Re: [PEIRCE-L] Pragmatic Semiosis and Mathematical abduction
Gary F and Jerry, A computer theorem prover that generates all possibilities and systematically eliminates (by deduction) the ones that generate contradictions could be called an abduction machine. GF: In the present context, this would imply that abduction is essentially mathematical, or at least that inquiry begins in the hypothetical realm. JLRC: Abduction is necessary for calculating the number of possible arrangements IN SPACE of the parts of the whole. Statistically, it generates the potential arrangements in space. This mathematical calculation of abduction is a logical function of the indices of sin-sign. I agree with both of you. But there's a difference between a machine and a well-informed human: The human uses insight (Thirdness) that can drastically reduce the blind search time. For small finite cases, the blind search by the computer can be far faster than the intelligent human. But humans can outperform computers in searches through large or even infinite spaces. Example: Self-driving cars outperform humans on limited-access highways where the computer has been trained on nearly all the options that might occur. But the average human is better in recognizing unusual cases on city streets where the number of possibilities is immense. In any case, this is just one of many cases where it's essential to distinguish (a) mathematics as the infinite totality of all patterns and teories about them, (b) the people who discover mathematical theories, and (c) the application of mathematics in other theoretical and practical sciences. John _ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations
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 Please clearly state at least one “distinctive quality of sign relations”. 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 _ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
Re: [PEIRCE-L] Semiotics, Semiosis, Sign Relations
Cf: Semiotics, Semiosis, Sign Relations • Discussion 9 http://inquiryintoinquiry.com/2021/08/14/semiotics-semiosis-sign-relations-discussion-9/ 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/248952679 Okay, I may have mixed up the meanings of “object” and “interpretant” in my plain language translations above? Re determination, I read “B is determined by A” as meaning the conjunction of ∀a ∈ A, ∃b ∈ B, ∃c ∈ C, R(a,b,c) and ∀a ∈ A, ∀c ∈ C, R(a,b,c) ∧ R(a,b',c) ⇒ b = b' ? Whether this is right depends on the answers to my previous questions. Dear Morgan, Let's look at the gloss I gave for Determination under the Definition ( https://oeis.org/wiki/Sign_relation#Definition ) of a Sign Relation ( https://oeis.org/wiki/Sign_relation ). • Determination. Peirce's concept of determination is broader in several directions than the sense of the word that refers to strictly deterministic causal-temporal processes. First, and especially in this context, he is invoking a more general concept of determination, what is called a formal or informational determination, as in saying “two points determine a line”, rather than the more special cases of causal and temporal determinisms. Second, he characteristically allows for what is called “determination in measure”, that is, an order of determinism that admits a full spectrum of more and less determined relationships. Other words for this general order of determination are structure, pattern, law, form, and one coming up especially in cybernetics and systems theory, constraint. It's what happens when not everything that might happen actually does. (The stochastic mechanic or the quantum technician will probably quip at this point, “At least, not with equal probability.”) Regards, Jon _ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
