Jon Alan, list, GF: a relation of negation can be either symmetrical or asymmetrical. I wonder which case applies to this early (1868) remark of Peirce’s: “The individual man, since his separate existence is manifested only by ignorance and error, so far as he is anything apart from his fellows, and from what he and they are to be, is only a negation” (EP1:55, CP 5.317). Either? Both? Neither?
JAS: I suggest that we interpret that particular statement in light of what comes right before it. GF: I think that goes without saying, but I don’t think your interpretation (copied below) answers the question. If the context involves “the ideal state of complete information”, then the contrast is between an ideal “individual” and an ideal “community” — not between real people and real communities. That might justify saying that the individual is absolutely and dyadically not the community, which (as I understand it) would make the negation symmetrical. On the other hand, if we interpret Peirce’s reference as being to the actual cognition of a real “individual man” rather than a logically strict individual, that would point to the asymmetry of the relation, if only because cognition takes time, and in real time the relation between past and future is asymmetrical. Even in more spatial terms, the relation between a community and a member of the community is obviously asymmetrical. As a quasi-corollary, I would say that mathematical logic which formalizes patterns in actual reasoning by omitting the time factor also eliminates the asymmetry of the antecedent-consequent relation. Whether this is true of Existential Graphs depends on how we interpret them; and how we interpret them depends (in reality) on what purpose we are using them for. By the way, my question was not intended as a terminological one, so John’s reply didn’t strike me as relevant. To me, the asymmetries of both logic and time are issues of positive science, even cenoscopy, not mathematics. As for Peirce’s proposition “Triadic Logic is universally true”, I’m still wondering what that could mean! (That there’s no such thing as falsity in Triadic Logic?) Also by the way, I corrected above the typo in my previous text (“(18)” for “(1868)”); sorry about that. Gary f. From: Jon Alan Schmidt <[email protected]> Sent: 20-Dec-20 15:30 To: [email protected] Subject: Re: [PEIRCE-L] Re: Asymmetry of Logic and Time (was multiple-valued logic) Gary F., List: I suggest that we interpret that particular statement in light of what comes right before it. CSP: Finally, as what anything really is, is what it may finally come to be known to be in the ideal state of complete information, so that reality depends on the ultimate decision of the community; so thought is what it is, only by virtue of its addressing a future thought which is in its value as thought identical with it, though more developed. In this way, the existence of thought now depends on what is to be hereafter; so that it has only a potential existence, dependent on the future thought of the community. (CP 5.316, EP 1:54-55, 1868) Note that Peirce wrote the article in which these quotes appear ("Some Consequences of Four Incapacities") at age 28, not 18. He is contrasting the individual human, "apart from his fellows," with "the community" whose collective thought would "be in the ideal state of complete information" after infinite inquiry and thus would know "what anything really is." This is the telos of the ongoing process of semiosis that Richard Kenneth Atkins calls "cognitive welding" in his 2016 book, Peirce and the Conduct of Life: Sentiment and Instinct in Ethics and Religion. To the extent that each of us suffers from "ignorance and error," we have a "separate existence" from the continuum of Truth that is represented in existential graphs by the sheet of assertion. Again, whether this "negation" is "symmetrical by composition" or unsymmetrical depends on whether excluded middle holds, such that every proposition is either true or false; and Peirce states plainly, "This assumption ... I consider utterly unwarranted, and do not believe it" (NEM 3:758, 1893). That is why "Triadic Logic does not conflict with Dyadic Logic; only, it recognizes, what the latter does not" such that "Triadic Logic is universally true" (R 339:515[344r], 1909).
_ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to [email protected] with no subject, and with the sole line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
