Definitions and Mathematical Knowledge
Book Details
Format
Paperback / Softback
Book Series
Elements in the Philosophy of Mathematics
ISBN-10
1009095994
ISBN-13
9781009095990
Publisher
Cambridge University Press
Imprint
Cambridge University Press
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Jan 16th, 2025
Print length
102 Pages
Weight
168 grams
Dimensions
22.70 x 15.10 x 0.80 cms
Product Classification:
Philosophy of science
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This Element explores the philosophical role of definitions in mathematical knowledge, examining their origins, epistemic roles, and formal constraints. It explores explicit, implicit, and axiomatic definitions, and their potential to yield mathematical knowledge.
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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