Re: Reply to Edwinia's View of Categories Re: Q1-6 comments

This will be my second (and therefore final) post to FIS of this week.
I'll reply to Jerry's comments. By the way, my name is Edwina not
Edwinia. (minor point but scientific attention to details does
matter).

Jerry said:
> Why is category theory a tetradic framework?
>
> A category operates, at a *minimum*, on four objects (domains and
> codomains) and three morphisms linking them to one another. Roughly
> speaking, a category operates concomitantly on three dyadic
> frameworks, two triadic frameworks and one tetradic framework.
>
> For example,
>
> *IF* one chose to define Pierce's "firstness", "secondness" and
> "thirdness" as morphisms ,
> *then* one could (possibly) construct a correspondence relation
> between the semantics of firstness, secondness and thirdness
> *and* the nature of the morphisms of a category.

Again, I disagree with the above images. First- you still have only
two 'realities': objects and morphisms linking the objects. That's
dyadic.
Second, what do you mean by a 'correspondenc relation between Peirce's
Firstness, Secondness and Thirdness Relations and category morphisms?
Remember, these Peircean actions are Relations and are each completely
different from the other. They can't be reduced to each other, and you
can't have a robust semiosic process without all three relations. And
these are Relations, not morphic categories.

Jerry said:
> Secondly, at issue is the nature of the four objects as related to
> the three morphisms. A precise logical relation within a category
> exists between the four objects and the three morphisms such that a
> logic coherence is generated among the four objects and three
> morphisms. (For an introductory text on categories, see the book by
> Lawvere, Conceptual Mathematics.)

I have the same concern: objects and morphisms. That's a dyad, no
matter how many objects and how many morphisms.

Jerry said:
> For example, in certain cases, the objects of a category can be
> logical propositions.

I have no problem with an object being a proposition. After all,
semiotics is essentially a logical process.

Jerry said:
> In another example, I have recently succeeded in developing a model
> of chemical species directly from the metaphysical primitives of
> matter, identity, space and time. Thus it became possible to
> construct an organic theory of communication based on an organic
> species as a mathematical species as alluded to within my abstract.
> This allows one to contrast it with the Shannon engineering approach
> (which is purely a formal syntactical structure without meaning).

I am presuming that these four: matter, identity, space and time are
NOT your four objects as stated above. I don't see how you can
separate them. I don't see that matter can exist without identity, and
that includes spatial and temporal paremeters. The point to the
Shannon approach is that it specifically tries to prevent the 'given
matter' from having any further relations. I think that that given
matter (the bit that is being transported) does have meaning - but
it's a frozen meaning that is not allowed to change.

Jerry:
> Tensions between the concepts of semiotics, semantics and syntax are
> related to the question of structure and the relations among such
> structures.

I think these terms: semiotics, semantics and syntax have little
relevance to each other and are hang-ons from the old period when
semiotics referred to literature and language. I think these terms
muddy things up now. A genuine semiotics must operate within a
'structure' (in literature/language, structure is called a syntax).
This structure is Thirdness, the normative habits. A genuine semiotics
must also generate meaning, ie, it must process energy/matter such
that this energy/matter can enter into relations with other
energy/matter. As such, this energy/matter is 'informed'; it is an
interpretant; it is information. The linguistic term for
interpretation or meaning is 'semantics'. So, the fact that you use
these three terms and separate them - semiotics, semantics
(interpretant) and syntax (normative habits). ...Well, I think that
these three terms ignore that semiotics IS a triadic process that
operates within a logical habitus (its 'structure', its syntax) and a
process of interpretation (its semantics). So- I simply don't see what
your use of the term 'semiotics'....separated from normative habits
and interpretation...ends up meaning.

Jerry said:
> Within category theory, one has substantial "logical space" to
> associate semiotic concepts with semantic concepts and with
> syntactical concepts. The above example illustrates an approach to
> resolving the tensions between semiotics and mathematical syntax in
> terms of associated structures of a category.

And that's exactly what I am talking about. I don't know what
semiotics means to you, Jerry, but the fact that you set it up as a
single term used along with the two other terms of semantics and
syntax means that its meaning has absolutely nothing to do with the
semiotics that I use. And I'm not a 'rogue' semiotician. The semiotic
process is triadic; it must develop a set of normative habits (again,
in language- called a syntax); to process the input-energy and
transform it to an interpretant (in linguistic terms, 'semantics').
The continued use of linguistic terms with semiotic terms ...simply
confuses everything.

Jerry said:

Let me close with a note of caution.
> Category theory is a theory of mathematics. Application of category
> theory to scientific questions is a very challenging undertaking
> because of its abstractness and the complex origin of its coherence.

I
ll second the note of caution. But- I'll say that semiosic theory is a
logical process and its application to science is challenging - but -
as you might see from the papers published using semiotics as applied
to science - it is highly productive.

That's it for the week. And I'm away next week.
Received on Tue Jul 9 19:41:04 2002