[CG] Re: Precursors Of Category Theory

Precursors Of Category Theory • 5 • https://inquiryintoinquiry.com/2024/05/29/precursors-of-category-theory-5-a/ ❝A demonstration rests in a finite number of steps.❞ — G. Spencer Brown • Laws of Form David Hilbert • “On the Infinite” (1925) ❝Finally, let us recall our real subject and, so far as the infinite is concerned, draw the balance of all our reflections. The final result then is: nowhere is the infinite realized; it is neither present in nature nor admissible as a foundation in our rational thinking — a remarkable harmony between being and thought. We gain a conviction that runs counter to the earlier endeavors of Frege and Dedekind, the conviction that, if scientific knowledge is to be possible, certain intuitive conceptions [Vorstellungen] and insights are indispensable; logic alone does not suffice. The right to operate with the infinite can be secured only by means of the finite. ❝The role that remains to the infinite is, rather, merely that of an idea — if, in accordance with Kant’s words, we understand by an idea a concept of reason that transcends all experience and through which the concrete is completed so as to form a totality — an idea, moreover, in which we may have unhesitating confidence within the framework furnished by the theory that I have sketched and advocated here.❞ (p. 392). References — • Hilbert, D. (1925), “On the Infinite”, pp. 369–392 in Jean van Heijenoort (1967/1977). • van Heijenoort, J. (1967/1977), From Frege to Gödel : A Source Book in Mathematical Logic, 1879–1931, Harvard University Press, Cambridge, MA, 1967. 2nd printing, 1972. 3rd printing, 1977. • Spencer Brown, G. (1969), Laws of Form, George Allen and Unwin, London, p. 54. Resources — Precursors Of Category Theory • https://oeis.org/wiki/Precursors_Of_Category_Theory Propositions As Types Analogy • https://oeis.org/wiki/Propositions_As_Types_Analogy Survey of Precursors Of Category Theory • https://inquiryintoinquiry.com/2024/05/24/survey-of-precursors-of-category-… Regards, Jon cc: https://www.academia.edu/community/VrKAKZ cc: https://mathstodon.xyz/@Inquiry/112502692087155139