List, John,Gary, Jon, Jon Allan Preamble of https://www.academia.edu/42930701/Nicotine_a_semiotic_confrontation_between_life_and_death
"This study is the third moment in a scientific approach of "knowledge by models" that perfectly suits Peirce's designs in this field. Indeed, Peirce classifies science in the following way (see C.S. Peirce, 1976: NEM, vol. IV, 1122]: *- mathematics, the study of ideal constructions without reference to their real existence**,* Here are my constructions: I consider two abstract categories X àYàZ on the one hand A1 àA2 àA3 …… àAn 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 categories 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. *This part can be controlled by a mathematician no semiotician**.* A computer tool can do that very well : see 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 ... -*empirics, the study of phenomena with the purpose of identifying their forms with those mathematics has studied,* 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, 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 triadic signs that direct attention to relationships between classes of signs by triplets between these elements This justifies that the forms I have built are suitable to fulfil this condition. *This part can be controlled by a semiotician no mathematician**.* The third Peirce's classes is: - *Pragmatics, the study of how we ought to behave in the ligth of the truths of empirics."* This is what is proposed in the following analysis. It follows Peirce's recommendations but is fallible and asks to be criticized." Be waiting and best regards, Robert Marty
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