more from Gottlob Frege

Single Idea 13608

[catalogued under 6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism]

Full Idea

Frege's logicism is the theory that mathematics has no special axioms of its own, but follows just from the principles of logic themselves, when augmented with suitable definitions.

Gist of Idea

Mathematics has no special axioms of its own, but follows from principles of logic (with definitions)


report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by David Bostock - Intermediate Logic 5.1

Book Reference

Bostock,David: 'Intermediate Logic' [OUP 1997], p.191

A Reaction

Thus logicism is opposed to the Dedekind-Peano axioms, which are not logic, but are specific to mathematics. Hence modern logicists try to derive the Peano Axioms from logical axioms. Logicism rests on logical truths, not inference rules.