nLab formalism

Context

Philosophy

Foundations

foundations

The basis of it all

 Set theory

set theory

Foundational axioms

foundational axioms

Removing axioms

Contents

Idea

Formalism is one of the classical schools of the philosophy of mathematics. Under this view, “mathematics is (better understood as) not a body of propositions representing an abstract sector of reality but is much more akin to a game, bringing with it no more commitment to an ontology of objects or properties than playing ludo or chess are normally thought to have”.

Formalism focuses on deduction rather than internal mathematical objects such as numbers, types, sets (material or structural), or categories.

David Hilbert was a famous proponent of formalism.

Last revised on August 20, 2026 at 16:30:32. See the history of this page for a list of all contributions to it.