Bernard (nice to hear from you), Robert, list, BM: As to the length your paper makes me shift in opinion : 3, 6 or 10 is probably a question of the required accuracy for the expected usage of the generated sign classes
-- A nice observation, Bernard. Robert, Is this what I ought to or could have drawn from your math. category theory? best, Auke > Op 10 mei 2020 om 16:42 schreef Bernard Morand <[email protected] > mailto:[email protected] >: > > > Robert and list > > I break the silence of retirement to thank you for your excellent proof > about the sign classes. > > I like proofs by induction because their simplicity throw out > definitively any doubt off the subject matter. > > Being given a chain of successive determinations of sign features, being > given the ordering of the three peircean phaneroscopic categories, the > number of the resulting classes of signs (as well as their affinities in > a lattice) is ipso facto known. Then the length of the sign features at > hand, be it 3 (triad) or 6 (hexad) or 10 enters as a parameter into the > calculation. > > But I think that basing your proof on the properties of mathematical > category theory makes room to go a little bit further, namely passing > from what you call "protosigns" to the signs themselves. First we have > to fix the length and the succession of the Ai objects chain. As to the > length your paper makes me shift in opinion : 3, 6 or 10 is probably a > question of the required accuracy for the expected usage of the > generated sign classes (I was more inclined to think that it was a > doctrinal question before having seen it as a "parameter"). The method > of separating two categories in order to apply functors from the one to > the other makes also things clearer I think. > > Then, there remain the question that has bothered me for many years now > : what was the motive of Peirce for inventing what he called "My second > way of dividing signs" into 66 classes ? I remain convinced that he was > creating his own machine, a workbench, in order to test the sign theory > by means of the phanerons observed in the so called real world. And more > broadly the relevance of the three categories themselves. > > This program has not yet been undertaken as far as I know. But your > work, Robert, makes it conceivable. > > Thanks > > Bernard > > Le 09/05/2020 à 16:12, Jon Awbrey a écrit : > > > > This is sequence No. A000217 ( https://oeis.org/A000217 ) > > in The On-Line Encyclopedia of Integer Sequences, > > N.J.A. Sloane (ed.), https://oeis.org/ > > See: https://oeis.org/wiki/Welcome > > > > > > > > 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 [email protected] > mailto:[email protected] . To UNSUBSCRIBE, send a message not to > PEIRCE-L but to [email protected] mailto:[email protected] with the line > "UNSubscribe PEIRCE-L" in the BODY of the message. More at > http://www.cspeirce.com/peirce-l/peirce-l.htm . > > >
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