List, Following ...
*B1 *– To state the *logical order* (of the discovery), we must follow Peirce "*I am partially inverting the historical order, in order to state the process in its logical order*"(CP 5.589, EP 2:54-55, 1898), as quoted by Jon Alan Schmidt. I recall the *chronological order* observed in part A ( https://list.iupui.edu/sympa/arc/peirce-l/2021-08/msg00177.html) : 1- observation of phanerons by "phaneroscopists" who identify "candidate" forms. Peirce himself has found forms that come from his knowledge of theoretical chemistry: the "valences" of the elements. 2- for each "candidate" form found, search in the mathematical repository or creation of isomorphic mathematical forms. 3-choosing, by the scientific community involved in the discovery, of the "best form." 4-generate, by pure mathematical activity, new mathematical forms to be submitted to a new validation process. What is then the order advocated by Peirce? It is the dependencies stated in his classifications of sciences with respect to mathematics, which generates the process of the Sciences of Discovery described below: 1- Mathematics (the "good" forms found in 3 above) 2- Cenoscopy - Philosophia prima- positive science (which rests upon familiar, general experience): continuation of the "phaneroscopic" activity which may give rise to the emergence of new competing candidates. 3- Phenomenology - Phaneroscopy (1904-) - study of Universal Categories (all present in any phenomenon): Firstness, Secondness, Thirdness. Work of the phaneroscopists driven by the mathematics of the 1. *"**Phaneroscopy... is the science of the different elementary constituents of all ideas. Its material is, of course, universal experience, -- experience I mean of the fanciful and the abstract, as well as of the concrete and real. Yet to suppose that in such experience the elements were to be found already separate would be to suppose the unimaginable and self-contradictory. They must be separated by a process of thought that cannot be summoned up Hegel-wise on demand. They must be picked out of the fragments that necessary reasonings scatter*, and* therefore it is that phaneroscopic research requires a previous study of mathematics.* (R602, after 1903 but before 1908") 4 - unchanged *The chronological order 1,2,3,4 is changed to logical order: 3, 2, 1, 4.* *"Phaneroscopists" cannot constitute a category in themselves and that, since they do not study mathematics, they would be better advised to collaborate with mathematicians who have "forms in mind".* In his writings, Peirce presents his research relative to the categories either in chronological order by reporting his observations (CP 1.284, 1.286), or in a logical order by reporting the result of his observations in formal terms, in particular by reasoning by analogy with the notion of valence in chemistry (CP 1.292 ) and more formally with the monad, dyad, and triad. *"I invite you to consider, not everything in the phaneron, but only its indecomposable elements, that is, those that are logically indecomposable, or indecomposable to direct inspection.[ … ] Fortunately, however, all taxonomists of every department have found classifications according to structure to be the most important*." (CP 1.288) Depending on the context, the "phaneroscopists" will find by "pressicive" observation and/or by "abstractive hypostatization", either pure forms (expressible in mathematical diagrams) or informal "bricolage" to which mathematicians may or may not give form. One finds in particular in Categories (Peirce) - Wikipedia <https://en.wikipedia.org/wiki/Categories_(Peirce)> the following compiled table: *Name:* *Typical characterization* *As universe of experience:* *As quantity* *Technical definition:* *Valence, "adicity":* Firstness Quality of feeling Ideas, chance, possibility. Vagueness, "some." Reference to a ground (a ground is a pure abstraction of a quality Essentially monadic (the quale, in the sense of the *such*,[11] <http://en.wikipedia.org/wiki/Categories_(Peirce)#cite_note-11> which has the quality). Secondness Reaction, resistance, (dyadic) relation. Brute facts, actuality. Singularity, discreteness, “this <http://en.wikipedia.org/wiki/Haecceity> Reference to a correlate (by its relate). Essentially dyadic (the relate and the correlate). Thirdness Representation, mediation. Habits, laws, necessity. Generality, continuity, "all". Reference to an interpretant*. Essentially triadic (sign, object, interpretant*). We see that the only terms that can be linked to mathematics are "monadic," "dyadic," and "triadic." No other mathematical object is mentioned. I conclude this part B1 by quoting an article ( https://www.jstor.org/stable/40321072, 2005) widely *by Cornelis de Wall*, who says much better than I do the impossibility of relegating mathematics and mathematicians to a corner where they would devote day and night in endless deductions, while self-proclaimed "phaneroscopists" would propose specific informal bricolage without "skeleton-sets" to support them: "By defining science in terms of the activities of its promoters, Peirce's division of the sciences largely comes down to a division of labor. This attitude toward science enables Peirce to argue that it is the mathematician who is best equipped to translate the more loosely constructed theories about groups of positive facts generated by empirical research into tight mathematical models: *'The results of experience have to be simplified, generalized, and severed from fact so as to be perfect ideas before they arc suited to mathematical use. They have, in short, to be adapted to the powers of mathematics and of the mathematician. It is only the mathematician who knows what these powers are; and consequently the framing of the mathematical hypotheses must be performed by the mathematician*.' (R 17:06!) Now what constitutes a well-equipped mathematician? The three mental qualities that in Peirce's view, come into play are imagination, concentration, and generalization. The first is, as Peirce put it, *"the power of distinctly picturing to ourselves intricate configurations*"; the second is *"**the ability to cake up a problem, bring it to a convenient shape for study, make out the gist of it, and ascertain without mistake just what it does and does not involve*"; the third is what allows us "*to see that what seems at first a snarl of intricate circumstances is but a fragment of a harmonious and comprehensible whole*" (R 252:20).6 In particular the power of generalization, which Peirce believes "*chiefly constitutes a mathematician*" (R 278a:9 l ), is a difficult skill to attain. Peirce's emphasis on imagination, concentration, and generalization draws the attention away from the notion that it is the premier business of mathematics to provide proofs." In section B2, I will study how some of the most prominent Peircean have confronted this dependence of phaneroscopy on mathematics and the responses they have provided. Best regards, Robert Marty 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.
