
without any loss.

[snip]

Franz


0
2/9/2004 11:06:58 PM
On 2/10/04 5:22 AM, "Jacques Guy" <jguy@alphalink.com.au> wrote:

> galathaea wrote:
> 
>> And that is the whole point of post.  To ask professionals to share any
>> thoughts on Heyting algebras in the foundations of their profession and
>> perhaps discuss broadening education on the topic.
> 
> So I did a search for "Heyting algebra" (no idea what the bloody
> thing is).
> 
> Found a definition at http://mathworld.wolfram.com/HeytingAlgebra.html

Ah...I didn't think to check MathWorld, oddly enough (clearly that's to my
benefit)...but I did do Wikipedia...

[snip]

> Looked at http://en.wikipedia.org/wiki/Heyting_algebra
> 
> Same stuff. 

I think I got a bit further than that...as near as I can tell (and
presumably galathea, with her dazzlingly concise rhetoric, will fail to let
me know if I'm right or not), a Heyting algebra is just a boolean algebra
(lattice w/ top & bottom) w/o "excluded middle" as an axiom...


Now we can all chime in and tell galathea how our research bears just on the
issues she claims are important in the context of educational reform.


:-|



Fred.

0
2/9/2004 11:09:29 PM

"Peter T. Daniels" wrote:

>
> Do you suppose practitioners of "pointless topology" even notice the
> inconcinnity?
>

Fancy word.  :-)

Another name for pointless topology is mereology--the theory of parts and
wholes.  Now a quick Google search turns up the following fragment...

-----
At 7:19 PM -0500 9/24/96, Stephen C. Carlson wrote:
>I looked this up in my Webster's Ninth New Collegiate:
>
>inconcinnity (ca. 1616): lack of suitability or congruity : INELEGENCE
>
>Its antonym's definition seems more useful:
>
>concinnity (1531): harmony or elegance of design esp. of literary style
> in adaptation of parts to a whole or to each other


I've seen the term used to describe a feature of Thucydides' style whereby
a parallelism is maintained with deliberate violation of perfect balance.
-----


I am certain that you have a technically precise usage, but Webster's Ninth
will suffice for an example of general usage I think.

At the Stanford Encyclopedia page,

 http://plato.stanford.edu/entries/mathematics-inconsistent/

you will find somethiing along the lines of

"Duality between incompleteness/intuitionism and
inconsistency/paraconsistency has at least two aspects.
First there is the above topological (open/closed) duality.
Second there is Routley * duality. Discovered by the
Routleys (1972) as a semantical tool for relevant logics,
the * operation dualises between inconsistent and incomplete
theories of the large natural class of de Morgan logics. Both
kinds of duality interact as well, where the * gives distinctive
duality and invariance theorems for open set and closed set
arithmetical theories. On the basis of these results, it is fair to
argue that both kinds of mathematics, intuitionist and
paraconsistent, are equally reasonable."



So, we have established all sorts of parallelisms....


Then we can also find the passage,

"...specifying a topological space by its closed sets is every
bit as reasonable as specifying it by its open sets. Yet the
logic of closed sets is known to be paraconsistent, ie. supports
inconsistent theories;"

which should be interpreted as a violation of "perfect balance."




Who can say what practitioners of pointless topology notice?

:-)

mitch



0
mitchs (45)
2/10/2004 12:40:35 AM
"Franz Heymann" wrote:
: "galathaea" wrote:
: > Do you believe von Neumann was a nut case?  Birkhoff?  Or are those two
: > names you never needed in your long, fruitful career?
:
: Neither of them was a physicist.  The nearest von Neumann came to physics
: was when he produced his proof that Quantum Mechanics does not allow the
: existence of hidden veriables to remove the limitations imposed by the
: statistical nature of its predictions.  He has been shown to be wrong in
: that, insofar as Bohm and Hiley have produced a deterministic
interpretation
: of QM, and have explicitly shown what the hiden variable is which allows
: this interpretation.

Well, if you discount his work on finalising the formulation of quantum
mechanics in terms of operator theory over Hilbert spaces (sometimes called
the von Neumann interpretation or the Dirac-von Neumann interpretation and a
common non-committal approach found in many texts), ignore his work on
ergodic theory, forget about his contributions to shock waves and
hydrodynamics, then you're pretty much right.

I have even commented many times about the mistakes in von Neumann's "no-go
theorem", and even mentioned realist interpretations in my original post.
You probably "missed" that...

: > There are numerous books dedicated to the logic of propositions on the
: > Hilbert spaces of quantum systems.
:
: Nonsense.  There is only one set of rules for conducting a logical
argument,
: namely the set propounded ny Aristotle.  Those are indeed the rules used
in
: using vectors in Hilbert space to make predictions of the behaviour of
: quantum systems.

Let's drop the term "logic".

Start with a Hilbert space H and a borel set B in H and an operator A.  All
quite common stuff.  Take the projection-valued measure P_A(B) as the
spectral projection associated with A over B.  This is all standard quantum
mechanics, and nothing controversial because we haven't "said" anything but
some mathematical constructions.  In fact, you can take the collection of
all projections P(H) over the Hilbert space, which has the structure of a
lattice, and any state determines a probability measure on this collection.
Given two different projections, their meet and their join is defined, and
with a complementation defined by the rules of quantum mechanics, we have
the mathematical structure of an algebra.  Its very similar to a Boolean
algebra except that noncommutativity gives it a slightly different
structure.

That's all there is to it.  That algebra happens to be a Heyting algebra,
but you don't have to worry about semantical analysis.  The mathematical
statement that only closed linear subspaces of Hilbert spaces are associated
with observables is as innocuous as Bohmian mechanics being merely a
mathematical use of the polar decomposition theorem.  I'm just talking about
an abstract algebra here, who's structure is used in quantum calculations.

And all I've been asking is whether others were finding that particular
mathematical structure in their fields.  But instead I get these anger
management cases, such as yourself Franz, who spam their own newsgroups with
a bunch of junk, displaying to anyone following their problematic
psychologies, their avoidance reactions and anger.  I get this crap where
the guys posting the most nonsense, the largest number of posts with
absolutely no content, complaining that somehow it is I spamming "their"
newsgroups.  Even though I have in the past posted to many of these
newsgroups, and have read all of them over some time, I get teritoriality
and lack of content, spamming post after spamming post, from those who in
the same breath accuse me of just those things.

The funny thing is, it won't stop _my_ posts.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/10/2004 3:04:13 AM
"Greg Lee" wrote:
: This "logical approach to language" is another problem for me.  What
little
: I know suggests to me that the logic of English, at least, is classical.
: E.g., DeMorgan's laws work, but they don't hold in intuitionist logic.
: I don't know what Heyting algebras are, but I gather from this discussion
: that they are weakened sorts of Boolean algebra, as intuitionist logic
: is a weakened sort of classical logic.  If that is roughly so, and if
: the logic of natural language is classical, wouldn't you expect to "have
: Heyting algebras in prominence"?  In other words, I don't see how finding
: some reason for using Heyting algebra to describe human language is any
: reason to believe that the logic of language is non-classical, nor any
: reason to bother with Heyting algebras, for that matter.

I've mentioned modal logics in a seperate leaf.  Not all topics of things we
talk about are described by classical logics.  There are many different
logics, with various sorts of implication.  Not all things we talk about can
even be framed in a classical style.  The study of necessity, possibility,
etc. in language leads one to many different logics.  Some are directly
represented by Heyting algebras, and many, if not all, of the rest can be
modeled in a Heyting model.

So its there for analysis of natural language, and both I and mitch have
posted references to such research.  But there is also the inference problem
of past linguistic relationships, and I have posted references to work that
shows the appearance of Heyting structures in such an analysis.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/10/2004 3:27:56 AM
galathaea  escribi� (Mon, 9 Feb 2004 12:27:32 -0800):

    galathaea> And this structure  is found all over the  place in the
    galathaea> sciences.   In  natural  language,  for  example,  much
    galathaea> communication is done in modalities where Boolean logic
    galathaea> is not  an appropriate  model.  Its found  in reasoning
    galathaea> about  the way we  model our  reality, or  in dynamical
    galathaea> systems,  or in  all  of  the topics  I  mention in  my
    galathaea> original  post.   All   of  those  things  are  Heyting
    galathaea> algebras.  All of the  things I have been talking about
    galathaea> in followups  are as well Heyting.  Not  all logics are
    galathaea> Heyting  represented  directly, but  then  the work  on
    galathaea> computability  shows  that  it  is likely  those  other
    galathaea> logics have no more modeling capability than that found
    galathaea> in  the  lambda calculus,  so  there  is  some kind  of
    galathaea> universality possible here.

I  don't know  if I  fully understood...   Are you  stating  here that
Heyting  algebras could represent  logics which  go beyond  the Turing
computability  (go  beyond   lambda  calculus)?   For  example,  brain
computability  is not  Turing equivalent,  as far  as I  know, because
brain computability is not algorithmic...
-- 
Sergio Roa Ovalle
Key fingerprint = 5427 E535 8E18 8B3B C38B  ADB5 9DF5 89DE FBF4 738C
0
s.roa (6)
2/10/2004 3:48:01 AM

Jacques Guy wrote:

> galathaea wrote:
>
> > The formal definition is the most accurate I can think of, but if you do not
> > already understand the relationship between logics and lattices, it can be
> > confusing.
>
> In my profession, a lattice is a thingie in the garden on which vines
> grow. In my wife's profession too. In my father's too (except that he
> called it "treillis"). In fact, in most people's professions it is
> that.
>

Either that or something that looks like salt.  :-)


>
> > Basically, the logical structure represented by Heyting algebras can be
> > interpreted as having a temporal structure.  "Truth" and "falsity" do not
> > apply in an absolute sense, as they do classically, but instead apply only
> > at certain times.  This is where the ideas of constructivism arise, that
> > there is no truth or falsity except what has been arrived at through a
> > process.  We construct our notions of truth.  Each moment of time is
> > associated with a particular state of knowledge, and sentences are evaluated
> > relative to a state of knowledge.
>
> �a va d�j� mieux!
>
> > Truth has a persistence property that
> > once a sentence is true for a particular state, it is true for all later
> > states as well.
>
> That is *weird*. Weird, but nice: I always wanted to be thirty again.
> So, having been thirty years old in a particular state of my life,
> I remain thirty until death do us part? Nice, but weird. Doesn't
> agree with the state of my waistline, nor of my eyesight either.
> So..., I'm not a Heyting algebra :-(
>

lol



>
> > This temporal ordering, in the general case, is only what is known as a
> > partial order and is not necessarily linear (though it can be).  This is why
> > such logics can also model possibility and certain forms of
> > counterfactuality.
>
> Why didn't you make that clear in the first place? No need for
> lattices either (your kind, whatever it is, not mine). It's clear
> enough like that.
>
> To me that reads like Prolog without a cut statement (which was a
> kludge in the first place). Bon, ben j'ai pig�. Apart from the
> persistence property of truth, of which I cannot make head or tail.
> It contradicts all my experience, even professional.

Everyone gets such nicely crafted tools these days.  But, one might ask whether
the history of the kludges is important.

The "lattice thingy" comes into this from dealing with historical decisions such
as that by Boole when he wrote

"The above sign, _is_ or _are_, may be expressed
by the symbol =."

                            --George Boole, "The Laws of Thought"

combined with Frege working from a different tradition.  He grounded his ontology
of Number with statements like

"The relationship of equality does not hold only amongst
numbers.  From this it seems to follow that it ought not to
be defined specially for this case.  One would think that
the concept of equality would already have been fixed,
from which, together with the concept of Number, it must
then follow when Numbers are equal to one another,
without requiring any further, special defintion."

                            --Gottlob Frege, "Foundations of Arithmetic"


The philosophical logicians have a number of justifications with regard to which I
am not qualified to speak.  However, absent any explicit need for a philosophy of
transfinite numbers and higher order logics, one may look at Goedel's completeness
theorem (in Enderton, for example) to see that part of it depends on the notion of
a congruence relation.  If one reads "Foundations of Arithmetic" it is clear that
this is precisely the kind of thing Frege is thinking about in his own statements.

As things turned out, the "simpler" mathematics for this was worked out later in
lattice theory.  The classic presentation -- aptly titled "Lattice Theory" -- is
by Garrett Birkhoff.  Given some fixed set, the various ways of partitioning the
set into equivalence relations can be organized as a directed graph that also
satisfies certain lattice axioms.  What you get is a lattice of equivalence
relations.  Moreover, we have that every congruence relation is an equivalence
relation; but not every equivalence relation is a congruence relation.  So, you
have two kinds of "equals" in that they are accounted for differently.

The lattice of equivalence relations is primary by virtue of the fact that every
congruence relation is an equivalence relation.  But, the lattice of equivalence
relations is "nonmodular" and "geometric."  In contrast, the congruence relations
among those equivalence relations form their own lattice.  That lattice, called
the structure lattice, is "modular" and "Brouwerian."

So, the appearance of Heyting algebras in so many contexts arises from deeply
buried assumptions that are simply not presented.  We all take the equals sign for
granted.

:-)

mitch



0
mitchs (45)
2/10/2004 8:20:54 AM
In message <c093qg$nti$17@sparta.btinternet.com>, Franz Heymann 
<notfranz.heymann@btopenworld.com> writes
>
>"Richard Herring" <junk@[127.0.0.1]> wrote in message
>news:mcppO8Hi86JAFwWN@baesystems.com...
>> In message <102f9qnfgv3u5b2@corp.supernews.com>, galathaea
>> <galathaea@excite.com> writes
>> >"Richard Herring" wrote:
>> >: I think (I _hope_) you mean the philosophers or the psychologists. We
>> >: physicists aren't too happy about the cross-posting to sci.physics, and
>> >: I doubt if the functional-computer-langugage people are much less
>> >: bewildered.
>> >
>> >Why do you believe physicists "aren't too happy" to discuss quantum logic
>or
>> >the logic of evolving causal sets?
>>
>> I don't, and I recognise a strawman argument when I see it.  I'm talking
>> about this oddly crossposted thread, which is neither of the things you
>> mention.
>>
>> >Do you believe the "functional-computer-language people" don't like to
>> >discuss the lambda calculus, or that the Curry-Howard isomorphism
>bewilders
>> >them?
>> >
>> Likewise.
>
>Richard, I fail to see why you are being polite to these interlopers.

There are ways of being politely rude, and there are other ways (where's 
Uncle Al when you want him?)  In a former existence one of my functions 
was to deflate a pompous committee chairman before he got into full 
swing. It's a delicate art which requires continuous practice.

> There
>are newsgroups where their inane word spinning and semantically based
>nonsense might be discussed in greater comfort than in sci.physics, but they
>appear to be too dumb to realise that.

Any suggestions? ;-)

-- 
Richard Herring
0
Richard
2/10/2004 10:28:34 AM
"galathaea" <galathaea@excite.com> wrote in message
news:102gihct8rgimcf@corp.supernews.com...
> "Franz Heymann" wrote:
> : "galathaea" wrote:
> : > Do you believe von Neumann was a nut case?  Birkhoff?  Or are those
two
> : > names you never needed in your long, fruitful career?
> :
> : Neither of them was a physicist.  The nearest von Neumann came to
physics
> : was when he produced his proof that Quantum Mechanics does not allow the
> : existence of hidden veriables to remove the limitations imposed by the
> : statistical nature of its predictions.  He has been shown to be wrong in
> : that, insofar as Bohm and Hiley have produced a deterministic
> interpretation
> : of QM, and have explicitly shown what the hiden variable is which allows
> : this interpretation.
>
> Well, if you discount his work on finalising the formulation of quantum
> mechanics in terms of operator theory over Hilbert spaces (sometimes
called
> the von Neumann interpretation or the Dirac-von Neumann interpretation

Dirac beat van Neumann to the try line..

> and a
> common non-committal approach found in many texts), ignore his work on
> ergodic theory, forget about his contributions to shock waves and
> hydrodynamics, then you're pretty much right.

Von Neumann was a mathematician.

> I have even commented many times about the mistakes in von Neumann's
"no-go
> theorem", and even mentioned realist interpretations in my original post.
> You probably "missed" that...

Yes.  I try to avoid reading what you write.

> : > There are numerous books dedicated to the logic of propositions on the
> : > Hilbert spaces of quantum systems.

The logic involved is ordinary Aristotelean logig.

> : Nonsense.  There is only one set of rules for conducting a logical
> argument,
> : namely the set propounded ny Aristotle.  Those are indeed the rules used
> in
> : using vectors in Hilbert space to make predictions of the behaviour of
> : quantum systems.
>
> Let's drop the term "logic".

Hear hear..
>
> Start with a Hilbert space H and a borel set B in H and an operator A.
All
> quite common stuff.  Take the projection-valued measure P_A(B) as the
> spectral projection associated with A over B.  This is all standard
quantum
> mechanics, and nothing controversial because we haven't "said" anything
but
> some mathematical constructions.  In fact, you can take the collection of
> all projections P(H) over the Hilbert space, which has the structure of a
> lattice, and any state determines a probability measure on this
collection.
> Given two different projections, their meet and their join is defined, and
> with a complementation defined by the rules of quantum mechanics, we have
> the mathematical structure of an algebra.  Its very similar to a Boolean
> algebra except that noncommutativity gives it a slightly different
> structure.

Qiut bragging and preaching to the converted about your knowledge of the
background to the use of Hilbert space in quantum mechanics.
>
> That's all there is to it.  That algebra happens to be a Heyting algebra,

I don't care what you wish to call it.  It sounds as if you are telling me
that I have been using prose all my life without knowing.

> but you don't have to worry about semantical analysis.  The mathematical
> statement that only closed linear subspaces of Hilbert spaces are
associated
> with observables is as innocuous as Bohmian mechanics being merely a
> mathematical use of the polar decomposition theorem.  I'm just talking
about
> an abstract algebra here, who's structure is used in quantum calculations.

Stop bullshitting.  It smells.
>
> And all I've been asking is whether others were finding that particular
> mathematical structure in their fields.  But instead I get these anger
> management cases, such as yourself Franz,

Yes.  My anger will abate when you move this spammed thread to your own
newsgroup and leave the others in peace.

> who spam their own newsgroups with
> a bunch of junk,

I do not ever initiate crossposts and I am throwing around junk in this
thread to get you to move it out of sci.physics.  YOU started this infantile
crossposting.  Now YOU get rid of it.

> displaying to anyone following their problematic
> psychologies, their avoidance reactions and anger.  I get this crap where
> the guys posting the most nonsense, the largest number of posts with
> absolutely no content, complaining that somehow it is I spamming "their"
> newsgroups.  Even though I have in the past posted to many of these
> newsgroups, and have read all of them over some time, I get teritoriality
> and lack of content, spamming post after spamming post, from those who in
> the same breath accuse me of just those things.
>
> The funny thing is, it won't stop _my_ posts.

No.  I had noticed that much earlier.

Goodbye, troll.

Franz


0
2/10/2004 11:19:16 AM
Franz Heymann wrote the following to
   alt.philosophy, comp.lang.functional, sci.lang, sci.physics and
   sci.psychology.theory :

[... irrelevant text removed ]

> Stop bullshitting.  It smells.

 > ... My anger will abate when you move this spammed thread to your own
> newsgroup and leave the others in peace.
> 
> 
>>who spam their own newsgroups with
>>a bunch of junk,
> 
> 
> I do not ever initiate crossposts and I am throwing around junk in this
> thread to get you to move it out of sci.physics.  YOU started this infantile
> crossposting.  Now YOU get rid of it.
[...]


> 
> Goodbye, troll.
> 
> Franz


I admit that learning from mister Heymann that he had a brilliant and successful
career, I tried to track him on Internet. Unfortunately, I found only several
hundreds of his postings to different newsgroups and other lists.

And, what I find really remarkable, almost everything shows the same deep
intelligence, brilliant ideas, sympathy towards his conversation partners,
and in general the elegance of a true gentleman, as exemplified above.

Such nice people are rare today, and we should protect them. Please, dear
people, help mister Heymann! Don't make him angry, since he seems to be
very fragile, and, God forbids, he might have some heart attack. We know
already that because of all your nasty postings he has permanent gastric
problems, and this might be dangerous. We see already, looking at his
texts, that his hands are trembling. Yes, he needs help... Thank you.


Jerzy Karczmarczuk
who follows ONLY comp.lang.functional,
and who is very happy that such a profound genius and world-renowned
scholar rendered us his unforgettable visit. We didn't have anything
comparable for the last 10 years or more.




0
karczma (331)
2/10/2004 12:06:35 PM
galathaea wrote:
 
> And that is the whole point of post.  To ask professionals to share any
> thoughts on Heyting algebras in the foundations of their profession and
> perhaps discuss broadening education on the topic.

So I did a search for "Heyting algebra" (no idea what the bloody
thing is).

Found a definition at http://mathworld.wolfram.com/HeytingAlgebra.html

"An algebra which is a special case of a logos."

Looked up "logos":

"A generalization of a Heyting algebra which replaces Boolean 
algebra in "intuitionistic" logic."

Lovely. So far, I have found out that a Heyting algebra
was a special case of a generalization of a Heyting
algebra. I know Boolean algebra, I know what logic is,
but I have no idea what quote-intuitionistic-unquote 
means. Terrific.

Looked at http://en.wikipedia.org/wiki/Heyting_algebra

Same stuff. 

Not one single straight example, like, you know, 
"two eggs added to three eggs make five eggs. Now
look: three eggs and two eggs also add up to five 
eggs. The order doesn't matter. That's what we mean 
by [piece of jargon].

Oh, sure there is a link "examples" in the Wikipedia.
So you click on it, and what to you get?

Examples 

Every topology provides a complete Heyting algebra in form 
of its open set lattice. In this case, the element A&rArr;B 
is the interior of Ac&cup;B, where Ac denotes the complement 
of the open set A. Not all complete Heyting algebras are of 
this form. These issues are studied in pointless topology, 
where complete Heyting algebras are also called frames or 
locales.

At that stage it became topological for me to continue.

You want to "ask professionals to share any thoughts on 
Heyting algebras in the foundations of their profession"
you make clear what you're talking about first. (And I
have no idea either what the "foundation of my profession"
could possibly mean. Lovely words, though. They do
sound grand.)

Ce qui se con�oit clairement s'exprime clairement.
0
jguy (7)
2/10/2004 1:22:21 PM
In sci.lang galathaea <galathaea@excite.com> wrote:
> "Greg Lee" wrote:
> : This "logical approach to language" is another problem for me.  What
> little
> : I know suggests to me that the logic of English, at least, is classical.
> : E.g., DeMorgan's laws work, but they don't hold in intuitionist logic.
> : I don't know what Heyting algebras are, but I gather from this discussion
> : that they are weakened sorts of Boolean algebra, as intuitionist logic
> : is a weakened sort of classical logic.  If that is roughly so, and if
> : the logic of natural language is classical, wouldn't you expect to "have
> : Heyting algebras in prominence"?  In other words, I don't see how finding
> : some reason for using Heyting algebra to describe human language is any
> : reason to believe that the logic of language is non-classical, nor any
> : reason to bother with Heyting algebras, for that matter.

> I've mentioned modal logics in a seperate leaf.  Not all topics of things we
> talk about are described by classical logics.

A logic is for describing how we reason, not for describing "topics of things
we talk about".

> There are many different
> logics, with various sorts of implication.

That's very true.

>  Not all things we talk about can even be framed in a classical style.

That's debatable, but what is the relevance, anyway?  You seem to be
identifying logic with morphology.  Finding representations for
expressions of a natural language may or may not tell anything about
how people make inferences with these expressions.  You would make your
point here if you would just give an example of an argument given
in natural language the inferences in which are classically correct, but
which is actually incorrect, where an application of Heyting algebra
can somehow demonstrate the incorrectness.  Or an argument which is
actually correct, but which is not classical???y correct.

Just one example.

>  The study of necessity, possibility,
> etc. in language leads one to many different logics.

That's very true.  I don't always go where someone wants to lead me.
There would have to be evidence.  I know a little about the fundamentals
of modal logic.  I'm unaware of any serious attempt to show that any
of these logics can predict or even describe details of usage of "must",
"may", "should", ...  And in some cases, anyway, reasoning with modal
operators can be represented within classical logic, as when "possibly p"
is taken to be equivalent to "there exists a world in which p".

....
-- 
Greg Lee <greg@ling.lll.hawaii.edu>
0
greg1021 (22)
2/10/2004 1:55:45 PM
"Richard Herring" <junk@[127.0.0.1]> wrote in message
news:2tm9yrFSJLKAFw$z@baesystems.com...
> In message <c093qg$nti$17@sparta.btinternet.com>, Franz Heymann
> <notfranz.heymann@btopenworld.com> writes
> >
> >"Richard Herring" <junk@[127.0.0.1]> wrote in message
> >news:mcppO8Hi86JAFwWN@baesystems.com...
> >> In message <102f9qnfgv3u5b2@corp.supernews.com>, galathaea
> >> <galathaea@excite.com> writes
> >> >"Richard Herring" wrote:
> >> >: I think (I _hope_) you mean the philosophers or the psychologists.
We
> >> >: physicists aren't too happy about the cross-posting to sci.physics,
and
> >> >: I doubt if the functional-computer-langugage people are much less
> >> >: bewildered.
> >> >
> >> >Why do you believe physicists "aren't too happy" to discuss quantum
logic
> >or
> >> >the logic of evolving causal sets?
> >>
> >> I don't, and I recognise a strawman argument when I see it.  I'm
talking
> >> about this oddly crossposted thread, which is neither of the things you
> >> mention.
> >>
> >> >Do you believe the "functional-computer-language people" don't like to
> >> >discuss the lambda calculus, or that the Curry-Howard isomorphism
> >bewilders
> >> >them?
> >> >
> >> Likewise.
> >
> >Richard, I fail to see why you are being polite to these interlopers.
>
> There are ways of being politely rude, and there are other ways (where's
> Uncle Al when you want him?)  In a former existence one of my functions
> was to deflate a pompous committee chairman before he got into full
> swing. It's a delicate art which requires continuous practice.

Penny to a pound you fail in this instance.  {:-))

>
> > There
> >are newsgroups where their inane word spinning and semantically based
> >nonsense might be discussed in greater comfort than in sci.physics, but
they
> >appear to be too dumb to realise that.
>
> Any suggestions? ;-)

sci.lang, whatever that may mean.  {:-)

Franz


0
2/10/2004 2:29:31 PM
In message <c0apsa$ju4$1@sparta.btinternet.com>, Franz Heymann 
<notfranz.heymann@btopenworld.com> writes
>
>"Richard Herring" <junk@[127.0.0.1]> wrote in message
>news:2tm9yrFSJLKAFw$z@baesystems.com...
>> In message <c093qg$nti$17@sparta.btinternet.com>, Franz Heymann
>> <notfranz.heymann@btopenworld.com> writes
>> >
>> >"Richard Herring" <junk@[127.0.0.1]> wrote in message
>> >news:mcppO8Hi86JAFwWN@baesystems.com...
>> >> In message <102f9qnfgv3u5b2@corp.supernews.com>, galathaea
>> >> <galathaea@excite.com> writes
>> >> >"Richard Herring" wrote:
>> >> >: I think (I _hope_) you mean the philosophers or the psychologists.
>We
>> >> >: physicists aren't too happy about the cross-posting to sci.physics,
>and
>> >> >: I doubt if the functional-computer-langugage people are much less
>> >> >: bewildered.
>> >> >
>> >> >Why do you believe physicists "aren't too happy" to discuss quantum
>logic
>> >or
>> >> >the logic of evolving causal sets?
>> >>
>> >> I don't, and I recognise a strawman argument when I see it.  I'm
>talking
>> >> about this oddly crossposted thread, which is neither of the things you
>> >> mention.
>> >>
>> >> >Do you believe the "functional-computer-language people" don't like to
>> >> >discuss the lambda calculus, or that the Curry-Howard isomorphism
>> >bewilders
>> >> >them?
>> >> >
>> >> Likewise.
>> >
>> >Richard, I fail to see why you are being polite to these interlopers.
>>
>> There are ways of being politely rude, and there are other ways (where's
>> Uncle Al when you want him?)  In a former existence one of my functions
>> was to deflate a pompous committee chairman before he got into full
>> swing. It's a delicate art which requires continuous practice.
>
>Penny to a pound you fail in this instance.  {:-))
>
No takers.

>> > There
>> >are newsgroups where their inane word spinning and semantically based
>> >nonsense might be discussed in greater comfort than in sci.physics, but
>they
>> >appear to be too dumb to realise that.
>>
>> Any suggestions? ;-)
>
>sci.lang,

Speaking as a regular there too, no. Those who study language have no 
more patience than you with inane word spinning and semantically based 
knowledge. Or dumbness.

>whatever that may mean.  {:-)
>
<reaches for dictionary>
The ordered arrangement of ascertained knowledge about language, 
including the methods by which such knowledge is extended and the 
criteria by which its truth are tested?

-- 
Richard Herring
0
Richard
2/10/2004 3:02:20 PM
galathaea wrote:

> The formal definition is the most accurate I can think of, but if you do not
> already understand the relationship between logics and lattices, it can be
> confusing.

In my profession, a lattice is a thingie in the garden on which vines
grow. In my wife's profession too. In my father's too (except that he
called it "treillis"). In fact, in most people's professions it is
that.
 
> Basically, the logical structure represented by Heyting algebras can be
> interpreted as having a temporal structure.  "Truth" and "falsity" do not
> apply in an absolute sense, as they do classically, but instead apply only
> at certain times.  This is where the ideas of constructivism arise, that
> there is no truth or falsity except what has been arrived at through a
> process.  We construct our notions of truth.  Each moment of time is
> associated with a particular state of knowledge, and sentences are evaluated
> relative to a state of knowledge.

�a va d�j� mieux!

> Truth has a persistence property that
> once a sentence is true for a particular state, it is true for all later
> states as well.

That is *weird*. Weird, but nice: I always wanted to be thirty again.
So, having been thirty years old in a particular state of my life,
I remain thirty until death do us part? Nice, but weird. Doesn't
agree with the state of my waistline, nor of my eyesight either.
So..., I'm not a Heyting algebra :-(
 
> This temporal ordering, in the general case, is only what is known as a
> partial order and is not necessarily linear (though it can be).  This is why
> such logics can also model possibility and certain forms of
> counterfactuality.

Why didn't you make that clear in the first place? No need for 
lattices either (your kind, whatever it is, not mine). It's clear
enough like that.

To me that reads like Prolog without a cut statement (which was a
kludge in the first place). Bon, ben j'ai pig�. Apart from the
persistence property of truth, of which I cannot make head or tail.
It contradicts all my experience, even professional.
0
jguy (7)
2/10/2004 5:04:28 PM

Jerzy Karczmarczuk wrote:

> Franz Heymann wrote the following to
>    alt.philosophy, comp.lang.functional, sci.lang, sci.physics and
>    sci.psychology.theory :
>
> > I do not ever initiate crossposts and I am throwing around junk in this
> > thread to get you to move it out of sci.physics.  YOU started this infantile
> > crossposting.  Now YOU get rid of it.
>
> I admit that learning from mister Heymann that he had a brilliant and successful
> career, I tried to track him on Internet. Unfortunately, I found only several
> hundreds of his postings to different newsgroups and other lists.
>

This is probably a bit unfair.  If his statements on sci.physics are to be believed,
Mr. Heymann is late in his career.  Consequently, his contributions are unlikely to
be found on the Internet.

In the strictest sense, he is also justified to a small degree--but, it is very
small.  Mathematical physics is not physics.  However, it is what people have to
learn in order to discuss physics intelligently.  They may not have to learn about
the quantum logic described on Hilbert spaces directly.  But, it is a miniscule step
from that construction to Heisenberg algebras.

So, let's run some Google searches.  My apologies to those that do not understand
the metaphysics of physics--just consider this a lesson on Orwellian Newspeak.

First, as a simple base point, here is a link to a paper discussing spinors and
Clifford algebras

 http://www.math.columbia.edu/~woit/notes19.pdf

The next chapter is on Heisenberg algebras

 http://www.math.columbia.edu/~woit/notes20.pdf

So, anyone interested can read the first two paragraphs to see that Galathaea's
remarks about Hilbert spaces actually have ground in papers that discuss the
mathematics of quantum mechanics (although the paper stresses that it is *not*
quantum mechanics).

Now, when I run a Google search on "spinors physics" I get 31,900 hits

When I run a Google search on "Clifford algebras physics" I get 8,410 hits

When I run a Google search on "SO(3) physics" I get 3,300,000 hits

When I run a Google search on "spin(n) physics" I get 603,000 hits.

You will find these various terms in the first paper mentioned above.

To be fair, Mr Heymann also admitted not to be particularly knowledgeable about a
Casimir "something or another" (I certainly have no inclination to go back and check
the exact statement).

The reason I bring this up has to do with what happens when I run a Google search on
"nilpotent Lie group physics."  In that case I only get 316 hits.  And on the page,

 http://www.innerx.net/personal/tsmith/Lie.html

we get the particular statement comparing significations,

"The real homology algebra of a simple Lie group is a
Grassmann algebra, as it is generated by odd (i.e., anticommutative)
elements. However, from them we can get, in the enveloping
algebra, multilinear symmetric forms, one for each generator;
.... in physics they are called Casimir invariants, in mathematics
the invariants of the Weyl group. ...".



And further searches associate these Casimir invariants with solvable Lie
groups--and, surprisingly, the very notion of mass.  This particular topic was
associated with Poincare symmetries.  So, I naturally ran a search on "Casimir
invariant Poincare" to turn up only 59 hits.

I did find one hit that was very interesting to me.  Here is a letter of complaint
to the Nobel Committee about vested interests in physics

 http://www.scientificethics.org/ir00007.htm

Its author writes:

"At this point physicists with vested interests on quarks
voice the view that quarks have masses thus being able
to characterize gravity.  A separation between science and
politics is here needed for our own dignity, let alone to
remain scientists. The sole possible way for a mass to
characterize gravity is that of being the eigenvalue of the
second order Casimir invariant of the Poincare� symmetry.
This is positively, absolutely impossible for quarks, as well
known."



I do not know enough physics to comment.  But, what I can say is that the author is
strongly complaining about the failure to check current interpretations against the
historical record of ideas that led to our modern physical theories.

Here is a nontechnical presentation (for the sci.physics crowd) discussing various
issues on hadronic mechanics that mentions Poincare symmetries and mass.

 http://www.i-b-r.org/ir00019b.htm

I look forward to reading it in the future.


In any case, I apologize to the people not on sci.physics.  Galathaea is trying to
discuss a relatively straightforward concept that is ubiquitous across many fields.
It does not get generally get discussed in people's educational training because it
originates in protest to a program of investigation that never met its burden of
proof.

It is my personal opinion that Mr. Heymann should be ashamed of himself.  However
USENET was orignally used no longer applies.  There are many intelligent people who
were unable to participate in full-fledged doctoral programs.  They should not be
treated badly by those who have had that opportunity when they come to these online
communities.  But, as someone on sci.math has just made clear to me, there is no
such thing as objective right and wrong.

So, take your best shot Mr. Heymann.  I am ignorant in physics only because they
asked me learn mathematics that you were able to pick up mid-career in context.

You can't lose.


:-)

mitch



0
mitchs (45)
2/10/2004 11:11:52 PM
"Sergio Roa Ovalle" wrote:
: I  don't know  if I  fully understood...   Are you  stating  here that
: Heyting  algebras could represent  logics which  go beyond  the Turing
: computability  (go  beyond   lambda  calculus)?   For  example,  brain
: computability  is not  Turing equivalent,  as far  as I  know, because
: brain computability is not algorithmic...

We're still not sure whether the brain can exceed the bounds of
computability yet.  There have been those who have argued against
computability and pointed to creative tasks, but none of these have been
proven yet to exceed computability.  Its a difficult task.  We have to model
the process somehow, and modeling usually cannot exceed computation.  One
example I've seen that is able to capture a non-computable task is through
mapping an infinte amount of time into a finite observed time through clever
use of black holes.  Then we could have the halting problem and related
solved.  But many of the models that do seem to capture our observations of
neuronal firing patterns are computable.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/11/2004 8:44:56 AM
"Jacques Guy" wrote:
: galathaea wrote:
: > Truth has a persistence property that
: > once a sentence is true for a particular state, it is true for all later
: > states as well.
:
: That is *weird*. Weird, but nice: I always wanted to be thirty again.
: So, having been thirty years old in a particular state of my life,
: I remain thirty until death do us part? Nice, but weird. Doesn't
: agree with the state of my waistline, nor of my eyesight either.
: So..., I'm not a Heyting algebra :-(

Hello! =)

Just wanted to point out that your reasoning would be false even in a
Boolean logic.  The object you refer to with the term "I" does not have an
age property.  Your "I" has many different ages at different locations in
time.  When you say "I am thirty years old", the statement really intends
the full proposition "I am thirty years old (at some time, the present tense
meaning the time spoken)" which was true or false at that time.  You still
were thirty-years-old-at-that-time even today.  The analysis can be done
using your age today and the time since you spoke the statement in a
completely constructive argument.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/11/2004 8:58:29 AM
galathaea <galathaea@excite.com> wrote:

> "Sergio Roa Ovalle" wrote:
> : I  don't know  if I  fully understood...   Are you  stating  here that
> : Heyting  algebras could represent  logics which  go beyond  the Turing
> : computability  (go  beyond   lambda  calculus)?   For  example,  brain
> : computability  is not  Turing equivalent,  as far  as I  know, because
> : brain computability is not algorithmic...
> 
> We're still not sure whether the brain can exceed the bounds of
> computability yet.  There have been those who have argued against
> computability and pointed to creative tasks, but none of these have been
> proven yet to exceed computability.  Its a difficult task.  We have to model
> the process somehow, and modeling usually cannot exceed computation.  One
> example I've seen that is able to capture a non-computable task is through
> mapping an infinte amount of time into a finite observed time through clever
> use of black holes.  Then we could have the halting problem and related
> solved.  But many of the models that do seem to capture our observations of
> neuronal firing patterns are computable.

I think the issue is whther or not physics is computable. If so, then
the capacities of any physical system is computable. Since the brain is
a physical system [unsupported by warranted premise], it will be
computable by any UTM complex enough to model it using physical laws.

But I suspect that there will need to be an input of truly random noise
to stop it getting stuck in suboptimal stable states.
-- 
John Wilkins
john@wilkins.id.au   http://wilkins.id.au
"Men mark it when they hit, but do not mark it when they miss" 
                                               - Francis Bacon
0
john_SPAM (2)
2/11/2004 8:07:29 PM

John Wilkins wrote:

> galathaea <galathaea@excite.com> wrote:
>
> > "Sergio Roa Ovalle" wrote:
> > : I  don't know  if I  fully understood...   Are you  stating  here that
> > : Heyting  algebras could represent  logics which  go beyond  the Turing
> > : computability  (go  beyond   lambda  calculus)?   For  example,  brain
> > : computability  is not  Turing equivalent,  as far  as I  know, because
> > : brain computability is not algorithmic...
> >
> > We're still not sure whether the brain can exceed the bounds of
> > computability yet.  There have been those who have argued against
> > computability and pointed to creative tasks, but none of these have been
> > proven yet to exceed computability.  Its a difficult task.  We have to model
> > the process somehow, and modeling usually cannot exceed computation.  One
> > example I've seen that is able to capture a non-computable task is through
> > mapping an infinte amount of time into a finite observed time through clever
> > use of black holes.  Then we could have the halting problem and related
> > solved.  But many of the models that do seem to capture our observations of
> > neuronal firing patterns are computable.
>
> I think the issue is whther or not physics is computable.

This is a tricky question.  :-)

Within threshold logic, there is a particular "idiosyncracy" with respect to
logical equivalence and exclusive disjunction.  You can find discussion of this in
the footnote to Lemma 4 of

 http://citeseer.nj.nec.com/feigelson97forbidden.html

Naturally, the community of philosophical logicians want to say that the truth
table semantics are "obvious" and "simple."  But, where their concerns lead to
questions about higher-order logics, threshold logic leads to the combinatorial
topology of Roth.  Sze-Tsen Hu cites two articles:

Algebraic Topological Methods for the Synthesis of Switching Systems I
Transactions of the American Mathematical Society, Vol. 88, pp. 301-328
July, 1958

Algebraic Topological Methods for the Synthesis of Switching Systems II
Annals of the Harvard Computational Laboratory, Vol 29, pp. 543-558
November, 1960

The issue has to do with the difference between a threshold function and a
switching function.  Essentially, threshold functions are associated with linear
separability--visually, that would be a line (or linear hypersurface) separating
the plane (or space) so that the separating surface segragates the domain points
into the on-set and off-set of the function.

In terms of physics, one is suddenly thrust into the complex plane.

The first place you want to be looking at here is the modular group of linear
fractional tranformations.  These functions partition the complex plane so that
the real axis becomes a separating surface.  More precisely, real numbers map to
real numbers; complex numbers with a postive imaginary component map to complex
numbers with a positive imaginary component; and complex numbers with a negative
imaginary component map to complex numbers with a negative imaginary component.

I note that the elliptic modular function seems particularly important...  Here's
a quote from a physics forum,

Dr. Kaku: Hyperspace is all there is, we think. 11
dimensional hyperspace is probably the maximum
number of dimensions you can reach before the
mathematics becomes inconsistent. There are mathematical
identities which only work in 10 and 26 dimensions
(for strings) which make string theory work. The theory is
inconsistent with other dimensions, such as 13 or higher.
The mathematical genius who first discovered these "magic"
numbers was Ramanujan, the great mathematical mystic. He
showed that the elliptic modular function only had its marvelous
properties in 26 dimensions. By the way, the life of
Ramanujan is so fantastic, that a Hollywood movie was made
of his life. The movie is called "Good Will Hunting." Actor
Matt Damon is Ramanujan in the movie. Now, we know that
one application of Ramanujan's work was to show that 26
dimensions was magical. Today, we have found that the next
magic number is 10 and this makes superstrings possible. So,
we think that our universe is floating in a larger multiverse which
is 11 dimensional. At Harvard, the 12th dimension has been
explored, twice now. It is called F theory (M for mother, F for
father). However, F-theory may be a fluke rather than a really
fundamental theory. 12 dimensions is rather difficult to work in,
and it's not clear if we really need 12 dimensions. Also, it's not
clear if there are really two times."


Ramanujan is not that mystical if you understand the significance of the
sexigesimal number system.

And, without the fundamental theorem of algebra showing that the complex number
system is algebraically closed, the "obviousness" of truth table semantics is not
at all obvious to me.

I could keep going with the mathematics, but I know it is a little much.  :-)



> If so, then
> the capacities of any physical system is computable.

One of the consequences of the axiom of determinacy in set theory would be that
every set of real numbers is measurable.

This axiom can be justified as reflecting the "descriptive applicability" of
mathematics.  But, the axiom of choice is not compatible with it.  That is not an
issue for "realism in language" since there are choice functions that are
compatible with it--they are just countable.



> Since the brain is
> a physical system [unsupported by warranted premise]

I would love an explanation of "unsupported by unwarranted  premise" if you could
be so kind.  :-)


> , it will be
> computable by any UTM complex enough to model it using physical laws.
>
> But I suspect that there will need to be an input of truly random noise
> to stop it getting stuck in suboptimal stable states.

How random can "scientific" (Hobbes, for instance) explanations be?  And, the
axiom of determinacy is expressed in a game-theoretic form that could be
interpreted as answering that question.

:-)

mitch




0
mitchs (45)
2/11/2004 9:02:37 PM
mitch <mitchs@rcnNOSPAM.com> wrote:

> > Since the brain is
> > a physical system [unsupported by warranted premise]
> 
> I would love an explanation of "unsupported by unwarranted  premise" if
> you could be so kind.  :-)

Typo: "unsupported *but* warranted" :-)
-- 
John Wilkins
john_SPAM@wilkins.id.au   http://wilkins.id.au
"Men mark it when they hit, but do not mark it when they miss" 
                                               - Francis Bacon
0
john_SPAM (2)
2/11/2004 10:57:53 PM
"Franz Heymann" wrote:
[...]
: Q[ui]t bragging and preaching to the converted about your knowledge of the
: background to the use of Hilbert space in quantum mechanics.
: >
: > That's all there is to it.  That algebra happens to be a Heyting
algebra,
:
: I don't care what you wish to call it.  It sounds as if you are telling me
: that I have been using prose all my life without knowing.

So at least you somewhat agree with the formulation, though I actually had
expected you to object at this point that what I just described does not
completely axiomatise a Heyting algebra compared to some of the descriptions
I given.  Of course, some of my references (particularly Coecke's work and
the consistent histories approach to quantisation) illustrate a natural
embedding, so I'm not bs'ing here, but I was kinda expecting you to bring it
up in protest.  Anyway...

So you have this calculus on projections which, due to their
noncommutativity in general, gives a particular algebra.  This corresponds
in a very natural way to functions over state space in classical mechanics,
through the canonical transformation of operators into the classical
framework of poisson manifolds.  And these do commute, and the corresponding
construction on them is Boolean.

So...

The difference between quantum "logic" and Boolean "logic" is somehow
captured in the different algebras over their respective categories of
spaces (the category of Hilbert spaces versus the category of Poisson
manifolds) and the structure of functors between these two categories is
constrained to respect these two algebraic structures.  So we have, now,
actual algebraic information about the nature of quantisation.

Modern theories in quasitriangular Hopf bialgebras describe the
deformation-algebraic approach to quantisation.  Other physicists are
looking at similar mathematical structures to generalise or apply to new
contexts.  This transformation from Boolean algebra and quantum algebra is a
key to understanding the process of quantisation because it gives
information such as cohomological constraint.

And the term "logic" is quite justified in this context.  By dropping the
term above, I was not backing down from the usage.  Projections and their
probability-measured lattice correspond to a very common way that physicists
interpret sentences in quantum mechanics.

In other words, how do you assign a model "truth" value to:

"Given two ideal open slits, x cm apart and a detector screen y cm behind
the slits, and an electron fired as some given Phi plane wave towards the
slits, the electron will be measured at position p on the detector."

without refering to the probabilistic projections?

I certainly do not see a true or false coming out of that, for any specific
input parameters.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/12/2004 2:58:14 AM
mitch wrote:
>
> I have a degree in mathematics.  The reason I have a degree in mathematics is
> because I was going to fail out of college.  I had never had problems until
> calculus in college.  All of a sudden, my grades depended on the ability to write
> proofs.  I dropped out of school in my second year.  When I returned, I took a
> course on intermediate logic followed by a course on Kant's "Critique of Pure
> Reason."

Do you mean your math education did not properly confront you with the task of 
formulating proofs until college ? <shudder>

> One of the reasons I have an interest in what Galathaea is doing is because I
> realize that the history of this situation is simply perverse.

Where does the perversion start ? In some sense, since it's present in the 
guise of symmetries that we quotient out to learn meanings of words, 
mathematics is from the first days of our educations misrepresented as that 
which has numbers as prerequisite.

Cheers, MC

0
borcis (46)
2/12/2004 12:05:00 PM

Morris Carr� wrote:

> mitch wrote:
> >
> > I have a degree in mathematics.  The reason I have a degree in mathematics is
> > because I was going to fail out of college.  I had never had problems until
> > calculus in college.  All of a sudden, my grades depended on the ability to write
> > proofs.  I dropped out of school in my second year.  When I returned, I took a
> > course on intermediate logic followed by a course on Kant's "Critique of Pure
> > Reason."
>
> Do you mean your math education did not properly confront you with the task of
> formulating proofs until college ? <shudder>
>

For the most part, yes.  I did have a prior geometry course, but the teacher was
unenthusiastic.  I guess I merely associated the detail as a characteristic of geometry
rather than mathematics as a whole.



>
> > One of the reasons I have an interest in what Galathaea is doing is because I
> > realize that the history of this situation is simply perverse.
>
> Where does the perversion start ? In some sense, since it's present in the
> guise of symmetries that we quotient out to learn meanings of words,
> mathematics is from the first days of our educations misrepresented as that
> which has numbers as prerequisite.
>

Indeed.  If there is any technical depth behind the phrase "quotient out", I would
appreciate a longer opinion.

With respect to Heyting algebras, however, the debate can be isolated to Kant's opinion
that mathematics and logic are distinct.  To give you some sense of how the opinion has
evolved, here is a statement by Paul Halmos when formulating his ideas about algebraic
semantics,

"Logic is usually studied from the '1' approach,
i.e., the emphasis is on truth and provability, and
consequently, on filters.  Since the dual '0' approach
uses the algebraically more natural concept of
ideal, the remainder of this exposition (addressed
to mathematicians, rather than to professional
logicians) will be couched in terms of the logically
less pleasant concepts of falsehood and refutability."

He had been motivated by Tarski's work on cylindrical algebras--something pretty much
ignored by the philosophical logicians.

Quite naturally, Halmos said that his ideas should not be applied to the fundamental
questions facing philosophical logicians.  But, that is exactly what gets manipulated
with forcing languages to prove the independence of the continuum hypothesis.  It is a
"quotient out" process that uses algebraic-topological methods.

If you then try to say that the independence result is questionable because it "mixes
metaphors," you cannot even get a discussion.  The philosophical logicians are able to
remain proof-oriented because the syncategorematic definition of standard first-order
quantifiers is infallibly defensible.

So I use the word "perversion."  Let me try to give you some idea about where my
concern lies.

Several weeks ago I had been in a used book store.  I found an economics textbook with
the 26 equations that explain the United States economy.  I suppose that I should go
purchase that book if it is still available.  But, this in not because I place any
particular faith in its contents.

It is the number 26 that is bothering me.

The people doing superstrings in physics are looking at symmetries in 26 dimensions.  I
own a particularly comprehensive text with much of the related mathematics.  But, just
to see what I mean, here is a quote from a physics forum that I posted in another part
of the thread,


"Dr. Kaku: Hyperspace is all there is, we think. 11
dimensional hyperspace is probably the maximum
number of dimensions you can reach before the
mathematics becomes inconsistent. There are mathematical
identities which only work in 10 and 26 dimensions
(for strings) which make string theory work. The theory is
inconsistent with other dimensions, such as 13 or higher.
The mathematical genius who first discovered these "magic"
numbers was Ramanujan, the great mathematical mystic. He
showed that the elliptic modular function only had its marvelous
properties in 26 dimensions. By the way, the life of
Ramanujan is so fantastic, that a Hollywood movie was made
of his life. The movie is called "Good Will Hunting." Actor
Matt Damon is Ramanujan in the movie. Now, we know that
one application of Ramanujan's work was to show that 26
dimensions was magical. Today, we have found that the next
magic number is 10 and this makes superstrings possible. So,
we think that our universe is floating in a larger multiverse which
is 11 dimensional. At Harvard, the 12th dimension has been
explored, twice now. It is called F theory (M for mother, F for
father). However, F-theory may be a fluke rather than a really
fundamental theory. 12 dimensions is rather difficult to work in,
and it's not clear if we really need 12 dimensions. Also, it's not
clear if there are really two times."


Here is the paper where Heyting algebras and the number 26 come into play,

 http://www.illc.uva.nl/Publications/ResearchReports/MoL-2001-09.text.pdf

I certainly do not expect you to understand the work.  But, if you open the file and
scroll down to Section 6.4 (Finite projective formulas of two variables) you will find
the discussion of interest.  There are lots of "pictures."

One thing to note, here.  The description of truth-table semantics uses two symbols 'T'
and 'F' organized in dyslexic symmetry.  Those are the symmetries at which the
physicists are looking.  The geometric symmetries generate long lists of palindromic
tables.  Fortunately, experiment has a way of identifying assymmetric invariants.  The
Heyting algebras seem to ground the system, somehow.

But, I cannot even engage discussion of these matters because it is "not  mathematics"
in the eyes of men who judge these things.

I just find myself wondering if the Tower of Babel has exactly 26 stories.

:-)

mitch





0
mitchs (45)
2/12/2004 8:38:16 PM
mitch,

I have wanted to reply to this for some time and build more of a
conversation with you, but I had felt it important to first focus on
establishing legitimacy and fight the various alpha battles that always
arise when unfamiliar concepts are introduced.  I hope you didn't feel
ignored, and I really appreciate your expositions throughout the threads.
As you are quite aware, these kinds of things take time (the sci.logic
threads being a great example), but I feel that your work has been a great
first step and this thread is my effort at pushing through the weakened
boundaries.  I suspect that the first wave of negativity among these groups
is almost finished, which will allow expansion into particular topics (with
less cross-posting, of course!).  This will alow me to focus on strategic
targetting in a way that doesn't antagonise territorial characters, because
I think it is obvious that that has been a main objection (and should only
occur probably once or twice a year... ;) ).

"mitch" wrote:
: It would be difficult to explain just how much delusional
: nonsense with which this question has presented me through
: life.  There is little doubt in my mind that the battle
: between mathematicians and other members of society has
: raged from the earliest days of civilization.  In order
: for our language skills to keep us alive, certain words
: must have "magical" properties.  Undoubtedly, the same men
: (and women [that is said respectfully although probably
: vacuous]) who figured out when to plant and harvest were
: also responsible for taxes and levies.  There are
: fragments of Linear A from Crete complaining about the
: Egyptian scribes.

Yes, you seem to be reading right out of my signature!  Magic, to me, is the
skill of manipulating the world for a particular goal.  Prediction or
prognostication is a very useful goal done through the clever manipulation
of words (or abstractly, symbols) and games played upon them, which as you
mention, is the origins of numerology and later science.  It amuses me that
the manipulation of collections of people is often done through words (or
"spells"), often on paper, such as through popular rhetoric, employment
contracts, or law(*&#% Egyptian scribes!).

: In modern times, the advocacy of Russell's logicism has
: created presentations of mathematics that are totally
: disconnected from the idiomatic needs of other subjects.

Absolutely.

: I have a degree in mathematics.  The reason I have a
: degree in mathematics is because I was going to fail out
: of college.  I had never had problems until calculus in
: college.  All of a sudden, my grades depended on the
: ability to write proofs.  I dropped out of school in my
: second year.  When I returned, I took a course on
: intermediate logic followed by a course on Kant's
: "Critique of Pure Reason."  with the addition of one
: more extracurricular topic--namely, topology--I suddenly
: became quite good.  Although I was unable to recover
: from the poor performance in my first year, I still
: ended up with the highest GPA among mathematics
: graduates at my school.

The teaching of proof methods is one of the most lacking of all parts of
mathematical education.  I think it is very much due to the lack of
conceptual preparation where fields are expanded into full semester or year
college courses.  Every field takes some time to become familiar with its
pantheon of objects and their specific property and transformation tool
kits.  That's why I like topics like category theory where you can present a
map of a field as a graph.  If mathematics was presented as objects and
methods (plural!) of reasonng about them, I feel it would assist students
tremendously in seeing common proof structures and open the way to science
being approached in the same way.

: One of the reasons I have an interest in what Galathaea is doing is
because I
: realize that the history of this situation is simply perverse.  Of course,
there
: may simply be no way to decide how to treat the subject.  Their is a sense
in
: which we have obsfucated all of our unanswerable questions with an
impenetrable
: language.  :-)

I am more optimistic.  We are obsessive animals, particularly about
abstraction and language.  Our babies stare at objects longer than any other
animals.  We utter more.  We obviously have excelled in it to great benefit.

I use to write a lot about the nonverbal realm of thought, and there is much
content in our expression, subtle timing differences, body language,
inflection, sources of creativity, that is difficult to express inside of
language.  There is a lot of romanticism in the idea that such difficulties
cannot be overcome, much as in Hofstadter and other's appeals against the
Church-Turing thesis, and I very much associated myself with these movements
for some time.

Eventually, though, I began to see language not as a sterile, antihumanistic
approach to the world, but as a very human thing.  I saw a rich background
of meaning with which to unveil great models of the world.  I saw it more
playfully, as a game.  This way of viewing language only began to grow on me
as I studied the various logics of our reasoning, and stepped out of the
classical ansatz.  I identified with the Polish logicians and their goals.

And slowly, my old romanticism against language has turned into a romantic
mysticism very much in favor of language as our way to build meanings about
the world.  I see our models as slowly, as through a fog, displaying to us
the naked beauty of our universe.  And what I see so far makes me believe
that there is a natural way in which to educate our youth about the entire
structure of reasoning, mathematics, and science.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/12/2004 9:39:20 PM
"mitch" wrote:
: You might also wish to visit the pages,
:
:  http://plato.stanford.edu/entries/logic-paraconsistent/
:
:  http://plato.stanford.edu/entries/mathematics-inconsistent/

I realised yesterday that I had seen the discussion of the dualities
mentioned before.  They were talking about co-Heyting algebras, where the
boundary

@a = a /\ ~a

is not necessarily empty.  The boundary is a derivation

@(a /\ b) = ((@a) /\ b) \/ (a /\ (@b)).

F. W. Lawvere mentions that such algebras seem to portray the "birth" of
geometric notions in "Intrinsic boundary in certain mathematical toposes
exemplify 'logical' operators not passively preserved by substitution".

I knew about Priest's involvement in such systems, through readings in books
like Richard Kirkham's "Theories of truth: a critical introduction", but had
not seen this particular connection so explicilty before.  I guess its time
to go hunt down Priest and the others in the bibs...

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/12/2004 11:48:54 PM
mitch wrote:
> 
> Morris Carr� wrote:
>>
>>Do you mean your math education did not properly confront you with the task of
>>formulating proofs until college ? <shudder>
>>
> 
> For the most part, yes.  I did have a prior geometry course, but the teacher was
> unenthusiastic.  I guess I merely associated the detail as a characteristic of geometry
> rather than mathematics as a whole.

Ah, teacher enthusiasm. Curiously, when I looked back at my pre-college math 
education, my main regret was with how the curriculum had done away with this 
traditional role of geometry in teaching proofs, not so much because of skills 
but because of the loss of historical perspective - the skills were kept thru 
an early intro to 1-st order logic for proofs, which indeed saves from the 
pitfall you sketch, and Monge-style "descriptive geometry" on the other hand 
for spatial intuition. And I really regret not having been subjected to a more 
formal presentation of projective geometry that would have promoted duality to 
priviledged attention. I mean, substituting projective geometry to euclidean 
geometry, while focussing attention on duality, I feel represents a minimal 
revision to pre-19th century curricula to incorporate a nutshell 
representation of later intuitions - good math milk-teeth equipment.

>>>One of the reasons I have an interest in what Galathaea is doing is because I
>>>realize that the history of this situation is simply perverse.
>>
>>Where does the perversion start ? In some sense, since it's present in the
>>guise of symmetries that we quotient out to learn meanings of words,
>>mathematics is from the first days of our educations misrepresented as that
>>which has numbers as prerequisite.
> 
> Indeed.  If there is any technical depth behind the phrase "quotient out", I would
> appreciate a longer opinion.

Not really, I just meant to point out that inferring the meaning of a word 
from a system of occurences in context, amounts to the observation of a 
symmetry spanning these contexts - and that's a vague sense for "symmetry".

One could also try to point at the similarity (maybe subdued for 
English-language pupils) between tables of arithmetic and tables of verb 
conjugations. The only further intuition I have about this at the moment, is 
that one could argue for a pervasive role of symmetries in our learning 
processes (eg including nervous systems and sociology) that puts them in the 
background like good teachers who facilitate learning the foreground content 
they teach, while abstracting themselves from it. Finally I'd link this to 
John Baez's parable of "decategorification as the original sin".

> 
> With respect to Heyting algebras, however, the debate can be isolated to Kant's opinion
> that mathematics and logic are distinct.

BTW, I retained from somewhere that Kant downplayed non-euclidean geometries 
or more exactly, euclidean models of non-euclidean geometries, on the ground 
more or less that the primitive objects of these models unmistakably stretched 
the a priori meanings of words. I've been unable to recover a reference and 
would be grateful for it by any chance - since it is exactly against this form 
of objection that I feel projective duality deserves attention.

> To give you some sense of how the opinion has
> evolved, here is a statement by Paul Halmos when formulating his ideas about algebraic
> semantics,
> 
> "Logic is usually studied from the '1' approach,
> i.e., the emphasis is on truth and provability, and
> consequently, on filters.  Since the dual '0' approach
> uses the algebraically more natural concept of
> ideal, the remainder of this exposition (addressed
> to mathematicians, rather than to professional
> logicians) will be couched in terms of the logically
> less pleasant concepts of falsehood and refutability."

Ok, thanks.

> 
> He had been motivated by Tarski's work on cylindrical algebras--something pretty much
> ignored by the philosophical logicians.
> 
> Quite naturally, Halmos said that his ideas should not be applied to the fundamental
> questions facing philosophical logicians.  But, that is exactly what gets manipulated
> with forcing languages to prove the independence of the continuum hypothesis.  It is a
> "quotient out" process that uses algebraic-topological methods.
> 
> If you then try to say that the independence result is questionable because it "mixes
> metaphors," you cannot even get a discussion.  The philosophical logicians are able to
> remain proof-oriented because the syncategorematic definition of standard first-order
> quantifiers is infallibly defensible.
> 
> So I use the word "perversion."  Let me try to give you some idea about where my
> concern lies.

This is couched in terms that defeat my culture, although I wouldn't assume it 
relates to none of my own intuitions. I'll risk the superficial and probably 
off-topic remark that the ban on mixing metaphors I believe to be a heuristic 
slogan specific to English-language education - with corresponding dead angles.

Also, I'd tend to picture the perversity of the current situation in broader 
terms relating to the shape of the specialisation tree. One of my contentions 
is that many logical intuitions are made explicit at a level of abstraction 
way above the educational optimum - a level of abstraction high enough to 
obscure the isomorphism with political and ethical issues of broad concern. 
Another contention is that science at this level sorely misses a niche for 
competent artistry.

> 
> Several weeks ago I had been in a used book store.  I found an economics textbook with
> the 26 equations that explain the United States economy.  I suppose that I should go
> purchase that book if it is still available.  But, this in not because I place any
> particular faith in its contents.
> 
> It is the number 26 that is bothering me.
....

No this appears a relatively different story to me. There was a time when 10 
and 26 were the only magical dimensionality expounded by string, M- or 
F-theory, and they stand out so neatly that squinting hard allows to match 
these two numbers to the cardinalities of our dominant alphabets, eg the latin 
alphabet and the arabic digits, which kind of harmonizes with your wonder

> 
> I just find myself wondering if the Tower of Babel has exactly 26 stories.
> 

Regards, MC



0
borcis (46)
2/13/2004 10:38:00 AM

Morris Carr� wrote:

> mitch wrote:
> >
> > Morris Carr� wrote:
> >>
> >>Do you mean your math education did not properly confront you with the task of
> >>formulating proofs until college ? <shudder>
> >>
> >
> > For the most part, yes.  I did have a prior geometry course, but the teacher was
> > unenthusiastic.  I guess I merely associated the detail as a characteristic of geometry
> > rather than mathematics as a whole.
>
> Ah, teacher enthusiasm. Curiously, when I looked back at my pre-college math
> education, my main regret was with how the curriculum had done away with this
> traditional role of geometry in teaching proofs, not so much because of skills
> but because of the loss of historical perspective - the skills were kept thru
> an early intro to 1-st order logic for proofs, which indeed saves from the
> pitfall you sketch, and Monge-style "descriptive geometry" on the other hand
> for spatial intuition. And I really regret not having been subjected to a more
> formal presentation of projective geometry that would have promoted duality to
> priviledged attention. I mean, substituting projective geometry to euclidean
> geometry, while focussing attention on duality, I feel represents a minimal
> revision to pre-19th century curricula to incorporate a nutshell
> representation of later intuitions - good math milk-teeth equipment.
>

Yes.

But, there are still problems with the first-order understanding of issues.  The concept of
set as formulated in Zermelo-Fraenkel set theory is archetypical.  It would merely be a
matter of belief to accept that axiomatization as corresponding with descriptive sets.

They now have two axioms (the axiom of determinacy and the axiom of projective determinacy)
that capture much of the complexity for descriptive sets.  They are game-theoretic.


>
> >>>One of the reasons I have an interest in what Galathaea is doing is because I
> >>>realize that the history of this situation is simply perverse.
> >>
> >>Where does the perversion start ? In some sense, since it's present in the
> >>guise of symmetries that we quotient out to learn meanings of words,
> >>mathematics is from the first days of our educations misrepresented as that
> >>which has numbers as prerequisite.
> >
> > Indeed.  If there is any technical depth behind the phrase "quotient out", I would
> > appreciate a longer opinion.
>
> Not really, I just meant to point out that inferring the meaning of a word
> from a system of occurences in context, amounts to the observation of a
> symmetry spanning these contexts - and that's a vague sense for "symmetry".
>
> One could also try to point at the similarity (maybe subdued for
> English-language pupils) between tables of arithmetic and tables of verb
> conjugations. The only further intuition I have about this at the moment, is
> that one could argue for a pervasive role of symmetries in our learning
> processes (eg including nervous systems and sociology) that puts them in the
> background like good teachers who facilitate learning the foreground content
> they teach, while abstracting themselves from it. Finally I'd link this to
> John Baez's parable of "decategorification as the original sin".
>

I looked at the statement in

 http://math.ucr.edu/home/baez/week121.html

For my part, I have been blaming Descartes for putting the numbers on the plane.  :-)

On alt.philosophy Immortalist did a long posting using search engine summaries.  One of them
caught my eye because it mentioned an Arabic philosopher discussing what seemed to be like
the mind/body problem.  It had been phrased in religious terms, but it seemed right.

Now, to the extent that my knowledge is not failing me, there had been no zero in Western
Europe until the Moorish libraries in Spain had been translated.  Notre Dame and French
mathematics was one of the first recipients.  So, there was a second culture clash with the
sexigesimal number system, the first being Pythagoras visit to Sumer.

The Sumerians had been anecdotally aware of Pythagorean triples.  But, they had no geometric
theory for it.  Rather they were simply using the sexigesimal number system (60=3*4*5).
Fortunately for them, some rather simple (but large) multiplication tables gave them what
they needed for astronomical timekeeping.

The third clash with the sexigesimal number system may have been Ramanujan.

Still.  I am not disagreeing with Baez entirely.  Sumer was a civilization with tax
collectors.  :-)



>
> >
> > With respect to Heyting algebras, however, the debate can be isolated to Kant's opinion
> > that mathematics and logic are distinct.
>
> BTW, I retained from somewhere that Kant downplayed non-euclidean geometries
> or more exactly, euclidean models of non-euclidean geometries, on the ground
> more or less that the primitive objects of these models unmistakably stretched
> the a priori meanings of words. I've been unable to recover a reference and
> would be grateful for it by any chance - since it is exactly against this form
> of objection that I feel projective duality deserves attention.
>

I can't help you there.  But Dover has published a translation of his Logic in English.  I
picked it up the other day, and, I can try to explain his objection in some modern terms.
But, I have no interpretation of his intended meaning of "a priori."

Kant distinguishes clearly between universality, induction, and analogy.  He observes that
induction is good enough to characterize generality.  It is not, however, good enough to
characterize universality.

We can compare that with the recursive definitions of truth used for models in intermediate
logic.  They are problematic, and, that drives us back to categorial reasoning.  This is the
wrong approach to the problem, however.  I think that a proper selection from among the
determinacy axioms will give the first-order system in which work can be done
proof-theoretically.

The other direction is analogy.  It really does not end until you drive the analysis to
inconsistency.  It appears that we have reached that saturation in several fields.  Mark
Steiner has written a book entitled "The Applicability of Mathematics as a Philosophical
Problem" which discusses the "descriptive ability" of mathematics.  He uses the label
"Pythagoreanism."  But, the real criticism probably can be found lurking in the last chapter
of "Geometric Structures in Nonlinear Physics" by Robert Hermann.  At some point, physicists
actually have to solve a quantization problem.

From the pure logic side of the question, universal quantification is syncategorimatically
defined.  In other words, one must have a definition for 'all.'  Kant chose to frame the
problem as the ideality of space and time.  At the very least, that seems to ground
defeasible inheritance reasoning in descriptive set theory.

[...]

> > If you then try to say that the independence result is questionable because it "mixes
> > metaphors," you cannot even get a discussion.

[...]

> I'll risk the superficial and probably
> off-topic remark that the ban on mixing metaphors I believe to be a heuristic
> slogan specific to English-language education - with corresponding dead angles.

I see.  :-)

If I understand, then I agree about dead angles.


>
>
> Also, I'd tend to picture the perversity of the current situation in broader
> terms relating to the shape of the specialisation tree. One of my contentions
> is that many logical intuitions are made explicit at a level of abstraction
> way above the educational optimum - a level of abstraction high enough to
> obscure the isomorphism with political and ethical issues of broad concern.
> Another contention is that science at this level sorely misses a niche for
> competent artistry.
>

My interest in these questions has led me to start looking more closely at Enlightenment
philosphy.  It is interesting how the meaning of "science" seems to have changed.  I wish I
were more versed in this material now.



>
> >
> > Several weeks ago I had been in a used book store.  I found an economics textbook with
> > the 26 equations that explain the United States economy.  I suppose that I should go
> > purchase that book if it is still available.  But, this in not because I place any
> > particular faith in its contents.
> >
> > It is the number 26 that is bothering me.
> ...
>
> No this appears a relatively different story to me. There was a time when 10
> and 26 were the only magical dimensionality expounded by string, M- or
> F-theory, and they stand out so neatly that squinting hard allows to match
> these two numbers to the cardinalities of our dominant alphabets, eg the latin
> alphabet and the arabic digits, which kind of harmonizes with your wonder
>

It does more than that.  I understand it specifically in those terms.  A "theory of
everything" cannot exclude statistical entropy.  Moreover, I do not necessarily say this with
an anthropic principle in mind.  There is a sense in which mathematicians are between physics
(analogy/Pythagoreanism) and logic (induction/recursion) when it comes to people making
particular claims about truth and falsity.

I understand a lot of the connections between the two.  But, I have not yet worked out every
detail.  :-)

Thanks.

:-)

mitch



0
mitchs (45)
2/14/2004 9:30:14 PM
"Franz Heymann" <notfranz.heymann@btopenworld.com> wrote in message news:<c093qh$nti$19@sparta.btinternet.com>...
> "Jacques Guy" <jguy@alphalink.com.au> wrote in message
> news:4028DB0D.7701@alphalink.com.au...
> > galathaea wrote:
> >
> > > And that is the whole point of post.  To ask professionals to share any
> > > thoughts on Heyting algebras in the foundations of their profession and
> > > perhaps discuss broadening education on the topic.
> >
> > So I did a search for "Heyting algebra" (no idea what the bloody
> > thing is).
> >
> > Found a definition at http://mathworld.wolfram.com/HeytingAlgebra.html
> >
> > "An algebra which is a special case of a logos."
> >
> > Looked up "logos":
> >
> > "A generalization of a Heyting algebra which replaces Boolean
> > algebra in "intuitionistic" logic."
> >
> > Lovely. So far, I have found out that a Heyting algebra
> > was a special case of a generalization of a Heyting
> > algebra. I know Boolean algebra, I know what logic is,
> > but I have no idea what quote-intuitionistic-unquote
> > means. Terrific.
> 
> As soon as you encounter any word ending in "-ism" or "-istic" you may
> safely assume that there are kooks around, and you may drop the subject
> without any loss.

Is that what they call "textual analysis" ? 

;-)
0
2/16/2004 10:38:03 AM
"galathaea" <galathaea@excite.com> wrote in message news:<102fr9s1hcrhn7f@corp.supernews.com>...
> "Jacques Guy" wrote:
> : galathaea wrote:
> :
> : > And that is the whole point of post.  To ask professionals to share any
> : > thoughts on Heyting algebras in the foundations of their profession and
> : > perhaps discuss broadening education on the topic.
> :
> : So I did a search for "Heyting algebra" (no idea what the bloody
> : thing is).
> :
> : Found a definition at http://mathworld.wolfram.com/HeytingAlgebra.html
> :
> : "An algebra which is a special case of a logos."
> :
> : Looked up "logos":
> :
> : "A generalization of a Heyting algebra which replaces Boolean
> : algebra in "intuitionistic" logic."
> :
> : Lovely. So far, I have found out that a Heyting algebra
> : was a special case of a generalization of a Heyting
> : algebra. I know Boolean algebra, I know what logic is,
> : but I have no idea what quote-intuitionistic-unquote
> : means. Terrific.

Sir Jacques, I salute you!  Your skeptical incision will be a cutting
gem in any profession you lay your hand to.

Sincere adulation aside, I poked around just a little bit more, and it
seems likely you have found the absolutely worst short explanations
possible.  Sharing your apparent distaste for Brave New Ideas which
the young will flout, now casting all in terms of functors, now
Clifford algebras, now Heyting, I at least was able to determine that
a "Heyting algebra" is a generalization of a Boolean algebra.  As
generalizations go, so this one; we relax one of the laws of A to get
a generalized A.  (In this way we eventually get to " ", or the
Nameless Structure, having no structure at all and being a
generalization of all other generalizations.  But this will have to
wait to my upcoming web page).

Meanwhile, the specific structural element we remove from a Boolean
algebra to get to a Heyting algebra, standing back to watch the thing
totter like a child's toy, is apparently "the law of the excluded
middle".  (I'd forget the "logos" thing for now; that seems to be a
cul-de-sac).

The "law of the excluded middle" is apparently is one of at least
three closely related ideas which the uninformed might naively take to
be same idea, depending on exactly how one formaly states "either A
is, or it isn't". I've long been a fan of skepticism regarding this
law, not to found brave new worlds, but just to mildly suggest that
the unrecognized third possibility is often that "both statments A and
~A are nonsense"; neglect of which leads to paradoxes.

> That is horrible!  I have no idea what type of information that is supposed
> to convey, but it ends up just illustrating the existence of three phrases
> without any meaning.

Fantastic!

Now, as you have seen fit to cast your net to groups where all are not
all in on the joke, yet rife with crawling protoplasmic ooze of just
sufficient native intelligence to parse your meaning, why don't you
try your hand at a little concise exposition, with precision and
decision?

Why do you think Heyting algebras are the greatest thing since sliced
bread?

Hints:  be so concise that you seem to be writing just "."
(This should work out about right, given our varying views of
concision).
0
nulldev00 (40)
2/16/2004 5:27:04 PM
Edward Green wrote:

> The "law of the excluded middle" is apparently is one of at least
> three closely related ideas which the uninformed might naively take to
> be same idea, depending on exactly how one formaly states "either A
> is, or it isn't".

Do you mean or not to imply that the slogan I first proposed in favor of 
Heyting algebras :

666 ?? -- 666 ~ .666 ~ 2/3 ~ 1 - 1/3 ~ tertium non datur ~ the excluded middle
               ~ "either you are with us, or you are against us" !!

is faulty of disinformation because it either overspecializes the excluded
middle, or confuses different ideas ?

> I've long been a fan of skepticism regarding this
> law, not to found brave new worlds, but just to mildly suggest that
> the unrecognized third possibility is often that "both statments A and
> ~A are nonsense"; neglect of which leads to paradoxes.

not far from my feeling about "either you are with US, or you are against US".

> Why do you think Heyting algebras are the greatest thing since sliced
> bread?
> 
> Hints:  be so concise that you seem to be writing just "."
> (This should work out about right, given our varying views of
> concision).

First reason : they free us of the ambiguity of "lattice", at the cost of a 
little specialisation.

Second reason : Heyting rhymes with Hating. Wouldn't it be wonderful is some 
solidly subtle mathematical objects could be seized to regain control over 
matter abandoned to the vagrant stupidity of collective hates ?

0
ruses1 (38)
2/16/2004 10:35:54 PM
nulldev00@aol.com (Edward Green) wrote in message news:<2a0cceff.0402160927.29533193@posting.google.com>...
....
> Why do you think Heyting algebras are the greatest thing since sliced
> bread?

(Not answering for Jacques)

Expressed as a natural deduction rule, the excluded middle allows one
to infer what follows from both P and not P, for any sentence P.
But a sentence that follows from both P and not P is a presupposition
of P, by Strawson's definition.  The consequence of adopting the
excluded middle, then, is that it is impossible to have a false
presupposition.

Greg
0
greg1021 (22)
2/17/2004 1:44:56 AM

Edward Green wrote:

[...]

>  I've long been a fan of skepticism regarding this
> law, not to found brave new worlds, but just to mildly suggest that
> the unrecognized third possibility is often that "both statments A and
> ~A are nonsense"; neglect of which leads to paradoxes.
>

 http://plato.stanford.edu/entries/logic-paraconsistent/

 http://plato.stanford.edu/entries/mathematics-inconsistent/


On the first of these pages, you will find discussion of your exact complaint.  The second page is a
link from the first.  If you scroll down, you will eventually see a discussion of topos and closed
set topologies.  These are 'mathematical' (???) entities with relevance to Heyting algebras.

Curiously, after not being able to formulate a foundational approach, the logic community stepped in
for another renaming of the issues... So now mathematics is inconsistent (as opposed to the ways in
which it is used).

:-)

mitch



0
mitchs (45)
2/17/2004 2:30:36 AM

Edward Green wrote:

>
> Why do you think Heyting algebras are the greatest thing since sliced
> bread?
>

Galathaea will have to offer her own reason.  But, they seem to be needed to connect truth in
mathematical physics to truth in classical logic.

And, since 'T' and 'F' have no intrinsic meaning, the people who study the *mathematics* of truth
tables have isolated a combinatorial idiosyncracy involving logical equivalence and mutual
exclusion,

 http://citeseer.nj.nec.com/feigelson97forbidden.html

The footnote to Lemma 4 is the statement of interest.

So, contrary to fundamentalist fervor, you do not get truth in the universe for free; indeed, when
Frege first discussed these matters, he did not use 'T' and 'F.'  He spoke instead of "judgeable
content."

Turning to something that might reflect that idea, one can consider the complexity of Bradmetz model
of epistemic intentionality,

[begin fixed width]

                                                                 |--------|
             /-------------------------------------------------> |        |
            /                                               /--> |  K  p  |
           /                                               /     |        |
          /                                |--------|     /      |--------|
    |-----------|                   /----> |        |    /
    |           | -----------------/-----> |  B  p  | --/
    |           |                 /        |        |
    |           |     |---------|/    /--- |--------|
    |           |     |         | <--/       |   /|\
--> |  ~K that  | --> |  ~K if  |            |    |
    |           |     |         | <--\      \|/   |
    |           |     |---------|\    \--- |--------|
    |           |                 \        |        |
    |           | -----------------\-----> |  B ~p  | --\
    |-----------|                   \----> |        |    \
          \                                |--------|     \      |--------|
           \                                               \     |        |
            \                                               \--> |  K ~p  |
             \-------------------------------------------------> |        |
                                                                 |--------|

[end fixed width]

and think about how much simpler life is when one already knows that there is literature in logic
dealing with informationally incomplete systems.  Every problem should not be required to have an
individual solution that is later reduced to something using a Heyting algebra.  It is too much
work.

For an example of that, the logical model for relational databases is supposed to be based on set
theory.  But, the relational algebra of SQL must deal with NULL values.  I found one paper
discussing the matter in terms of Brouwerian semilattices.  I will place my faith in the accuracy of
that determination and observe that the "Brouwerian" part reflects the fact that databases are
information systems.

How many database programmers started their career with Boolean logic and how costly was that to
their employers?

:-)

mitch



0
mitchs (45)
2/17/2004 3:00:23 AM
"Edward Green" wrote:
: The "law of the excluded middle" is apparently is one of at least
: three closely related ideas which the uninformed might naively take to
: be same idea, depending on exactly how one formaly states "either A
: is, or it isn't". I've long been a fan of skepticism regarding this
: law, not to found brave new worlds, but just to mildly suggest that
: the unrecognized third possibility is often that "both statments A and
: ~A are nonsense"; neglect of which leads to paradoxes.

The paradoxes have traditionally been a field where logics have been
explored outside of the true / false dichotomy.  They help elucidate where
the abstraction fails and help us describe better what things like
consistency and completeness mean.

: > That is horrible!  I have no idea what type of information that is
supposed
: > to convey, but it ends up just illustrating the existence of three
phrases
: > without any meaning.
:
: Fantastic!
:
: Now, as you have seen fit to cast your net to groups where all are not
: all in on the joke, yet rife with crawling protoplasmic ooze of just
: sufficient native intelligence to parse your meaning, why don't you
: try your hand at a little concise exposition, with precision and
: decision?
:
: Why do you think Heyting algebras are the greatest thing since sliced
: bread?
:
: Hints:  be so concise that you seem to be writing just "."
: (This should work out about right, given our varying views of
: concision).

I'm on my third try now, and maybe with enough tries I can finally
communicate what I'm trying to get at.  I do appreciate the chance to work
things out and any critical analysis I can get.

I've given a lot of examples of Heyting algebras in cognitive research,
foundational math, computation theory, and models of reality.  Those are
fairly well established, and have a lot to do with my appreciation of them.

However, there are undertones to my reasons which, although I have tried to
be up front about them, have not been explored as critically as I hoped they
would.  This has to do with a connection I see with a kind of "monotheism".
In particular, I see a particular psychology that strives very hard to be
the "most correct", and although in and of itself, that can be a very useful
approach to "understanding", there are problems that often arise.  The
biggest problem I have seen is that I fear too many are lead to "follow" a
particular set of models with a zeal unwarranted by their logical study,
usually I find due to the rhetoric of certain "authorities".  An example I
often point to in physics is the regular attacks made against Bohmian
mechanics, when it merely expresses an isomorphism theorem in mathematics
and does not differ in any prediction from other interpretations of quantum
mechanics.

I see a similar problem as that found in Islamic fundamentalism and the "one
true way" psychology.  Its a problem I see responsible for bigotry and
racism throughout the world.  I think of the hierarchies in Rwanda set up by
the colonialists and the angry absolutists, badly abstracted good and evil
leading to holocaust there, just as similar ideas did in Germany.

And I've always felt that the same psychology that has lead to monotheistic
devotion throughout history has moved itself into the sciences, under the
pretense that science does give us that true and false that religion has
always claimed.  Which is nonsense.  Science is great at making predictions,
its agile and acrobatic and has done much in service to humanity.  But it
has not found truth.  It has only found models with good observational
match.

So, there are these two sides to what I want to talk about.  There is this
part of me that wants to separate them, to see if talking about usefulness
of alternate logics can be done without bringing up such issues as
monotheism and needs of an absolute.  But there is another part of me that
wants to be an evangelist for tolerance, to stand up confident and make the
connection that lies so deeply intertwined in my conception.  And I think
that this latter part of me is the dominant one, because I see a deep
sickness in humanity otherwise.

Perhaps this approach also gives a less technical idea of where I come from?
I've decided to post a series of descriptions of logic under the title "the
anticlassicalist" in order to chop up the approaches and give a deeper
insight into each area, including the logical foundations and lattice
algebraics.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/17/2004 6:33:53 AM
[sci.physics restored since I think that's where Ed is reading this]
In message <403183C7.EE695E6E@rcnNOSPAM.com>, mitch 
<mitchs@rcnNOSPAM.com> writes
>
>Edward Green wrote:
>
>>
>> Why do you think Heyting algebras are the greatest thing since sliced
>> bread?
>>
>
>Galathaea will have to offer her own reason.  But, they seem to be 
>needed to connect truth in
>mathematical physics to truth in classical logic.

I always had a vague idea that if "truth" meant anything at all in 
physics, it was something to do with correspondence to experimental 
observation. That's what entitles physics to drop the "meta", but it 
appears to be lacking in all this discussion of algebras.


PS Ed, meet Jacques; Jacques, meet Ed. I have an idea that you will find 
lots to discuss ;-)
-- 
Richard Herring
0
Richard
2/17/2004 9:45:08 AM
galathaea wrote:

> However, there are undertones to my reasons which, although I have tried to
> be up front about them, have not been explored as critically as I hoped they
> would.  This has to do with a connection I see with a kind of "monotheism".
> In particular, I see a particular psychology that strives very hard to be
> the "most correct", and although in and of itself, that can be a very useful
> approach to "understanding", there are problems that often arise.  The
> biggest problem I have seen is that I fear too many are lead to "follow" a
> particular set of models with a zeal unwarranted by their logical study,
> usually I find due to the rhetoric of certain "authorities".  An example I
> often point to in physics is the regular attacks made against Bohmian
> mechanics, when it merely expresses an isomorphism theorem in mathematics
> and does not differ in any prediction from other interpretations of quantum
> mechanics.

I surmise you agree then that it's maybe better to accuse by the name of 
"inertia" rather than by the name of "authorities", like "inertia" is the verb 
and "authority x" is a conjugation (this not to belittle the value of the 
existence of particular contextual proofs of inertia). Abuse of inertial 
power, would be the name of the crime. But, what if the Main Abuser is just a 
pathological propensity of our own minds ? I'll warrant you that some 
significant ideas of God deserve Heyting.

....
> wants to be an evangelist for tolerance

isn't that almost pleonastic ?

Cheers, MC


0
ruses1 (38)
2/17/2004 6:43:48 PM
Greg wrote:
 
> nulldev00@aol.com (Edward Green) wrote in message news:<2a0cceff.0402160927.29533193@posting.google.com>...

> > Why do you think Heyting algebras are the greatest thing since sliced
> > bread?

> (Not answering for Jacques)

My turn then. The greatest thing since sliced bread, �a va pas chercher
loin.
But the greatest thing since les rillettes de Connerr�, l'andouille de
Vire,
le kouign-amann, le foie gras du P�rigord, now THAT would be something.
Surtout depuis les rillettes et le foie gras. I see this is being
cross-posted to places like alt.philosophy et al. so I take the liberty
to recommend a highly philosophical work:

The Physiology of Taste by Jean Anthelme Brillat-Savarin.

www.abebooks.com has quite a few for sale, some for as little
as a tub of rillettes de Connerr�, some for as much as une
bo�te de foie gras, with truffles.

It will construct your education far, far, far better than
any algebras, be they Heyting or Loving.
0
jguy (7)
2/17/2004 9:44:01 PM
mitch wrote:

> Galathaea will have to offer her own reason.

The immediate thing would be to distinguish
between "reason" as in "any pissant's excuse
for spouting any bullshit" and "reason" as in
"rational thought".

I don't give a crawling fuck about ga-ga's 
excuses. As for ga-ga's rational thoughts,
I don't own a powerful enough microscope.
0
jguy (7)
2/17/2004 11:10:15 PM
mitch wrote:

>>I'll risk the superficial and probably
>>off-topic remark that the ban on mixing metaphors I believe to be a heuristic
>>slogan specific to English-language education - with corresponding dead angles.
> 
> I see.  :-)
> 
> If I understand, then I agree about dead angles.

note that english has compensations

for instance, the ease it allows to "X algebra"
- with X varying over author names etc,
up to things like "fake monster lie algebra" !

0
ruses1 (38)
2/18/2004 1:16:34 PM
Hi Galathaea,  You mentioned,
" part of me ... wants to be an evangelist for tolerance " ,

Dogmas,  such as monotheism and empiricism,
  are not the main problems today.

In 1971,  Nixon removed the dollar from the gold standard.
  The best way to measure the value of the dollar
  is the price of oil.

There was no oil crises back then ...
  There was only the bursting of the tech bubble
  and the subsequent plunge in the value of the dollar.

The same thing is happening today.

The solution is this:
  Control should be our only goal,
  not ever more consumption,  ever more GDP.

On the deck of U.S. aircraft carriers going to war,
  sailors in formation spelled out the word  " Freedom " .
  People will kill in the name of  " Freedom " .
   
But because material determinism is most probably absolute,
  our liberty,  like our gods,  are merely notional.

Because of all the  Trivial  choices that people have,
  they imagine that they have genuine freedom.
  They never stop to wonder why they don't have any
  real choices.  For example:
    Did they choose to be born ?
    Can they choose to live an active life far beyond 72 ?
    Can they choose to not breathe and yet still live ?

People are fighting for what ?  Trivial choices ?
0
me4 (19624)
2/20/2004 1:59:58 PM
Truth is neutralized (entropized)information!
Welcome to EMAH on
www.klevius.info
0
klevius (1)
2/20/2004 4:50:38 PM
"Jeff Relf" wrote:
: Hi Galathaea,  You mentioned,
: " part of me ... wants to be an evangelist for tolerance " ,
:
: Dogmas,  such as monotheism and empiricism,
:   are not the main problems today.
:
: In 1971,  Nixon removed the dollar from the gold standard.
:   The best way to measure the value of the dollar
:   is the price of oil.
:
: There was no oil crises back then ...
:   There was only the bursting of the tech bubble
:   and the subsequent plunge in the value of the dollar.
:
: The same thing is happening today.
:
: The solution is this:
:   Control should be our only goal,
:   not ever more consumption,  ever more GDP.
:
: On the deck of U.S. aircraft carriers going to war,
:   sailors in formation spelled out the word  " Freedom " .
:   People will kill in the name of  " Freedom " .
:
: But because material determinism is most probably absolute,
:   our liberty,  like our gods,  are merely notional.
:
: Because of all the  Trivial  choices that people have,
:   they imagine that they have genuine freedom.
:   They never stop to wonder why they don't have any
:   real choices.  For example:
:     Did they choose to be born ?
:     Can they choose to live an active life far beyond 72 ?
:     Can they choose to not breathe and yet still live ?
:
: People are fighting for what ?  Trivial choices ?

Hello Jeff!

Nice to see you are out here still giving the anal retentives some creative
punctuation to squirm about.  I had a yellow pepper sandwich today for
lunch.  It was really hot!

Are you feeling like a robot lately, kind of Vonnegutian?  I've seen you
mention these trivial choices a lot.

But they aren't trivial.  Butterfly wings and all that.  If you really
believe in determinism (and I think you do), embrace it emotionally!  Enjoy
the fact that your

    indentation

causes a series of events to occur which winds up challenging some internal
punctuation dogma of the new fundamentalists.  Watch it as the things you do
spread a wave of influence out into the throbbing mass of people.

There are very powerful forces out there.  Oil is certainly one of them.
Not all fights are destined to be resolved for the side we would like to
win, but that in no way implies submission.

There is something beautiful about the human drama.  Determinism only makes
it more majestic.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/20/2004 7:34:21 PM
"Morris Carr�" wrote:
: galathaea wrote:
:
: > However, there are undertones to my reasons which, although I have tried
to
: > be up front about them, have not been explored as critically as I hoped
they
: > would.  This has to do with a connection I see with a kind of
"monotheism".
: > In particular, I see a particular psychology that strives very hard to
be
: > the "most correct", and although in and of itself, that can be a very
useful
: > approach to "understanding", there are problems that often arise.  The
: > biggest problem I have seen is that I fear too many are lead to "follow"
a
: > particular set of models with a zeal unwarranted by their logical study,
: > usually I find due to the rhetoric of certain "authorities".  An example
I
: > often point to in physics is the regular attacks made against Bohmian
: > mechanics, when it merely expresses an isomorphism theorem in
mathematics
: > and does not differ in any prediction from other interpretations of
quantum
: > mechanics.
:
: I surmise you agree then that it's maybe better to accuse by the name of
: "inertia" rather than by the name of "authorities", like "inertia" is the
verb
: and "authority x" is a conjugation (this not to belittle the value of the
: existence of particular contextual proofs of inertia). Abuse of inertial
: power, would be the name of the crime. But, what if the Main Abuser is
just a
: pathological propensity of our own minds ? I'll warrant you that some
: significant ideas of God deserve Heyting.

There is a division which I do not agree is always appropriate for
identifying a person, but can sometimes be useful for identifying the way a
person thinks about a particular issue: Homo neophobus / neophilus.  There
is obviously a significant middle category that isn't thinking about the
issue at all, but they rarely interrupt the debate except to ask directions
to the restroom or whatever.  The distinction applies to how someone
approaches a problem.  Do they avoid trying to understand a new viewpoint if
it doesn't fit into their established mental model, or do they embrace the
evaluation of all models.  A model "inertia" is a perfect description, and
yes I believe it is more about the ability to change models than it is about
the choice of model sources.  You have hit on the exact point I was trying
to make concerning there being little difference between Saint Augustine or
P. A. M. Dirac for the particular point I want to make (and, just to avoid
the prognosticated misinterpretation, that is not comparing the empirical
justification of the models), but I like your words better.

I believe the gnostic monotheists have a clearer idea of the problems with a
Boolean God than expressed in the traditions through hierarchy and descent,
but I think they often are derived from a syncretism that evolved a more
panentheistic appreciation.  I don't believe some traditions would have a
problem with boulders created by a God being too heavy for the poor critter
to lift, for example.

: ...
: > wants to be an evangelist for tolerance
:
: isn't that almost pleonastic ?

In early Christianity, that was definitely a driving psychology for its
spread against more entrenched institutions, and that was very much the
image I wanted to evoke.  But I also like the modern connotations that give
the phrase a feel of the oxymoron.

-- 
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

galathaea: prankster, fablist, magician, liar


0
galathaea1 (62)
2/20/2004 8:09:31 PM
Hi Galathaea,  You greeted me with, " Hello Jeff ! " .

I use the phrase  " Hi XXX, "
  to initiate my retorts,
  it's kind of like saying,  " Start here " .
  ( Yes,  my English looks like source code )

You commented,
" Nice to see you are out here still giving 
  the anal retentives some creative punctuation 
  to squirm about. " .

I have no problem communicating with a select few,
  so it's fine with me if the others can't read it.

Re:  My ping to many people in Sci,physics,
  asking what they had to eat that day,
  ( To see who was lurking ) ,
You answered,
" I had a yellow pepper sandwich today for lunch. 
  It was really hot ! " .

Careful there,  my Nepalese housemate thinks
  spicy foods caused his dad to die prematurely !

Going off on a wild tangent-rant . . .
  My Asian Indian housemate gave me a series of bad checks,
  ( kited to almost 300 dollars )
  and he has since disappeared for almost a week now.
  And while he's a lavish-spending trust fund baby ...
  In all of 2003,  I earned less than 3 thousand,
  and I spent less than 4 thousand ...
  thus wiping out my meager savings.

Re:  My statement that people only have trivial options,
  pseudo options really,
  and how they shouldn't be fighting over such  " Freedoms ",
You asked,
" Are you feeling like a robot lately,
  kind of Vonnegutian ?
  I've seen you mention these trivial choices a lot. " .

Yea,  I realize that I'm being extremely repetitive.
  Once you've read my June 1991 post,
  you pretty much know everything I have to say.
  So I don't blame anyone for not responding.

Re:  My profound notion that
  we are all just prisoners of fate,
  playing jailhouse games,  trivial games.
You commented,
" But they aren't trivial.  Butterfly wings and all that.
  If you really believe in determinism 
  ( and I think you do ) ,  embrace it emotionally !
  Enjoy the fact that your indentation causes 
  a series of events to occur which winds up 
  challenging some internal punctuation dogma 
  of the new fundamentalists.  
  Watch it as the things you do spread 
  a wave of influence out into 
  the throbbing mass of people. " .

Wow,  you really are a fabulist  ( fablist ? ) .

But I could never,  with good conscience, 
  exploit the limits of my knowledge 
  in order to confabulate delusions of grandeur.

No,  I'm just my tiny set of ideas,
  confined to my tiny piece of space-time.
  " My "  ideas were locally passed on to me, 
  only to be locally sent on to others.
  I am profoundly a product of my society ...
  So there are millions of people just like me.

Re:  How I think that intolerance is caused
  by people who can't control their consumption,
  people who place too high a value on notional freedoms,
You replied,
" Not all fights are destined to be 
  resolved for the side we would like to win,
  but that in no way implies submission. " .

Like it or not,
  when it comes to the stuff that  Really  matters,
  we all are forced to submit.
0
me4 (19624)
2/21/2004 5:18:16 AM
Why are you crossposting this b.s. to sci.lang? Followups set.
-- 
Peter T. Daniels                       grammatim@att.net
0
grammatim (38)
2/21/2004 12:12:08 PM
"Peter T. Daniels" <grammatim@worldnet.att.net> writes:

> Why are you crossposting this b.s. to sci.lang? 

Hey, it's not exactly on-topic in comp.lang.functional, either!

> Followups set.

Ditto.

-kzm
-- 
If I haven't seen further, it is by standing in the footprints of giants
0
ketil (99)
2/21/2004 4:50:49 PM
galathaea wrote to: comp.lang.functional, sci.lang, sci.physics,
   sci.psychology.theory, and alt.philosophy -

> "Jeff Relf" wrote:
....
> : Because of all the  Trivial  choices that people have,
> :   they imagine that they have genuine freedom.
> :   They never stop to wonder why they don't have any
> :   real choices.  For example:
> :     Did they choose to be born ?
> :     Can they choose to live an active life far beyond 72 ?
> :     Can they choose to not breathe and yet still live ?

> Hello Jeff!
> 
> Nice to see you are out here still giving the anal retentives some creative
> punctuation to squirm about.  I had a yellow pepper sandwich today for
> lunch.  It was really hot!
> 
> Are you feeling like a robot lately, kind of Vonnegutian?  I've seen you
> mention these trivial choices a lot.

Dear gentlemen,

I must say that I don't understand why do you insist on limiting this
highly intellectual and productive exchange just to 5 newsgroups. I believe
that several fellows much less intelligent than you discovered that the
Art of Wisdom consists in sending such inspiring and deep postings to
at least 26 newsgroups, together with all the private addresses of all
effective and potential contributors...

I follow *ONLY* comp.lang.functional among mentioned groups. Oh, how grateful
am I that you haven't forgotten us. Yellow pepper sandwiches together with
breathing without living or vice versa is *JUST* what we need in order to
push our little domain a bit forward, to understand the true meaning of the
word "functional".

Thank you very much. I am convinced now that all you not only have an immense
methodological talent, but that you *deeply respect* other people's pursue of
knowledge and of happiness. I regret only that because of understandable modesty
many of you protect your private identities by pseudonynyms and fake addresses,
otherwise I wouldn't hesitate to send you my private generous thanks.

Please continue! Don't let anybody discourage you. Don't believe those nasty
voices who impute that you exploit newsgroups like some poor guys use the
voice recorder of a psychiatrist. I have heard worse lies, for example that
these multi-group discussion is a kind of artistic activity for mentally
desequilibrated people, who expressing themselves in such a way, before a wide
audience, calm themselves internally.

This cannot be true. But if (in which I personally don't believe, of course),
then we are happy being able to help you. Don't forget functional programmers!
As Jeff Relf says in another posting, even more deep:

 >  when it comes to the stuff that  Really  matters,
 >  we all are forced to submit.

So, continue your submissions.

Jerzy Karczmarczuk

0
karczma (331)
2/23/2004 8:57:33 AM
Hi Jerzy Karczmarczuk,

I'm not at all anonymous,
  I've only used just one handle since 1993.
  My spam intolerant NNTP server is  Individual.NET .
  And they recommend the  Me@Privacy.NET  address.

My real e-mail address is:  Jeff - Relf @ NCPlus . NET

The  XRef:  line is one of the XOVER headers,
  so you can quite easily block all posts from Sci.Physics .

In my newsreader,  40tude Dialog,
  the scoring looks like this:
    =-1  XRef  "Sci.Physics"
0
me4 (19624)
2/23/2004 9:34:43 AM
Jerzy Karczmarczuk wrote:

> Dear gentlemen,
 
> I must say that I don't understand why do you insist on limiting this
> highly intellectual and productive exchange just to 5 newsgroups.

Well met, Pan Karczmarczuk (sorry, I am afraid I got the vocative
of "Pan" wrong again).

I am all for spilling onto... er... whatsat again?
alt.playboy.pussy.binaries or whatever. 

At least, we might get some follow-ups worth having a look at.
0
jguy (7)
2/24/2004 4:04:30 AM
"galathaea" <galathaea@excite.com> wrote...
> I had a yellow pepper
> sandwich today for lunch.  It was really hot!
Personnellement hier j'ai bouff� un petit a�oli 
de derri�re les fagots l�, et j'vous RACONTE PAS
le jour d'huy le remugle *m�phitique* que j'exhale,
tous mes coll�gues de bureau sont raide morts !
0
y.euldede (1)
2/24/2004 12:43:52 PM
Reply: