In analytic philosophy, anti-realism is the position that the truth of a statement rests on its demonstrability through internal logic mechanisms, such as the context principle or intuitionistic logic, in direct opposition to the realist notion that the truth of a statement rests on its correspondence to an external, independent reality.Realism (1963) p. 146 In anti-realism, this external reality is hypothesis and is not assumed.Truth (1959) p. 24 (postscript)Simon Blackburn (2005 2008). "realism/anti-realism", The Oxford Dictionary of Philosophy, 2nd ed. revised, pp. 308–9. Oxford.
There are many varieties of anti-realism, such as metaphysical, mathematical, semantic, scientific, moral and epistemic. The term was first articulated by British philosopher Michael Dummett in an argument against a form of realism Dummett saw as 'colorless reductionism'.Realism (1963) p. 145
Anti-realism in its most general sense can be understood as being in contrast to a generic realism, which holds that distinctive objects of a subject-matter exist and have properties independent of one's beliefs and conceptual schemes. The ways in which anti-realism rejects these types of claims can vary dramatically. Because this encompasses statements containing abstract object (i.e. mathematical objects), anti-realism may apply to a wide range of philosophical topics, from Physical body to the theoretical entity of science, mathematical statements, mental states, events and processes, the past and the future.Realism (1963) pp. 147–8
On a more abstract level, model theory anti-realist arguments hold that a given set of 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 ancient Greek philosophy, nominalist (anti-realist) doctrines about universals were proposed by the Stoics, especially Chrysippus.John Sellars, Stoicism, Routledge, 2014, pp. 84–85: "Stoics have often been presented as the first nominalists, rejecting the existence of universal concepts altogether. ... For Chrysippus there are no universal entities, whether they be conceived as substantial Platonic Forms or in some other manner." In early modern philosophy, Conceptualism anti-realist doctrines about universals were proposed by thinkers like René Descartes, John Locke, Baruch Spinoza, Gottfried Wilhelm Leibniz, George Berkeley, and David Hume.David Bostock, Philosophy of Mathematics: An Introduction, Wiley-Blackwell, 2009, p. 43: "All of Descartes, Locke, Berkeley, and Hume supposed that mathematics is a theory of our ideas, but none of them offered any argument for this conceptualist claim, and apparently took it to be uncontroversial."Stefano Di Bella, Tad M. Schmaltz (eds.), The Problem of Universals in Early Modern Philosophy, Oxford University Press, 2017, p. 64 "there is a strong case to be made that Spinoza was a conceptualist about universals" and p. 207 n. 25: "Leibniz's conceptualism is the Ockhamist tradition..." In late modern philosophy, anti-realist doctrines about knowledge were proposed by the German idealist Georg Wilhelm Friedrich Hegel. Hegel was a proponent of what is now called inferentialism: he believed that the ground for the axioms and the foundation for the validity of the inferences are the right consequences and that the axioms do not explain the consequence.P. Stekeler-Weithofer (2016), "Hegel's Analytic Pragmatism" , University of Leipzig, pp. 122–4. Kant and Hegel held conceptualist views about universals.Oberst, Michael. 2015. "Kant on Universals." History of Philosophy Quarterly 32(4):335–352.A. Sarlemijn, Hegel's Dialectic, Springer, 1975, p. 21. In contemporary philosophy, anti-realism was revived in the form of empirio-criticism, logical positivism, semantic anti-realism and scientific instrumentalism (see below).
The "epistemic argument" against Platonism has been made by Paul Benacerraf and Hartry Field. Platonism posits that mathematical objects are abstract object entities. By general agreement, abstract entities cannot interact 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"Field, Hartry, 1989, Realism, Mathematics, and Modality, Oxford: Blackwell, p. 68). Whilst our knowledge of physical objects is based on our ability to perception them, and therefore to causally interact with them, there is no parallel account of how mathematicians come to have knowledge of abstract objects."Since abstract objects are outside the nexus of causes and effects, and thus perceptually inaccessible, they cannot be known through their effects on us" — Jerrold Katz, Realistic Rationalism, 2000, p. 15
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.
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 2000 book Realistic Rationalism. In this book, he put forward a position called realistic rationalism, which combines metaphysical realism and rationalism.
A more radical defense is to deny the separation of physical world and the platonic world, i.e. the mathematical universe hypothesis (a variety of mathematicism). In that case, a mathematician's knowledge of mathematics is one mathematical object making contact with another.
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 , 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 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.
One prominent variety of scientific anti-realism is instrumentalism, 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 and does not require proof for the existence or non-existence of X.
Different version of moral anti-realism deny different statements: specifically, non-cognitivism denies the first claim, arguing that moral statements have no meaning or truth content, Error Theory denies the second claim, arguing that all moral statements are false, and ethical subjectivism denies the third claim, arguing that the truth of moral statements is mind dependent.
Examples of anti-realist moral theories might be:
There is a debate as to whether moral relativism is actually an anti-realist position. While many versions deny the metaphysical thesis, some do not, as one could imagine a system of morality which requires you to obey the written laws in your country. Such a system would be a version of moral relativism, as different individuals would be required to follow different laws, but the moral facts are physical facts about the world, not mental facts, so they are metaphysically ordinary. Thus, different versions of moral relativism might be considered anti-realist or realist.
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