Nominalism

In metaphysics, nominalism is the view that universals and abstract objects do not actually exist other than being merely names or labels.

It is opposed to realist philosophies, such as Platonic realism, which assert that universals do exist over and above particulars, and to the hylomorphic substance theory of Aristotle, which asserts that universals are immanently real within them; however, the name "nominalism" emerged from debates in medieval philosophy with Roscellinus.

[6] Plato was perhaps the first writer in Western philosophy to clearly state a realist, i.e., non-nominalist, position: ... We customarily hypothesize a single form in connection with each of the many things to which we apply the same name. ...

[10][11] In medieval philosophy, the French philosopher and theologian Roscellinus (c. 1050 – c. 1125) was an early, prominent proponent of nominalism.

"I maintain", he wrote, "that a universal is not something real that exists in a subject ... but that it has a being only as a thought-object in the mind [objectivum in anima]".

Accordingly, he wrote, there is no reason to believe that there is an entity called "humanity" that resides inside, say, Socrates, and nothing further is explained by making this claim.

This is in accord with the analytical method that has since come to be called Ockham's razor, the principle that the explanation of any phenomenon should make as few assumptions as possible.

If the same concept is correctly and non-arbitrarily applied to two individuals, there must be some resemblance or shared property between the two individuals that justifies their falling under the same concept and that is just the metaphysical problem that universals were brought in to address, the starting-point of the whole problem (MacLeod & Rubenstein, 2006, §3d).

"The dismembering of the particulars, the dangerous attribution to individuals to a status of totalization of possibilities in themselves, all this will unfold in an existential fissure that is both objective and material.

Certain orthodox Hindu schools defend the realist position, notably Purva Mimamsa, Nyaya and Vaisheshika, maintaining that the referent of the word is both the individual object perceived by the subject of knowledge and the universal class to which the thing belongs.

Buddhists take the nominalist position, especially those of the Sautrāntika[19] and Yogācāra schools;[20][18] they were of the opinion that words have as referent not true objects, but only concepts produced in the intellect.

Nominalism arose in reaction to the problem of universals, specifically accounting for the fact that some things are of the same type.

For example, Fluffy and Kitzler are both cats, or, the fact that certain properties are repeatable, such as: the grass, the shirt, and Kermit the Frog are green.

Conceptualists hold a position intermediate between nominalism and realism, saying that universals exist only within the mind and have no external or substantial reality.

)[21] Finally, many philosophers prefer simpler ontologies populated with only the bare minimum of types of entities, or as W. V. O. Quine said "They have a taste for 'desert landscapes.'"

It fails to provide an account of what makes it the case that a group of things warrant having the same predicate applied to them.

[26] The conceptualist view approaches the metaphysical concept of universals from a perspective that denies their presence in particulars outside of the mind's perception of them.

David Armstrong, perhaps the most prominent contemporary realist, argues that such a trope-based variant of nominalism has promise, but holds that it is unable to account for the laws of nature in the way his theory of universals can.

[28][29] Ian Hacking has also argued that much of what is called social constructionism of science in contemporary times is actually motivated by an unstated nominalist metaphysical view.

[31] A notion that philosophy, especially ontology and the philosophy of mathematics, should abstain from set theory owes much to the writings of Nelson Goodman (see especially Goodman 1940 and 1977), who argued that concrete and abstract entities having no parts, called individuals, exist.

Goodman was himself drawing heavily on the work of Stanisław Leśniewski, especially his mereology, which was itself a reaction to the paradoxes associated with Cantorian set theory.

Leśniewski denied the existence of the empty set and held that any singleton was identical to the individual inside it.

[35] Aware that explicit thinking in terms of a divide between 'nominalism' and 'realism’ emerged only in the fifteenth century, scholars have increasingly questioned whether a fourteenth-century school of nominalism can really be said to have existed.

More fundamentally, Robert Pasnau has questioned whether any kind of coherent body of thought that could be called 'nominalism' can be discerned in fourteenth century writing.

Thus, hermeneutic nominalism is the hypothesis that science, properly interpreted, already dispenses with mathematical objects (entities) such as numbers and sets.

Meanwhile, revolutionary nominalism is the project of replacing current scientific theories by alternatives dispensing with mathematical objects (see Burgess, 1983, p. 96).

A recent study extends the Burgessian critique to three nominalistic reconstructions: the reconstruction of analysis by Georg Cantor, Richard Dedekind, and Karl Weierstrass that dispensed with infinitesimals; the constructivist re-reconstruction of Weierstrassian analysis by Errett Bishop that dispensed with the law of excluded middle; and the hermeneutic reconstruction, by Carl Boyer, Judith Grabiner, and others, of Cauchy's foundational contribution to analysis that dispensed with Cauchy's infinitesimals.