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.