> On Jul 9, 2025, at 10:23 AM, Matias <[email protected]> wrote: > > Dear Mr. Chandler, > > Thank you for your insightful question and for your comments on my original > post. I appreciate you prompting me to clarify my intentions. > > My primary interest is to understand the process of creative mathematical > reasoning. My interest in Peirce derives from this, as he proposed that > mathematical reasoning is intrinsically creative. Similarly, while I maintain > a broader interest in AI and other scientific fields for their own sake, for > the purposes of this specific discussion, my interest in them is only insofar > as they may help us to understand this process. > > What you say about chemical structure reminds me of what Emily Grosholz says > about "intelligible objects." Moreover, she explicitly compares the > intelligible objects of mathematics and the object of study of chemistry.
The poet turn of Ms Grosholz is very close to CSP’s own words: W:6, p.35 “The chemist sets up… … The procedure of the mathematician is closely analogous to this.” > > But all this is with respect to the object, and my focus is on the side of > the inquiry. In this respect, I suspect that what Peirce describes as > theorematic reasoning is similar to the way Margaret Boden describes Kekulé's > discovery of the benzene ring structure. He was working within a conceptual > space that excluded rings as possible structures, and Kekulé's breakthrough > was to propose a structure not readily conceivable within this conceptual > space. Here, the constraints have a role: first, guiding the investigation; > and subsequently, serving as a background to appreciate Kekulé's creative > idea. The necessity for a cognitive source of referential symbols / words / experimental images is needed in both cases. Note that the chemical reference system was in its infancy during CSP early years and co-matured with CSP himself and that his writings reflect this shifting foundations of meanings. Mathematical notations were well established - arithmetic as associative and distributive operations grounded computations. Chemical arithmetics was to be developed after CSP past; it was in primitive stages of development during his lifespan. > > What is disconcerting about Campos's view is that he seems to restrict the > experimentation upon diagrams to what is possible within a mathematical > system, and seems to be collapsing the object of inquiry with the particular > frames or representations from which we study it. Of course, it is very > possible that I am misunderstanding Campos. This potential misunderstanding > on the matter, particularly given my acknowledged lack of expertise in > Peirce's broader philosophy, is precisely what motivated my original > questions: first, to confirm my interpretation of his argument, and second, > to gauge the extent to which his view is representative within the > scholarship. > > Thank you again for your time and consideration. You are welcome. May I pose questions? Of what use do you seek this information? Poetry? What thoughts could be stipulated from these esoteric notions? How would semiosis be influenced by the distinction between externally grounded symbols and the internal playground of symbolic manipulations? Are you seeking syntagmata? Cheers Jerry > > Best regards, > > Matías Saracho > > > El mar, 8 jul 2025 a las 20:57, Jerry LR Chandler > (<[email protected] <mailto:[email protected]>>) > escribió: >> Hi >> >> First, are you interested serious science or merely probing the groundings >> and soundings of transformer theory? >> >> I have inserted some comments in the text that address your questions at a >> highly superficial level. >>> On Jul 8, 2025, at 10:20 AM, Matias <[email protected] >>> <mailto:[email protected]>> wrote: >>> >>> Dear List Members, >>> >>> I am interested in determining the kinds of creativity involved in >>> theorematical reasoning. For this inquiry, I am adopting Margaret Boden's >>> typology, which identifies three distinct creative processes: >>> combinatorial, exploratory, and transformational. This framework has led me >>> to consider the nature of the constraints imposed upon the transformations >>> allowed within the diagram of the premises during a theorematical >>> deduction, particularly as expressed in what Campos terms "experimental >>> hypothesis-making." In this regard, I would greatly appreciate your >>> insights on two specific questions: >>> >>> Is Campos accurate in equating "logical possibility" with "possible >>> within the mathematical system" as a constraint on the formulation of >>> experimental hypothesis-making in the following paragraph? >> >> I find this to be a bit strange. Yes, but… this is rather naive. >> >>> >>> Is it reasonable to assume that the views expressed by Campos in this >>> paragraph represent the standard interpretation of this matter within >>> Peircean scholarship? >> >> Even more strange! >> The question of “the form of the icon” allows combinatorial explosions…I >> suspect that CSP language here is addressing the very troubling issues of >> “chemical isomers", such as the mention of tartaric acids, Pasteur’s famous >> quanta objects with multiple crystalline forms/ >>> >>> Here is the citation from Campos (2010): >>> >>> "The logical possibility of the experimental diagram, within the assumed >>> mathematical framework, is a necessary condition that constrains what >>> experimental signs the imagination may submit for observation. As Peirce >>> put it generally in 1906, “that which is displayed before the mind’s >>> gaze—the Form of the Icon, which is also its object—must be logically >>> possible” (Peirce 1906b:C4.531). Logical possibility is in part a matter of >>> mathematical diagrams being subject to the normative rules of good >>> reasoning that Peirce’s logical critic prescribes, including for example, >>> for mathematical deduction, the law of the excluded middle and the law of >>> noncontradiction. But it is also a matter of what is possible to create >>> within a general hypothetical framework. As we have seen, for example, in >>> Euclidean geometry postulates affirm possibilities while axioms deny them. >>> Along with definitions, they are in fact the more general hypotheses that >>> frame a realm of possibility for mathematical investigation." (Campos, >>> 2010, The Imagination and Hypothesis-Making in Mathematics: A Peircean >>> Account, p. 337) >> >>> "As we have seen, for example, in Euclidean geometry postulates affirm >>> possibilities while axioms deny them." >> >> This is also a bit strange language. OK. Many would introduce the notions >> of axiological reasoning or some other abstractive terminology. >> >> Frankly, I can not imagine a “standard” for CSP terminology. >> At this point in history, more than a 100 years after he past, CSP’s >> writings are mostly a playground for philosophers; the scientists, logicians >> and linguistics have moved on decades ago. >> >> Just my opinions… >> >> Cheers >> >> Jerry >> >> >> >>> >>> I very much appreciate your invaluable comments. Thank you for your time >>> and consideration. >>> >>> Best regards, >>> >>> Matías Saracho >>> _ _ _ _ _ _ _ _ _ _ >>> ARISBE: THE PEIRCE GATEWAY is now at >>> https://cspeirce.com <https://cspeirce.com/> and, just as well, at >>> https://www.cspeirce.com <https://www.cspeirce.com/> . It'll take a while >>> to repair / update all the links! >>> ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON >>> PEIRCE-L to this message. 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