Blackwell Reference Online

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L ogic A system of principles to formalize the types of reasoning allowed by mathematical intuitionism , after which this logic is named. It denies the principles of classical logic, which are not countenanced by mathematical intuitionism. In its most important formation, it is a calculus developed by Arend Heyting in 1930, inspired by his teacher Brouwer . It supposes that mathematical objects are products of mental operations and that the truth of a mathematical statement is its provability, that is, the mental construction that would represent a proof of it. A mathematical statement is true if and only if we have a proof of it. Accordingly, no definite truth-table can be given for its connectives because a truth-table is based on the law of the excluded middle (or the principle of bivalence ), which holds that a statement must be either true or false, whether or not we know it to be true or false. But intuitionist logic claims that if we do not have a proof of a statement or a denial that it can be proved, then we cannot say that it is true or false. Hence it rejects the law of the excluded middle as a theorem . It diverges from classical logic also by denying other laws of negation . Intuitionist logic is closely related to anti-realism , which does not admit any mindindependent truth. “What is called intuitionist logic differs from the classical two-valued ... log in or subscribe to read full text