intuitionistic logic

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intuitionistic logic

(logic, mathematics)
Brouwer's foundational theory of mathematics which says that you should not count a proof of (There exists x such that P(x)) valid unless the proof actually gives a method of constructing such an x. Similarly, a proof of (A or B) is valid only if it actually exhibits either a proof of A or a proof of B.

In intuitionism, you cannot in general assert the statement (A or not-A) (the principle of the excluded middle); (A or not-A) is not proven unless you have a proof of A or a proof of not-A. If A happens to be undecidable in your system (some things certainly will be), then there will be no proof of (A or not-A).

This is pretty annoying; some kinds of perfectly healthy-looking examples of proof by contradiction just stop working. Of course, excluded middle is a theorem of classical logic (i.e. non-intuitionistic logic).

References in periodicals archive ?
Since social history puts on its agenda the representation of social as an obligatory preliminary to understanding and identifying society, we are allowed to turn upside down the principles of explanation and to go further in the constructivist logics which inspired so many historical and sociological works in the last twenty years.