Robert, List,
I strongly agree with your approach, and I would like to add three quotations by Peirce (copied below). They show that De Tienne has misunderstood the role of mathematics in Peirce's philosophy. But I am not claiming that ADT does not understand Peirce, People were doing mathematical thinking for thousands of years before anyone knew they were doing mathematics. What they were doing is diagrammatical reasoning, which creative mathematicians, especially Peirce, have always known is the foundation for mathematics. For quotations that emphasize that point, see the first 10 slides of a talk I presented at a Peirce session at an APA meeting in April 2015 and extended for a workshop hosted by Zalamea in Bogota: Peirce, Polya, and Euclid: Integrating logic, heuristics, and geometry, http://jfsowa.com/talks/ppe.pdf In the first sentence of ADT's slide 25 (see the attached file ADT25.jpg), he belittles Peirce's life's work: "we cannot count on mathematicians to help figure out what goes on in experience." That is contrary to all three quotations by CSP. There are indeed some mathematicians (pedantic, non-creative ones) whose guidance would be unreliable. But Peirce, Polya, Euclid, Archimedes, Einstein, and others quoted in ppe.pdf aren't among them. In the second sentence, the phrase "rest of us", which is intended to exclude mathematicians, is extremely insulting to Peirce and the many mathematicians quoted in ppe.pdf. In the third sentence, the question "how do we transition" is answered by Peirce: use diagrams! Diagrams are the form of mathematics where the mathematicians and the people who claim they know nothing about mathematics share common ground. John _____________________________________ Three quotations by Peirce: 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) My trichotomy is plainly of the family stock of Hegels three stages of thought, -- an idea that goes back to Kant, and I know not how much further. But the arbitrariness of Hegel's procedure, utterly unavoidable at the time he lived, -- and presumably, in less degree, unavoidable now, or at any future date, -- is in great measure avoided by my taking care never to miss the solid support of mathematically exact formal logic beneath my feet.... (R318, 1907, p. 37) The little that I have contributed to pragmatism (or, for that matter, to any other department of philosophy), has been entirely the fruit of this outgrowth from formal logic, and is worth much more than the small sum total of the rest of my work, as time will show. (CP 5.469, R318, 1907)
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