Antirealism

In analytic philosophy, anti-realism is an epistemological position first articulated by British philosopher Michael Dummett. The term was coined as an argument against a form of realism Dummett saw as 'colorless reductionism'.

In anti-realism, the truth of a statement rests on its demonstrability through internal logic mechanisms, such as Frege's context principle and Heyting's intuitionistic logic, in direct opposition to the realist notion that the truth of a statement rests on its correspondence to an external, independent reality. In anti-realism, this external reality is hypothetical and is not assumed.

Because it encompasses statements containing abstract ideal objects (i.e. mathematical objects), anti-realism may apply to a wide range of philosophic topics, from material objects to the theoretical entities of science, mathematical statement, mental states, events and processes, the past and the future.

The term "anti-realism" was introduced by Michael Dummett in his paper Realism in order 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 portraying 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 Platonic realists, the truth of a statement is proven 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. 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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