the form of predicate calculus that reflects intuitionism’s view of the nature of logical laws acceptable, from its point of view, for proofs of propositions in those areas of the deductive sciences (especially mathematics) that are essentially related to the concept of mathematical infinity.
In accordance with the views of intuitionism, there is no law of the excluded middle or law of removal of double negation in intuitionist logic. A formal logical system constructed by the Dutch mathematician A. Heyting in 1930, which covers the predicate calculus, is usually viewed as intuitionist logic. Even earlier, based on nonintuitionist considerations, a system of intuitionist logic as applied to the propositional calculus, a part of predicate calculus, was constructed by the Soviet scholar V. I. Glivenko. Heyting’s intuitionist logic is distinguished in that the content of the reasoning expressed in it is acceptable from the point of view of the intuitionism of the Dutch mathematician L. E. J. Brouwer.
With the development of constructivist schools in mathematics and logic, intuitionist logic was applied in these fields and therefore was frequently called constructive logic, although certain constructivist principles recognized by many representatives of these schools are absent in intuitionist logic, for example, the principle of constructive selection, introduced by the constructivist school headed by the Soviet mathematician A. A. Markov.