Auke, Bernard, List
I do not know if I understood where the reluctance was. It seems to me that
I may have to make some clarifications that will lead to avoid the
misunderstandings for which I am solely responsible.
1- Category theory lives its life independently of Peirce's semiotics.
However one can define a simple mathematical objects that are the functors
of a chain (considered as a algebraical category) of abstract objects
without name (and I was probably wrong to call them "objects of thought"
right away because I thought it's a way not to stray too far from Peirce =
"a cake for Cerberus"?) in another chain yet simpler of length 3 with three
objects rated 3.2,1 (which I should have called X, Y,Z = a second cake ...)
and also the natural transformations of (n +2)* (n +1)/2 functors that
allow to build a new category (a category of functors) that is also a
lattice. All of these terms are defined in Wikipedia at the top of the
corresponding pages.
2 - This being done I find that in his empirical research on signs Peirce
has used such chains only for n = 3, 6 and 10 ... but these are chains of Oà
Sà*I* for n = 3, OdàOiàSà.... etc.. (I don't care what we put in the suite
and the corresponding debates) ... et aussi que ces 3 categories
universelles sont ordonnées dans une chaîne 3à2à1 presuppositions (or
involutions, whatever)… from there it is obvious that abstract objects I
have built are the forms of these classes of signs... and whatever
Peirce's signs they are structured by these abstracts constructions ...
That's why I've consistently used Peirce's quote about the classification
of sciences, which he divides into:
"- mathematics, the study of ideal constructions without reference to their
real existence
-empirical, the study of phenomena in order *to identify their
forms with these mathematics studied*-
- Pragmatic, studying how we should behave in the ligth of
empirical truths."
(see C.S. Peirce, 1976: NEM, VOL. IV, 1122])
So I observed the first two steps of the research and I produced the study
on nicotine to show that we could tick the third... I showed this in more
detail at the beginning of this study.
I hope I have given the right clarifications otherwise I am ready to look
at the matter again...
Best,
Robert
Le dim. 10 mai 2020 à 18:14, <[email protected]> a écrit :
> 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]>:
>
>
> 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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