Editing Anti-realism (section)

=== Semantic anti-realism ===
{{main|Semantic anti-realism (epistemology)}}
The term "[[Semantic anti-realism (epistemology)|anti-realism]]" was introduced by [[Michael Dummett]] in his 1963 paper "Realism" in order to re-examine a number of classical philosophical disputes, involving such doctrines as [[nominalism]], [[Platonic realism]], [[idealism]] and [[phenomenalism]]. The novelty of Dummett's approach consisted in portraying these disputes as analogous to the dispute between [[intuitionism (philosophy of mathematics)|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 Platonic realists, the truth of a statement is proven in its correspondence to [[Objectivity (philosophy)|objective]] reality. Thus, intuitionists are ready to accept a statement of the form "P or Q" as true [[Disjunction and existence properties|only if we can prove P or if we can prove Q.]] In particular, we cannot in general claim that "P or not P" is true (the [[law of excluded middle]]), since in some cases [[Gödel's incompleteness theorems|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 <math>\exists x.\phi(x)</math>, without being able to produce any term <math>t</math> of which <math>\phi</math> holds.

Dummett argues that this notion of truth lies at the bottom of various classical forms of anti-realism, and uses it to re-interpret [[phenomenalism]], claiming that it need not take the form of [[reductionism]].

Dummett's writings on anti-realism draw heavily on the later writings of [[Ludwig Wittgenstein]], concerning meaning and rule following, and can be seen as an attempt to integrate central ideas from the ''[[Philosophical Investigations]]'' into the constructive tradition of [[analytic philosophy]] deriving from [[Gottlob Frege]].