mathematical logic deduction system, natural deduction, sequent calculus, lambda-calculus, judgment type theory, simple type theory, dependent type theory collection, object, type, term, set, element equality, judgmental equality, typal equality universe, size issues higher-order logic 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.