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

Paul M. Livingston ()
Additional contact information
Paul M. Livingston: University of New Mexico, Philosophy Department

A chapter in Handbook of the History and Philosophy of Mathematical Practice, 2024, pp 1461-1472 from Springer

Abstract: 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.

Keywords: Continuum; Discrete; Real numbers; Incommensurability; Intuitionism; Constructivism; Plato; Leibniz; Weyl; Russell; Poincare; Dedekind (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-40846-5_129

Ordering information: This item can be ordered from
http://www.springer.com/9783031408465

DOI: 10.1007/978-3-031-40846-5_129

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().