Bernard, It is so good to see you back on the list. Your contributions to list discussions have always been of interest and valued here. I'm sure I'm not alone in looking forward to your continued participation.
Best wishes always, Gary "Time is not a renewable resource." gnox *Gary Richmond* *Philosophy and Critical Thinking* *Communication Studies* *LaGuardia College of the City University of New York* On Sun, May 10, 2020 at 10:43 AM Bernard Morand <[email protected]> wrote: > 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 > > > > >
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