Nov 26, 2012
INTUITIONISM_Documented by Marsigit
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 law of excluded middle, A or not A, is disallowed since one cannot assume that it is always possible to either prove the statement A or its negation.
Intuitionism also rejects the abstraction of actual infinity; i.e., it does not consider as given objects infinite entities such as the set of all natural numbers or an arbitrary sequence of rational numbers. This requires the reconstruction of the most part of set theory and calculus, leading to theories highly different from their classical versions.