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In analytic philosophy, the term anti-realism is used to describe any position involving either the denial of an objective reality or the denial that verification-transcendent statements 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 
Michael Dummett 
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 of which holds.
Dummett argues that the intuitionistic notion of truth lies at the bottom of various classical forms of anti-realism. He uses this notion to re-interpret phenomenalism, claiming that it need not take the form of a reductionism (often considered untenable).
Dummett's writings on anti-realism also draw heavily on the later writings of Wittgenstein concerning meaning and rule following. In fact, Dummett's writings on anti-realism can be seen as an attempt to integrate central ideas from the Philosophical Investigations into analytical philosophy.
Anti-realism in the sense that Dummett uses the term is also often called semantic anti-realism.
Hilary Putnam's "internal realism" 
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Doubts about the possibility of definite truth have been expressed since ancient times, for instance in the skepticism of Pyrrho. Anti-realism about matter or physical entities also has a long history. It can be found in the idealism of Berkeley, as well as Hegel and other post-Kantians.
Metaphysical Realism vis-à-vis Internal Realism 
Anti-realist arguments 
Idealists are skeptics about the physical world, maintaining either: 1) that nothing exists outside the mind, or 2) that we would have no access to a mind-independent reality even if it may exist; 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. A concrete example of a situation where an individual's sensory input might be caused by something other than what he thinks is causing it is 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 — providing the interrelationships between the objects are the same. (Compare with symbol grounding).
Anti-realism in science 
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. For a brief discussion comparing such anti-realism to its opposite, realism, see (Okasha 2002, ch. 4). Ian Hacking (1999, p. 84) also uses the same definition. One prominent position in the philosophy of science is instrumentalism, which is a non-realist position. Non-realism takes a purely agnostic view towards the existence of unobservable entities: unobservable entity X serves simply as an instrument to aid in the success of theory Y. We need not determine the existence or non-existence of X. Some scientific anti-realists argue further, however, and deny that unobservables exist even as non-truth conditioned instruments. Arguments with reference to Anti-Realism may broadly be bifurcated for convenience; Substantial Arguments and Structural Arguments. Arguments qua its matter and Arguments qua its Format.
Anti-realism in mathematics 
Realism in the philosophy of mathematics is the claim that mathematical entities such as number have a mind-independent existence. The main forms are empiricism, which associates numbers with concrete physical objects; and Platonism, according to which numbers are abstract, non-physical entities.
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 concrete, 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 concrete, 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. ("An account of mathematical truth ..must be consistent with the possibility of mathematical knowledge"). Another way of making the point is that if the Platonic world were to disappear, it would make no difference to the ability of mathematicians to generate proofs, etc., which is already fully accountable in terms of physical processes in their brains.
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.
The argument hinges on the idea that a satisfactory naturalistic account of thought processes in terms of brain processes can be given for mathematical reasoning along with everything else. 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. A modern form of this argument is 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.
See also 
- Constructivist epistemology
- Crispin Wright
- Deflationary theory of truth
- Intuitionistic logic
- Irrealism (philosophy)
- Münchhausen Trilemma
- Neil Tennant (philosopher)
- Philosophical realism
- Simulated reality
- Theory of Everything (ToE)
- Field, Hartry, 1989, Realism, Mathematics, and Modality, Oxford: Blackwell, p. 68
- "Since abstract objects are outside the nexus of causes and effects, and thus perceptually inaccessible, they cannot be known through their effects on us" Katz, J. Realistic Rationalism, p. 15
- Philosophy Now: Mathematical_Knowledge_A_Dilemma Mathematical Knowledge: A dilemma
- Stanford Encyclopeida of Philosophy
- Benacceraf, 1973, p. 409
- Review of The Emperor's New Mind >
- Christine Baron, Manfred Engel (eds.) (2010). Realism/Anti-Realism in 20th-Century Literature. Rodopi: 2010. ISBN 978-90-420-3115-9
- Lee Braver (2007). A Thing of This World: a History of Continental Anti-Realism, Northwestern University Press: 2007.
- Michael Dummett (1963). Realism, reprinted in: Truth and Other Enigmas, Harvard University Press: 1978, pp. 145–165.
- Michael Dummett (1967). Platonism, reprinted in: Truth and Other Enigmas, Harvard University Press: 1978, pp. 202–214.
- Ian Hacking (1999). The Social Construction of What?. Harvard University Press: 2001.
- Samir Okasha (2002). Philosophy of Science: A Very Short Introduction. Oxford University Press.
- Semantic challenges to realism in the Stanford Encyclopedia of Philosophy