Jon AS, Gary R, List There is much more to say about continuity. But a preliminary discussion of the role of mathematics is essential. I changed the subject line to a quotation from NEM, p. 4.x: CSP: Philosophy requires exact thought, and all exact thought is mathematical thought. Especially, it behooves a sentimentalist to take double and triple pains to make his thought rigidly exact. For it is the nature of his cast of philosophical thought to be exceedingly dangerous if it is not bound down to a logic at least as rigid as that of Euclid... I have been bred in the lap of the exact sciences and I know what mathematical exactitude is, that is as far as I can see the character of my philosophical reasoning. Implication: The mathematics of metaphysics must be consistent with the mathematics of physics. For both sciences, the source of data is the experiences in the phaneron. The difference between them is in the kinds of questions one asks about those experiences. In every point of contact or overlap, the mathematics must be identical. The intro to NEM vol, 4 (pp. i to xxv) has many related quotations. For more discussion, see Carolyn Eisele's article "Mathematical methodology in the thought of Charles S. Peirce", https://www.sciencedirect.com/science/article/pii/0315086082901276 Peirce had a high regard for Kant, who had been strongly influenced by his study of math & physics before he wrote his famous critiques. See below for excerpts from an article on "Kant's philosophical development". Unlike Peirce, who learned mathematics from his father, Kant didn't learn much more than arithmetic until later in life. But as he learned more mathematics, his metaphysics became significantly deeper and richer. Kant's development provides further evidence for Peirce's claim that all exact thought is mathematical thought. Thinking in words is OK as a rough guide to the mathematical issues involved. But the conclusions must always be verified in terms of the mathematical details. John _________________________________________ Excerpts from "Kant's philosophical development": https://plato.stanford.edu/entries/kant-development/ Kant can be seen as defending pantheism, naturalism, evolution, cosmic expansion theory and holism, even when doing so was incompatible with an academic career... [He] was always cautious when writing on such topics... Kant's generalization unites Kepler's law of photo measurement (1604), Newton's law of universal gravitation (1697), and Coulomb's later law of electrostatic force (1785) as instantiations of the spread of energy.[15] Kant's law governs multiple forms of free radiation, not just light, gravity, and electrostatic force, but also radioactivity, radio waves, and sound. Its most famous application, in its first, Keplerian, instantiation, was Hubble's measure of the luminosity of distant variable stars (1924) which led to the discoveries of cosmic expansion and the Big Bang. Remarkable about his Newtonian conversion is not the change of heart, but the change in competence. His first publication, despite its brilliance, reveals his confusions over basic mechanics and a remedial grasp of the mathematics needed to understand Newton. His next group of works displays a firm grasp of celestial mechanics and a growing appreciation of the Principia.
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