Main Page See live article Alphabetical index Intuitionism In the philosophy of mathematics intuitionism , or neointuitionism (opposed to preintuitionism), is an approach to mathematics as the constructive mental activity of humans. Any mathematical object is considered to be a product of a construction of a mind , and therefore, the existence of an object is equivalent to the possibility of its construction. This contrasts with the classical approach, which states that the existence of an entity can be proved by refuting its non-existence. For the intuitionist, this is invalid; the refutation of the non-existence does not mean that it is possible to find a constructive proof of existence. As such, intutionism is a variety of mathematical constructivism ; but it is not the only kind. Intuitionism takes the validity of a mathematical statement to be equivalent to its having been proved; what other criteria can there be for truth (an intuitionist would argue) if mathematical objects are merely mental constructions? This means that an intuitionist may not believe that a mathematical statement has the same meaning that a classical mathematician would. For example, to say A or B , to an intuitionist, is to claim that either A or B can be proved . In particular, the | |
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