Philosophy of Logic & Mathematics · The status of mathematical objects

Mathematical Intuitionism / Constructivism

Mathematical existence requires construction, and truth is understood through proof.

What it claims

Intuitionism grounds mathematics in constructive activity rather than an independently completed domain of objects. It rejects an unrestricted appeal to truth beyond possible proof, including universal bivalence and unrestricted excluded middle. Brouwer treats mathematics as mental construction prior to language: claiming existence requires a construction, rather than only a nonconstructive argument that nonexistence would be contradictory.

Nearby positions

Key thinkers

L. E. J. Brouwer · Arend Heyting · Michael Dummett · Errett Bishop · Per Martin-Löf