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Introduction to the History and Philosophy of Mathematical Practice in Constructing the Reals

In: Handbook of the History and Philosophy of Mathematical Practice

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  • Paul M. Livingston

    (University of New Mexico, Philosophy Department)

Abstract

The ancient problem of the relationship of the continuous to the discrete, since its discovery by the Greeks, has posed a range of immensely fruitful challenges to both philosophical and mathematical thought, leading to a variety of mathematical and conceptual innovations whose positive development actively continues today. In this brief section introduction, I selectively outline some significant moments at which this problem has provided important historical occasions for concrete mathematical innovation as well as closely linked philosophical insights, before introducing the particular contributions of the section authors to historical and contemporary research and practice into the nature and structure of the continuum, the construction of real numbers, the foundations of analysis, and the logical, set-theoretical, and computational underpinnings of the structure of continuously valued numbers in the most general sense, in both constructive and nonconstructivist contexts.

Suggested Citation

  • Paul M. Livingston, 2024. "Introduction to the History and Philosophy of Mathematical Practice in Constructing the Reals," Springer Books, in: Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice, pages 1461-1472, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-40846-5_129
    DOI: 10.1007/978-3-031-40846-5_129
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