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 Dummet 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 portarying 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, they 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 , without being able to produce any term of which 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 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 Frege.
Idealists maintain a skepticism about the physical world, arguing either: 1) that nothing exists outside the mind, or 2) that we would have no access to a mind-independent reality, even if it exists. The latter case often takes the form of a denial of the idea that we can have 'unconceptualised' experiences (see Myth of the Given). Conversely, most realists (specifically, indirect realists) hold that perceptions or sense data are caused by mind-independent objects. But this introduces the possibility of another kind of skepticism: since our understanding of causality is that the same effect can be produced by multiple causes, there is a lack of determinacy about what one is really perceiving, as in the brain in a vat scenario.
On a more abstract level, model theoretic arguments hold that a given set of symbols in a theory can be mapped onto any number of sets of real-world objects--each set being a "model" of the theory--provided the relationship between the objects is the same. (Compare with symbol grounding.)
In philosophy of science, anti-realism applies chiefly to claims about the non-reality of "unobservable" entities such as electrons or genes, which are not detectable with human senses. One prominent position in the philosophy of science is instrumentalism, which is a non-realist position which takes a purely agnostic view towards the existence of unobservable entities, in which the unobservable entity X serves as an instrument to aid in the success of theory Y does not require proof for the existence or non-existence of X.
Some scientific anti-realists, however, deny that unobservables exist, even as non-truth conditioned instruments.
In the philosophy of mathematics, realism is the claim that mathematical entities such as 'number' have an observer-independent existence. Empiricism, which associates numbers with concrete physical objects, and Platonism, in which numbers are abstract, non-physical entities, are the preeminent forms of mathematical realism.
The "epistemic argument" against Platonism has been made by Paul Benacerraf and Hartry Field. Platonism posits that mathematical objects are abstract entities. By general agreement, abstract entities cannot interact causally with physical entities ("the truth-values of our mathematical assertions depend on facts involving platonic entities that reside in a realm outside of space-time") Whilst our knowledge of physical objects is based on our ability to perceive them, and therefore to causally interact with them, there is no parallel account of how mathematicians come to have knowledge of abstract objects.
Field developed his views into fictionalism. Benacerraf also developed the philosophy of mathematical structuralism, according to which there are no mathematical objects. Nonetheless, some versions of structuralism are compatible with some versions of realism.
Anti-realist arguments hinge on the idea that a satisfactory, naturalistic account of thought processes can be given for mathematical reasoning. One line of defense is to maintain that this is false, so that mathematical reasoning uses some special intuition that involves contact with the Platonic realm, as in the argument given by Sir Roger Penrose.
Another line of defense is to maintain that abstract objects are relevant to mathematical reasoning in a way that is non causal, and not analogous to perception. This argument is developed by Jerrold Katz in his book Realistic Rationalism.
A more radical defense is to deny the separation of physical world and the platonic world, i.e. the mathematical universe hypothesis. In that case, a mathematician's knowledge of mathematics is one mathematical object making contact with another.