Dear John,

I think that the text "*Modeling in Humanities: the case of Peirce's
Semiotics (Part A*)" that I just published answers your question. I
maintain that retaining a definition of the sign that does not incorporate
the internal determinations of the sign by the object and the interpreter
by the sign does not allow us to classify signs. But you can still try to
find a meaning to each of the 6 combinations of S, O, I by not using the
interdependence of the categories, which translates into the
phenomenological constraint according to which::* "It is evident that a
Possible can determine nothing but a Possible; it is equally so that a
Necessitant can be determined by nothing but a Necessitant.*" (EP2: 481).
This constraint is the only one that allows us to control the combinatory
explosion.
...
Honorary Professor; Ph.D. Mathematics; Ph.D. Philosophy
fr.wikipedia.org/wiki/Robert_Marty
*https://martyrobert.academia.edu/ <https://martyrobert.academia.edu/>*



Le sam. 14 août 2021 à 18:45, Jon Awbrey <[email protected]> a écrit :

> Cf: Semiotics, Semiosis, Sign Relations • Discussion 10
>
> https://inquiryintoinquiry.com/2021/08/14/semiotics-semiosis-sign-relations-discussion-10/
>
> Re: Semiotics, Semiosis, Sign Relations • Discussion 8
>
> https://inquiryintoinquiry.com/2021/08/13/semiotics-semiosis-sign-relations-discussion-8/
>
> Re: Category Theory
>
> https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/sign.20relations
> ::: Morgan Rogers
>
> https://categorytheory.zulipchat.com/#narrow/stream/233104-theory.3A-logic/topic/sign.20relations/near/249456735
>
> <QUOTE MR:> Please clearly state at least one “distinctive quality of sign
> relations”. </QUOTE>
>
> Dear Morgan,
>
> Sign relations are triadic relations.
>
> Can any triadic relation be a sign relation?
>
> I don’t know.  I have pursued the question myself whether any
> triadic relation could be used somehow or other in a context
> of communication, information, inquiry, learning, reasoning,
> and so on where concepts of signs and their meanings are
> commonly invoked — there’s the rub — it’s not about what
> a relation is “intrinsically” or “ontologically” at all
> but a question of “suitability for a particular purpose”
> as they say in all the standard disclaimers.
>
> What Peirce has done is to propose a definition intended to capture an
> intuitive, pre-theoretical, traditional concept of signs and their uses.
> To put it on familiar ground, it’s like Turing’s proposal of his namesake
> machine to capture the intuitive concept of computation.  That is not a
> matter to be resolved by à priori dictates but by trying out candidate
> models in the intended applications.
>
> I gave you what I consider Peirce’s best definition of a “sign”
> in relational terms and I pointed out where it needs filling out
> to qualify as a proper mathematical definition, most pointedly in
> the further definitions of “correspondence” and “determination”.
>
> That is the current state of the inquiry as it stands at this site …
>
> Regards,
>
> Jon
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