Saturday, September 20, 2008 4:47 PM, Rob Freeman wrote:
> I would welcome comments on a possible relationship between gauge
> theories in physics, Category Theory in maths, and semantics.
Rob,
If you welcome comments it must be satisfied. (01)
If more seriously, you are raising two complex issues: the relationships of
semantics with theoretical physics, as empirical science, and fundamental
mathematics, as formal science.
To grasp how these fields interact, one need to know what semantics really
is and how it should be classified. A realistic scientific approach will
tell you that there is also theoretical semantics and empirical semantics.
First one has to know that semantics is about the relationships among three
heterogeneous entities: signs and symbols, constructs and ideas, and
objective reality (individuals, aggregates, substances, objects, states,
changes, relations) [note, they all are parts of reality]. Also, note, the
nature meaning relation, both triadic and cyclic, is analyzed by ontology.
We say: Signs Designate; Constructs Mean, with Sense, Reference and
Representation, and hence Signs Signify, where Signification is composition
of Designation and Meaning. So, if you cut the meaningful triple as a binary
relation of signs and constructs, then you restrict yourself with conceptual
semantics, as a formal semantics. Another So, in a strict sense, Semantic
Web is about Signification of web resources and non-web resources.
Empirical semantics is all about the semantics of symbols and signs, of all
sorts and kinds: natural signs and sign processes (semiosis); natural
languages; speech acts, social symbols and actions and relationships, or
cultural signs. To this domain refers natural semiotics, as biosemiotics,
linguistic semantics, psycholinguistic semantics, the arts, etc.
Theoretical semantics is all about semantics of constructs (concepts,
predicates, statements, theories), of all sorts and types: constructs in
general (general semantics), mathematical constructs (model theory),
scientific constructs (semantics of science), or commonsense knowledge
(semantics of common knowledge).
Now you can answer your question yourself, I just hint... Any good
scientific theory suggests three types of axioms, or the meaning of a theory
is mainly defined by a set of key axioms:
background assumptions (ontological concepts, axioms and rules);
mathematical axioms and rules;
factual axioms and rules;
semantic axioms, rules and assumptions. (02)
Summing up: the signification or meaning of theories, their senses,
reference and representation, intension or extension, are mainly defined by
a set of key axioms.
Semantics defines the meaning of scientific theories, physical and
mathematical, acting as a full real semantics for physical theories, like as
the gauge theories, providing representation assumptions and correspondence
rules for its constructs, like space, time, transformation, gauge group,
gauge field, rate of change, interaction, global symmetry and local
symmetry. At last, it acts as formal semantics for formal theories, like as
logical formalisms and languages, mathematical set theory or category
theory, ''abstract nonsense'', with its content, categories, objects,
morphisms, mapping, transformation, functors, altogether with their
properties. (03)
Hope this will be of some use for your further study, as well as for the
neophytes. (04)
azamat abdoullaev (05)
<What is true is also good and beautiful, pleasing and valuable; what is
false is also evil and ugly, painful and useless.> (06)
----- Original Message -----
From: "Rob Freeman" <lists@xxxxxxxxxxxxxxxxxxx>
To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
Sent: Saturday, September 20, 2008 4:47 PM
Subject: Re: [ontolog-forum] Axiomatic ontology (07)
> John,
>
> Can't see how this is relevant.
>
> It seems like you have interpreted my reference to "geometric
> theories" as a reference to our perception of space.
>
> I was thinking more of gauge theories in physics or Category Theory in
> maths.
>
> I would welcome comments on a possible relationship between gauge
> theories in physics, Category Theory in maths, and semantics.
>
> -Rob
>
> On Wed, Sep 17, 2008 at 9:34 PM, John F. Sowa <sowa@xxxxxxxxxxx> wrote:
>> Rob,
>>
>> In my 1984 book, I emphasized that both continuous and discrete aspects
>> are fundamental to perception, cognition, and reasoning. I also cited
>> Kenneth Pike's _Unified Theory of Human Behavior_ in which he showed
>> how that distinction extends to every aspect of human life.
>>
>> RF> In contrast your "pursuing" presentation
>> >
>> > http://www.jfsowa.com/talks/pursuing.pdf
>> > mentioned what you call "continuous" theories which should be
>> > seen as underlying discrete categories.
>> >
>> > Is that a change? Are you moving from a "network of theories"
>> > model to an underlying "continuous" model?
>>
>> The big brains of the primates evolved for the purpose of
>> coordinating rather heavy monkeys and apes as they swung from tree
>> to tree. It's no accident that human aviators have a remarkable
>> ability in aerial dogfights. Any of their remote ancestors who
>> didn't have good hand-eye coordination in high-speed 3-D action
>> were summarily removed from the gene pool.
>>
>> On the other hand (or brain), the purpose of perception is to
>> subdivide continuous reality into familiar percepts or concepts
>> to which well-learned responses can be applied instantly without
>> requiring lengthy chains of reasoning. The words of language
>> are naturally tied to those percepts and concepts.
>>
>> The great advance of Homo sapiens over the apes results from the
>> possibility of metalevel reasoning about those discrete units.
>> Logic is an abstraction from that aspect of language. (See my
>> next note in response to Pat Hayes.)
>>
>> John
>
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