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]> 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 and, just as well, at > 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. PEIRCE-L posts should go to [email protected] . > ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to [email protected] with > UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the > body. More at https://list.iu.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.
_ _ _ _ _ _ _ _ _ _ ARISBE: THE PEIRCE GATEWAY is now at https://cspeirce.com and, just as well, at 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. PEIRCE-L posts should go to [email protected] . ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to [email protected] with UNSUBSCRIBE PEIRCE-L in the SUBJECT LINE of the message and nothing in the body. More at https://list.iu.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.
