# Anti-realism

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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'. [1]

Analytic philosophy is a style of philosophy that became dominant in the Western world at the beginning of the 20th century. The term can refer to one of several things:

Epistemology is the branch of philosophy concerned with the theory of knowledge.

Sir Michael Anthony Eardley Dummett, FBA was an English academic described as "among the most significant British philosophers of the last century and a leading campaigner for racial tolerance and equality." He was, until 1992, Wykeham Professor of Logic at the University of Oxford. He wrote on the history of analytic philosophy, notably as an interpreter of Frege, and made original contributions particularly in the philosophies of mathematics, logic, language and metaphysics. He was known for his work on truth and meaning and their implications to debates between realism and anti-realism, a term he helped to popularize. He devised the Quota Borda system of proportional voting, based on the Borda count. In mathematical logic, he developed an intermediate logic, already studied by Kurt Gödel: the Gödel–Dummett logic.

## Contents

In anti-realism, 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. [2] In anti-realism, this external reality is hypothetical and is not assumed. [3] [4]

In the philosophy of language, the context principle is a form of semantic holism holding that a philosopher should "never ... ask for the meaning of a word in isolation, but only in the context of a proposition".

Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof. In particular, systems of intuitionistic logic do not include the law of the excluded middle and double negation elimination, which are fundamental inference rules in classical logic. Intuitionistic logic is one example of a logic in a family of non-classical logics called paracomplete logics: logics that refuse to tautologically affirm the law of the excluded middle.

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. [5]

Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.

A mathematical object is an abstract object arising in mathematics. The concept is studied in philosophy of mathematics.

The past is the set of all events that occurred before a given point in time. The past is contrasted with and defined by the present and the future. The concept of the past is derived from the linear fashion in which human observers experience time, and is accessed through memory and recollection. In addition, human beings have recorded the past since the advent of written language. The first known use of the word "past" was in the fourteenth century; it developed as the past participle of the middle english verb passen meaning "to pass."

## Varieties

### Metaphysical anti-realism

One kind of metaphysical anti-realism maintains 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. [6] 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. The main alternative to this sort of metaphysical anti-realism is metaphysical realism.

Skepticism or scepticism is generally a questioning attitude or doubt towards one or more items of putative knowledge or belief or dogma. It is often directed at domains, such as the supernatural, morality, theism, or knowledge. Formally, skepticism as a topic occurs in the context of philosophy, particularly epistemology, although it can be applied to any topic such as politics, religion, and pseudoscience.

In the philosophy of perception, the theory of sense data was a popular view held in the early 20th century by philosophers such as Bertrand Russell, C. D. Broad, H. H. Price, A. J. Ayer, and G. E. Moore. Sense data are taken to be mind-dependent objects whose existence and properties are known directly to us in perception. These objects are unanalyzed experiences inside the mind, which appear to subsequent more advanced mental operations exactly as they are.

Causality is efficacy, by which one process or state, a cause, contributes to the production of another process or state, an effect, where the cause is partly responsible for the effect, and the effect is partly dependent on the cause. In general, a process has many causes, which are also said to be causal factors for it, and all lie in its past. An effect can in turn be a cause of, or causal factor for, many other effects, which all lie in its future. Multiple philosophers have believed that causality is metaphysically prior to notions of time and space.

On a more abstract level, model-theoretic anti-realist arguments hold that a given set of symbols in a theory can be mapped onto any number of sets of real-world objectseach set being a "model" of the theory—provided the relationship between the objects is the same (compare with symbol grounding.)

In mathematics, model theory is the study of classes of mathematical structures from the perspective of mathematical logic. The objects of study are models of theories in a formal language. A set of sentences in a formal language is one of the components that form a theory. A model of a theory is a structure that satisfies the sentences of that theory.

A symbol is a mark, sign or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different concepts and experiences. All communication is achieved through the use of symbols. Symbols take the form of words, sounds, gestures, ideas or visual images and are used to convey other ideas and beliefs. For example, a red octagon may be a symbol for "STOP". On a map, a blue line might represent a river. Numerals are symbols for numbers. Alphabetic letters may be symbols for sounds. Personal names are symbols representing individuals. A red rose may symbolize love and compassion. The variable 'x', in a mathematical equation, may symbolize the position of a particle in space.

A theory is a contemplative and rational type of abstract or generalizing thinking, or the results of such thinking. Depending on the context, the results might, for example, include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several related meanings.

In ancient Greek philosophy, nominalist (anti-realist) doctrines about universals were proposed by the Stoics, especially Chrysippus. [7] [8] In early modern philosophy, conceptualist anti-realist doctrines about universals were proposed by thinkers like René Descartes, John Locke, Baruch Spinoza, Gottfried Wilhelm Leibniz, George Berkeley, and David Hume. [9] [10] 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. [11] Kant and Hegel held conceptualist views about universals. [12] [13] In contemporary philosophy, anti-realism was revived in the form of empirio-criticism, logical positivism, semantic anti-realism and scientific instrumentalism (see below).

Ancient Greek philosophy arose in the 6th century BC and continued throughout the Hellenistic period and the period in which Ancient Greece was part of the Roman Empire. Philosophy was used to make sense out of the world in a non-religious way. It dealt with a wide variety of subjects, including astronomy, mathematics, political philosophy, ethics, metaphysics, ontology, logic, biology, rhetoric and aesthetics.

Chrysippus of Soli was a Greek Stoic philosopher. He was a native of Soli, Cilicia, but moved to Athens as a young man, where he became a pupil of Cleanthes in the Stoic school. When Cleanthes died, around 230 BC, Chrysippus became the third head of the school. A prolific writer, Chrysippus expanded the fundamental doctrines of Zeno of Citium, the founder of the school, which earned him the title of Second Founder of Stoicism.

Early modern philosophy is a period in the history of philosophy at the beginning or overlapping with the period known as modern philosophy.

### Semantic anti-realism

The term "anti-realism" was introduced by Michael Dummett in his 1982 paper "Realism" in order to re-examine a number of classical philosophical disputes, involving such doctrines as nominalism, Platonic 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.

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.

### Scientific anti-realism

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. [14] [15]

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.

Some scientific anti-realists, however, deny that unobservables exist, even as non-truth conditioned instruments.

### Mathematical anti-realism

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" [16] ) 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. [17] [18] [19]

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.

#### Counterarguments

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. [20]

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.

## Related Research Articles

In metaphysics, nominalism is a philosophical view which denies the existence of universals and abstract objects, but affirms the existence of general or abstract terms and predicates. There are at least two main versions of nominalism. One version denies the existence of universals – things that can be instantiated or exemplified by many particular things. The other version specifically denies the existence of abstract objects – objects that do not exist in space and time.

In metaphysics, the problem of universals refers to the question of whether properties exist, and if so, what they are. Properties are qualities or relations that two or more entities have in common. The various kinds of properties, such as qualities and relations, are referred to as universals. For instance, one can imagine three cup holders on a table that have in common the quality of being circular or exemplifying circularity, or two daughters that have in common being the female offsprings of Frank. There are many such properties, such as being human, red, male or female, liquid, big or small, taller than, father of, etc. While philosophers agree that human beings talk and think about properties, they disagree on whether these universals exist in reality or merely in thought and speech.

Platonic idealism usually refers to Plato's theory of forms or doctrine of ideas.

Platonic realism is a philosophical term usually used to refer to the idea of realism regarding the existence of universals or abstract objects after the Greek philosopher Plato. As universals were considered by Plato to be ideal forms, this stance is ambiguously also called Platonic idealism. This should not be confused with idealism as presented by philosophers such as George Berkeley: as Platonic abstractions are not spatial, temporal, or mental, they are not compatible with the later idealism's emphasis on mental existence. Plato's Forms include numbers and geometrical figures, making them a theory of mathematical realism; they also include the Form of the Good, making them in addition a theory of ethical realism.

In metaphysics, a universal is what particular things have in common, namely characteristics or qualities. In other words, universals are repeatable or recurrent entities that can be instantiated or exemplified by many particular things. For example, suppose there are two chairs in a room, each of which is green. These two chairs both share the quality of "chairness", as well as greenness or the quality of being green; in other words, they share a "universal". There are three major kinds of qualities or characteristics: types or kinds, properties, and relations. These are all different types of universals.

Reality is the sum or aggregate of all that is real or existent, as opposed to that which is merely imaginary. The term is also used to refer to the ontological status of things, indicating their existence. In physical terms, reality is the totality of the universe, known and unknown. Philosophical questions about the nature of reality or existence or being are considered under the rubric of ontology, which is a major branch of metaphysics in the Western philosophical tradition. Ontological questions also feature in diverse branches of philosophy, including the philosophy of science, philosophy of religion, philosophy of mathematics, and philosophical logic. These include questions about whether only physical objects are real, whether reality is fundamentally immaterial, whether hypothetical unobservable entities posited by scientific theories exist, whether God exists, whether numbers and other abstract objects exist, and whether possible worlds exist.

The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics, and purports to provide a viewpoint of the nature and methodology of mathematics, and to understand the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts.

In philosophy of science and in epistemology, Instrumentalism is a methodological view that ideas are useful instruments, and that the worth of an idea is based on how effective it is in explaining and predicting phenomena. Instrumentalism is a pragmatic philosophy of John Dewey that thought is an instrument for solving practical problems, and that truth is not fixed but changes as problems change. Instrumentalism is the view that scientific theories are useful tools for predicting phenomena instead of true or approximately true descriptions.

Scientific realism is the view that the universe described by science is real regardless of how it may be interpreted.

Abstract and concrete are classifications that denote whether the object that a term describes has physical referents. Abstract objects have no physical referents, whereas concrete objects do. They are most commonly used in philosophy and semantics. Abstract objects are sometimes called abstracta and concrete objects are sometimes called concreta. An abstract object is an object that does not exist at any particular time or place, but rather exists as a type of thing—i.e., an idea, or abstraction. The term abstract object is said to have been coined by Willard Van Orman Quine. The study of abstract objects is called abstract object theory.

In metaphysics, conceptualism is a theory that explains universality of particulars as conceptualized frameworks situated within the thinking mind. Intermediate between nominalism and realism, the conceptualist view approaches the metaphysical concept of universals from a perspective that denies their presence in particulars outside the mind's perception of them. Conceptualism is anti-realist about abstract objects, just like immanent realism is.

In metaphysics, realism about a given object is the view that this object exists in reality independently of our conceptual scheme. In philosophical terms, these objects are ontologically independent of someone's conceptual scheme, perceptions, linguistic practices, beliefs, etc.

In philosophy, universality is the idea that universal facts exist and can be progressively discovered, as opposed to relativism. In certain theologies, universalism is the quality ascribed to an entity whose existence is consistent throughout the universe, whose being is independent of and unconstrained by the events and conditions that compose the universe, such as entropy and physical locality.

Moderate realism is a position in the debate on the metaphysics of universals that holds that there is no realm in which universals exist, nor do they really exist within particulars as universals, but rather universals really exist within particulars as particularised, and multiplied.

Metaphysics is the branch of philosophy that investigates principles of reality transcending those of any particular science. Cosmology and ontology are traditional branches of metaphysics. It is concerned with explaining the fundamental nature of being and the world. Someone who studies metaphysics can be called either a "metaphysician" or a "metaphysicist".

The following outline is provided as an overview of and topical guide to metaphysics:

Structuralism is a theory in the philosophy of mathematics that holds that mathematical theories describe structures of mathematical objects. Mathematical objects are exhaustively defined by their place in such structures. Consequently, structuralism maintains that mathematical objects do not possess any intrinsic properties but are defined by their external relations in a system. For instance, structuralism holds that the integer 1 is exhaustively defined by being the successor of 0 in the structure of the theory of natural numbers. By generalization of this example, any integer is defined by their respective place in this structure of the number line. Other examples of mathematical objects might include lines and planes in geometry, or elements and operations in abstract algebra.

Realism, Realistic, or Realists may refer to:

In the philosophy of mathematics, Benacerraf's identification problem is a philosophical argument, developed by Paul Benacerraf, against set-theoretic Platonism. In 1965, Benacerraf published a paradigm changing article entitled "What Numbers Could Not Be". Historically, the work became a significant catalyst in motivating the development of mathematical structuralism.

## References

1. Realism (1963) p. 145
2. Realism (1963) p. 146
3. Truth (1959) p. 24 (postscript)
4. Blackburn, Simon ([2005] 2008). "realism/anti-realism," The Oxford Dictionary of Philosophy , 2nd ed. revised, pp. 308–9. Oxford.
5. Realism (1963) pp. 147–8
6. Karin Johannesson, God Pro Nobis: On Non-metaphysical Realism and the Philosophy of Religion , Peeters Publishers, 2007, p. 26.
7. 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.".
8. 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."
9. 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 related to] the Ockhamist tradition..."
10. P. Stekeler-Weithofer (2016), "Hegel's Analytic Pragmatism", University of Leipzig, pp. 122–4.
11. Oberst, Michael. 2015. "Kant on Universals." History of Philosophy Quarterly32(4):335–352.
12. A. Sarlemijn, Hegel's Dialectic, Springer, 1975, p. 21.
13. Hacking, Ian (1999). The Social Construction Of What?. Harvard University Press. p. 84.
14. Okasha, Samir (2002). Philosophy of Science: A Very Short Introduction. Oxford University Press.
15. Field, Hartry, 1989, Realism, Mathematics, and Modality, Oxford: Blackwell, p. 68
16. "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