In analytic philosophy, the term anti-realism is used to describe any position involving either the denial of an objective reality of entities of a certain type or the denial that verification-transcendent statements about a type of entity are either true or false. This latter construal is sometimes expressed by saying "there is no fact of the matter as to whether or not P." Thus, we may speak of anti-realism with respect to other minds, the past, the future, universals, mathematical entities (such as natural numbers), moral categories, the material world, or even thought. The two construals are clearly distinct and often confused. For example, an "anti-realist" who denies that other minds exist (i. e., a solipsist) is quite different from an "anti-realist" who claims that there is no fact of the matter as to whether or not there are unobservable other minds (i. e., a logical behaviorist).
Anti-realism in philosophy
The term was coined by Michael Dummett, who introduced it in his paper Realism to re-examine a number of classical philosophical disputes involving such doctrines as nominalism, conceptual realism, idealism and phenomenalism. The novelty of Dummett's approach consisted in seeing these disputes as analogous to the dispute between intuitionism and Platonism in the philosophy of mathematics.
According to intuitionists (anti-realists with respect to mathematical objects), the truth of a mathematical statement consists in our ability to prove it. According to platonists (realists), the truth of a statement consists in its correspondence to objective reality. Thus, intuitionists are ready to accept a statement of the form "P or Q" as true only if we can prove P or if we can prove Q: this is called the disjunction property. In particular, we cannot in general claim that "P or not P" is true (the law of Excluded Middle), since in some cases we may not be able to prove the statement "P" nor prove the statement "not P". Similarly, intuitionists object to the existence property for classical logic, where one can prove , without being able to produce any term t of which φ holds.
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