constructivism

Constructivism, in the philosophy of mathematics, is a school of thought that emphasizes mental constructions as the primary objects of mathematical discourse. Introduced by L.E.J. Brouwer, it challenges traditional mathematical principles that are considered nonconstructive and therefore meaningless. This perspective contrasts with other schools like formalism and logicism.1

A key aspect of constructivism is its objection to nonconstructive arguments, which do not explicitly show how a mathematical object is formed or proven to exist. For example, a proof might establish that an irrational number with a certain property exists without providing the specific number itself. This focus on explicit construction is central to the constructivist approach to mathematics.2