Definitions and Mathematical Knowledge

This Element provides a comprehensive analysis of the formal criteria and epistemological roles of mathematical definitions.

Andrea Sereni (Author)

9781009095990, Cambridge University Press

Paperback / softback, published 16 January 2025

102 pages
22.8 x 15.1 x 0.6 cm, 0.17 kg

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.

1. Introduction
2. Definitions and foundations
3. Explicit definitions
4. Implicit definitions
5. Primitive implicit definitions: Axioms and abstractions
6. Elucidations and explications
7. Knowledge by definition
References.

Subject Areas: Philosophy of science [PDA]