Foundations of Mathematics

Mathematical and Formal Logic

What is intuitionism?

There are some people within philosophy and mathematics who reject the formalism of mathematics and believe in intuitionism, which says that words and formulas have significance only as a reflection of the mind’s activity. Intuitionists believe that a theorem is meaningful only if it represents a mental construction of a mathematical or logical entity. This is different from the classical approach that states that the existence of an entity can be proven by refuting its non-existence. For example, if you said “A or B” to an intuitionist, he or she believes that either A or B can be proved; but if you said, “A or not A,” this is not allowed, since you cannot assume that it is always possible to either prove or disprove statement A.


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