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Series:   Elements in the Philosophy of Mathematics

Definitions and Mathematical Knowledge

Published online by Cambridge University Press:  05 December 2024

Andrea Sereni
Andrea Sereni
Affiliation:
Scuola Universitaria Superiore IUSS Pavia

Summary

This Element discusses the philosophical roles of definitions in the attainment of mathematical knowledge. It first focuses on the role of definitions in foundational programs, and then examines their major varieties, both as regards their origins, their potential epistemic roles, and their formal constraints. It examines explicit definitions, implicit definitions, and implicit definitions of primitive terms, these latter being further divided into axiomatic and abstractive. After discussing elucidations and explications, various ways in which definitions can yield mathematical knowledge are surveyed.
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Keywords

mathematical definitionsaxiomsabstraction principlesfoundations of mathematicsmathematical knowledge
Type
Element
Information
Series: Elements in the Philosophy of Mathematics
Online ISBN: 9781009091084
Publisher: Cambridge University Press
Print publication: 16 January 2025

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Definitions and Mathematical Knowledge
  • Andrea Sereni, Scuola Universitaria Superiore IUSS Pavia
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Definitions and Mathematical Knowledge
  • Andrea Sereni, Scuola Universitaria Superiore IUSS Pavia
  • Online ISBN: 9781009091084
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