Definitions and Mathematical Knowledge

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

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.