Anti-realism

In analytic philosophy, anti-realism is an opposed position to a particular type of 'realism' taking the form of a species of 'reductionism'. That was coined by a British philosopher Michael Dummett as a colorless reductionism. In anti-realism, as opposed to realism, some outer hypothetical being is not assumed.

For realists, the truth of a statement is by virtue of a reality existing independently of us, whereas, for anti-realists, it is by virtue of another mechanism based on Frege's context principle and Heyting's intuitionistic logic under the modified Brouwer's intuitionism.

Since disputed statements containing abstract ideal objects (like mathematical objects) are also encompassed in anti-realism, one may speak of this stance with respect to material objects, the theoretical entities of science, mathematical statement, mental states, events and processes, the past and the future.

The term "anti-realism" 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 ${\displaystyle \exists x.\phi (x)}$, without being able to produce any term ${\displaystyle t}$ of which ${\displaystyle \phi }$ holds.

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