Helmut, John,Jon, List You have made a wise decision ... Stopping would be better ...😊
Ok... In terms of "dependency," "determinations" or "involutions," or "objects of thought" and even "categories, I made too many concessions to Cerberus ... Indeed I do not even need to call "objects of thought" the objects Ai and "determinations" the successive arrows, nor do I need to name the relationships between categories that I could just note Xà Yà Z, or even as a result call protosigns these formal constructions. In doing so I wanted to anticipate their ability to give form to Peirce's empirical proposals on the functioning of signs in human minds and even in other fields. I thought about improving the acceptability of my approach and apparently I did not succeed. I understood that this made me enter prematurely in the battlefield of the choices of trichotomies, the correct definition of the sign (in this respect I must recall that I published 76 from CP, NEM, MS and LW still available on peirce.org), etc ... Etc... So I should point out that if we consider two abstract categories X à Yà Z on the one hand A1 à A2 à A3 …… à An on the other hand (with all axioms checked for the composition of the arrows) It is found that there are exactly (n + 2)*(n +1)/2 covariant functors from the first to the second and that, moreover, this set of functors is naturally organized in a lattice structure by the natural transformations of functors that we know how to define on this set. A computer tool can do that very well (patrick-benazet.chez-alice.fr/treillis_en_ligne/lattices) This lattices are compounds mathematical objects, not very complex if n not too large ... Indeed for n = 3 there are 10 functors, 28 for n = 10, 66 for n = 10 ... If I take up the Peirce's classification of sciences that John Sowa has emphasized above: JS > "This quotation is important for understanding his 1903 classification. It shows that the empirical aspects of science require mathematics to interpret experiences in the phaneron." these objects are part of the"*ideal constructions without reference to their real existence,**" of the mathematics …"* Now, as soon as we see that Peirce is proposing after years of studying the functioning of: - *phenomena* (phanerons) in human minds that he reduces to 3 major categories (corroborated by a reduction theorem: Herzberger, Burch, Marty), between which he recognizes relationships of involution - and also *signs* in social life,starting with three-item signs that he calls Object, Sign and Interpretant, of which a very large number includes the term "determines" (it appears 76 times - it is a coincidence - in the 76 definitions of the sign) and that he classifies them into ten classes, and then when the sign expands to six elements with 28 classes, ... - and even that it highlight*s affinities* between the signs that direct attention to relationships between classes of signs by triplets between these elements then, and only then are you justified in saying that these forms you have built are the ones to which he refers in the second part of his classification: *"Empirics, the study of phenomena with the purpose of identifying their forms with those *mathematics* has studied*," >From then on you can have an instrument of knowledge to study the practices of communication and meaning: *"Pragmatics, the study of how we ought to behave in the light of the truths of empirics.*" ((NEM, vol.IV, p. 1122) Le mer. 29 avr. 2020 à 22:56, robert marty <[email protected]> a écrit : > Thank you John for this information. I believe that a reassessment of the > importance of mathematics in Peirce's work must be obtained from the > community of Peirceans. > As for Hegel's mathematical competence, Peirce was not very charitable : > "He has usually overlooked external Secondness, altogether. In other > words, he has committed the trifling oversight of forgetting that there is > a real world with real actions and reactions. Rather a serious oversight > that. Then Hegel had the misfortune to be unusually deficient in > mathematics. He shows this in the very elementary character of his > reasoning. " (CP 1.368) > > Robert > > Le mer. 29 avr. 2020 à 20:48, John F. Sowa <[email protected]> a écrit : > >> Jon and Robert, >> >> This issue illustrates an important point about Peirce's development. >> His ideas were constantly "growing" (Peirce's own word), and he kept >> revising his terminology as he continued to find new ways of relating his >> ideas to one another and to the common vocabulary of his day (much of which >> he defined for the Century Dictionary). >> >> JAS> That passage is from R 1345, dated c. 1896, and thus was written >> several years prior to Peirce's much more comprehensive classification of >> 1903. It seems to me that empirics became phenomenology >> >> Yes, but it does not contradict what he wrote in 1896. Unless Peirce >> explicitly rejects something he wrote earlier, we must consider it a valid >> aspect of his thought. And we should try to understand what differences, >> if any, there may be in the different choices of words. >> >> Instead of saying that empirics became phenomenology, it's better to say >> that empirics, phenomenology, and phaneroscopy are three related, but >> slightly different ways of talking about closely related issues. >> >> RM> I always thought that the most peircean of the classifications of >> sciences was this one : >> >> CSP> *Mathematics* the study of ideal constructions without reference to >> their real existence, Empirics, the study of phenomena with the purpose of >> identifying their forms with those *mathematics* has studied, Pragmatics, >> the study of how we ought to behave in the light of the truths of >> empirics." (NEM, vol.IV, p. 1122) >> >> This quotation is important for understanding his 1903 classification. >> It shows that the empirical aspects of science require mathematics to >> interpret experiences in the phaneron. >> >> And the passage from 1896 should be compared with R602, which Peirce >> wrote a few years after 1903. In R602, Peirce goes back to the issues >> about the role of mathematics. (See http://jfsowa.com/peirce/r602.htm ) >> >> A comparison of the 1896 version with the later two shows the differences >> and the similarities between Peirce's views and Hegel's. >> >> Husserl, by the way, earned his PhD in mathematics. In his book on >> diagrammatology, Frederik Stjernfelt showed many of the similarities >> between Peirce's phaneroscopy and Husserl's version of phenomenology. I >> strongly recommend Stjernfelt's book for its insights into the ways that >> two mathematicians addressed closely related issues. >> >> John >> >
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