Theory that interprets mathematical statements as true if and only if there is a proof of them and as false just in case there is a disproof of them. Constructivism opposes the Platonist interpretation, which construes mathematical statements as referring to a domain of timeless mathematical objects existing independently of our knowledge of them (see form, Platonism). For the constructivist, certain classically valid forms of logical inference (e.g., the law of excluded middle, the law of double negation, the postulation of infinite sets) may no longer be employed unrestrictedly in constructing mathematical proofs (see logic). The constructivist therefore recognizes fewer mathematical proofs and theorems than does the Platonist. See also intuitionism.

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