JOURNAL ARTICLE

A.C. Paseau and Wesley Wrigley  The Euclidean Programme.

  • Published In: Philosophia Mathematica, 2025, v. 33, n. 1. P. 112 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Hellman, Geoffrey 3 of 3

Abstract

The article focuses on the examination of the Euclidean Programme (EP), which represents a traditional form of epistemological foundationalism in mathematics, emphasizing knowledge derived from self-evident axioms. It discusses the historical roots of the EP, its principles, and its relevance to contemporary mathematics, particularly in relation to the axiomatic method. The authors critique the requirement for axioms to be "self-evident," highlighting challenges posed by specific axioms like the parallel postulate and mathematical induction. The article concludes with a proposal for a modern replacement of the EP, suggesting that axioms should be "evident on a conception," using the Axiom of Infinity as a key example. [Extracted from the article]

Additional Information

  • Source:Philosophia Mathematica. 2025/02, Vol. 33, Issue 1, p112
  • Document Type:Article
  • Subject Area:Mathematics
  • Publication Date:2025
  • ISSN:0031-8019
  • DOI:10.1093/philmat/nkae021
  • Accession Number:185320532
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