Reflections on the Axiomatic Approach to Continuity

John L. Bell
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John L. Bell: University of Western Ontario

Chapter Chapter 5 in Axiomatic Thinking II, 2022, pp 131-143 from Springer

Abstract: Abstract In Hilbert’s paper “Axiomatic Thinking”—the published version of his 1917 Zürich talk - he touches on the axiomatic treatment of continuity and, as he puts it, “the dependence of the propositions of a field of knowledge on the axiom of continuity”. By the “axiom of continuity”, Hilbert seems to mean a number of things. In this paper I speculate on the various meanings Hilbert may have ascribed to the term. I focus in particular on interpreting the “axiom of continuity” as the central principal of Synthetic Differential Geometry that all real functions are smooth.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-77799-9_5

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DOI: 10.1007/978-3-030-77799-9_5

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