Robert, List: I think that we might have finally landed on some common ground here, as I have no major objections to what is described below as "the *chronological order* of discovery," especially since the poset (3→2→1) is rightly described as "a *candidate *to be the 'skeleton-set' of phenomenology" (emphasis mine). I look forward to seeing what is forthcoming in the subsequent "parts."
My biggest quibble so far is the ongoing attribution to André De Tienne of *hostility *towards mathematics and mathematicians, which I believe is a misreading of his actual stance. I understand his motivation (and that of this slow read) to be simply calling attention to phaneroscopy as a distinct practice, such that it is neither overlooked completely nor *conflated with* mathematics. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Sun, Aug 15, 2021 at 4:51 AM robert marty <robert.mart...@gmail.com> wrote: > 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/>* >
_ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to l...@list.iupui.edu with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iupui.edu/sympa/help/user-signoff.html . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
