Re: [PEIRCE-L] How do we formalize the triadic sign?

2024-05-06 Thread Jerry LR Chandler
Robert; List- > On Jan 8, 2024, at 9:18 AM, robert marty wrote: > > You know very well that we don't mention "what goes without saying" in > mathematics. For example, when Peirce names the classes of signs, he doesn't > note that symbols are legisigns, any more than he mentions that the three

Re: [PEIRCE-L] How do we formalize the triadic sign?

2024-01-08 Thread robert marty
Jon, List, One more effort ... if you take the definition of a mathematical category, you'll see that you only need to "flatten" your diagram a little to get the category O → S → I. To do this, we'll consider the abstract category X → Y → Z with three abstract objects X, Y and Z and not two but th

Re: [PEIRCE-L] How do we formalize the triadic sign?

2024-01-08 Thread robert marty
That's okay Jerry ... I'm just trying to stay within the framework of exact philosophy as Peirce sees it : *The doctrine of exact philosophy, as I understand that phrase, is, that all danger of error in philosophy will be reduced to a minimum by treating the problems as mathematically as possible,

Re: [PEIRCE-L] How do we formalize the triadic sign?

2024-01-08 Thread Jerry LR Chandler
> On Jan 8, 2024, at 9:18 AM, robert marty wrote: > > Jerry, List > > You know very well that we don't mention "what goes without saying" in > mathematics. > Sorry, Robert. Interesting but hardly compelling response. Human communications in multidisciplinary forums such as this are open t

Re: [PEIRCE-L] How do we formalize the triadic sign?

2024-01-08 Thread robert marty
Jerry, List You know very well that we don't mention "what goes without saying" in mathematics. For example, when Peirce names the classes of signs, he doesn't note that symbols are legisigns, any more than he mentions that the three iconic signs are rhematic. Since my diagram represents a categor

Re: [PEIRCE-L] How do we formalize the triadic sign?

2024-01-08 Thread Jon Alan Schmidt
List: Here is a modified version of my EG with the two dyadic relations of determining now included. Erasing them in accordance with the usual transformation rules gives the other version of my original EG as posted on Friday, its only difference from the one below being the convention for where t

Re: [PEIRCE-L] How do we formalize the triadic sign?

2024-01-08 Thread robert marty
Ben, List You are confronted with the mathematical notion of the composition of morphisms. This notion appears as an axiom in the definition of a category. Category theory is the study of mathematical structures and their relationships. It's a unifying notion that began with the observation that m

Re: [PEIRCE-L] How do we formalize the triadic sign?

2024-01-07 Thread Jerry LR Chandler
> On Jan 7, 2024, at 9:10 AM, robert marty wrote: > > It's clear, then, that the composition of the two determinations gives rise > to the triadic relation for Peirce. That's why I've underlined "therefore." > Consequently, the formalization is simplified considerably, without any loss > of

Re: [PEIRCE-L] How do we formalize the triadic sign?

2024-01-07 Thread Jon Alan Schmidt
Ben, List: I share your concern about describing the *genuine *triadic relation of mediating (or representing) with its three correlates (sign, object, interpretant) as if it were reducible to dyadic relations of determining, which could only be true if it were a *degenerate *triadic relation. It

Re: [PEIRCE-L] How do we formalize the triadic sign?

2024-01-07 Thread Edwina Taborsky
Ben, list I remember discussions on this list about that paragraph with follows the p. 271 warning in this text “A Sign, or Representamen, is a First which stands in such a genuine triadic relation to a Second, called its Object, as to be capable of determining a Third, called its Interpretan

Re: [PEIRCE-L] How do we formalize the triadic sign?

2024-01-07 Thread Ben Udell
Hi, Robert, all, I wish a whole lot of us 15 or 20 years ago had noticed a paragraph that you quote in your message, /The conceptions of a First, improperly called an "object," and of a Second should be carefully distinguished from those of Firstness or Secondness, both of which are involv

[PEIRCE-L] How do we formalize the triadic sign?

2024-01-07 Thread robert marty
Cécile, List I present here, in the most condensed form possible, the merits of a purely algebraic formalization of Peirce's semiotics, entirely indexed to the history of its development. *How do we distinguish the correlates of a triadic sign?* *How do we formalize the triadic sign?* This q