List, My initial comment was to salute Jon Alan's message (Peirce-l - Re: [PEIRCE-L] AndrÃ(c) De Tienne: Slow Read slide 23 - arc (iupui.edu) <https://list.iupui.edu/sympa/arc/peirce-l/2021-08/msg00133.html>, with a single quote from Peirce that I thought particularly adapted to introduce the objectivity necessary to understand the current debate started with André de Tienne's slow read bellicose towards mathematics and mathematicians... I wanted to exploit the general scope, but this finally led me to a too-long text, the basis of a future article and/or book chapter. So I propose it to the debate in several parts ... a quick read, so to speak ... Here is the quote from JAS and then the part (A):
*"The only end of science, as such, is to learn the lesson that the universe has to teach it. In Induction it simply surrenders itself to the force of facts. But it finds, at once--I am partially inverting the historical order, in order to state the process in its logical order--it finds I say that this is not enough. It is driven in desperation to call upon its inward sympathy with nature, its instinct for aid, just as we find Galileo at the dawn of modern science making his appeal to il lume naturale. But in so far as it does this, the solid ground of fact fails it. It feels from that moment that its position is only provisional. It must then find confirmations or else shift its footing. Even if it does find confirmations, they are only partial. It still is not standing upon the bedrock of fact. It is walking upon a bog, and can only say, this ground seems to hold for the present. Here I will stay till it begins to give way.* (CP 5.589, EP 2:54-55, 1898)[emphasize mine] Modeling in Humanities: the case of Peirce's Semiotics. Chronological, logical and sociological aspects. A- the *chronological order* of discovery is: 1- the abstract observation of phenomena; it suggests that three categories in relation of "involvement" are candidates for a complete description of phenomena (this is the work of the "phaneroscopists" with Peirce at the forefront, of course) 2- the search in the mathematical repository for an object in strict correspondence (i.e. isomorphism) with these observations (otherwise mathematicians can create new ad-hoc objects). We find a very simple object which fulfils these conditions. It is a candidate to be the "skeleton-set" of phenomenology. It is a very simple structure of order called (Poset). 3 - the inductive phase: by going back to the phenomena provided with this abstract form, one verifies in each particular field [such as Experience (see Houser), relative predicates, psychology, etc], the relevance and the correctness of the abstract observation made in point 1. It is an implementation phase which verifies that the formal structure is well inscribed in each field of knowledge. This verification is possible thanks to the mathematical language provided in point 2, which is stripped of substance from the specificities of each of the fields in which the abstractions have been made. It is a common language that allows us to verify the universality of the first extraction (realized more than a century ago by Peirce). 4 - In the purely mathematical field, we can now generate new forms with all guarantees of universality since they are independent of any real existence. As we have a Poset, we can in this (algebraic) category of Posets, not only generate new Posets, but also benefit from all the possibilities of linking them to other mathematical structures (graphs for example). One can then proceed to"natural" (formal) extensions and then return to the abstract observations of the "phaneroscopists", starting with those of Peirce, in order to "see" (sometimes literally by observing various mathematical diagrams: Veen or representations with points and arrows) if there is the possibility of finding other skeleton-sets which would be endowed with the same utility and the same universality. This is notably the case for the 10 classes of signs, which are not only generated but are also naturally classified in a particular structure of Poset called Lattice. Peirce did not have this structure at his disposal, since it only really became established in the mathematical field in 1940 (Birkhoff). However, he had the intuition of it by identifying "affinities" (CP 2.264) between classes, thanks to which he traced diagrams which it is easy to show that they are inscriptions of the mathematical lattice in Peirce's semiotic theory.One can easily spend time on the hexadic signs and discover that this is not possible for the decadic sign as long as new observations have not shown how to classify the four new trichotomies with relations of determination. Everyone will realize that this chronological order is the one I have personally followed. But I used the "on" and not the "I", because I claim without fear of being contradicted, that any other mathematician, connoisseur of Peirce's writings or any connoisseur of Peirce who would make the effort to go towards this mathematics, certainly abstract, but not very technical, would come to the same conclusions as I did. I am the inventor (1977) in the sense that this term is used in archaeology; in fact, in archaeology, an invention is the discovery of an archaeological site or object. The term "inventor" is used to qualify the person responsible for this discovery. What I have just described is the chronology of a mathematical model of phaneroscopy and Peirce's semiotics. The "phaneroscopists", the "bricoleurs" in Lévi-Strauss' non-pejorative sense, the "informed" mathematicians, are the actors. By necessity, mathematicians have a particular role that Peirce has described with precision: "… *Thus, the mathematician does two very different things: namely, he first frames a pure hypothesis stripped of all features which do not concern the drawing of consequences from it, and this he does without inquiring or caring whether it agrees with the actual facts or not; and, secondly, he proceeds to draw necessary consequences from that hypothesis"* (CP 3.559). Honorary Professor; Ph.D. Mathematics; Ph.D. Philosophy fr.wikipedia.org/wiki/Robert_Marty *https://martyrobert.academia.edu/ <https://martyrobert.academia.edu/>*
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