Definitions and Mathematical Knowledge

Erscheinungsjahr 2025
ISBN: 978-1-009-51767-6
Verlag: Cambridge University Press

Buch, Englisch, 75 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 313 g

Reihe: Elements in the Philosophy of Mathematics

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.

Autoren/Hrsg.

Sereni, Andrea

Fachgebiete

• Geisteswissenschaften Philosophie Wissenschaftstheorie, Wissenschaftsphilosophie

Inhaltsverzeichnis

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.