Editing Nominalism (section)

==Varieties<!--Predicate nominalism', 'Resemblance nominalism', and 'Class nominalism' redirect here-->==
There are various forms of nominalism ranging from extreme to almost-realist. One extreme is '''predicate nominalism'''<!--boldface per WP:R#PLA-->, which states that Fluffy and Kitzler, for example, are both cats simply because the predicate 'is a cat' applies to both of them. And this is the case for all similarity of attribute among objects. The main criticism of this view is that it does not provide a sufficient solution to the problem of universals. 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.<ref>MacLeod & Rubenstein (2006), §3a.</ref>

Proponents of '''resemblance nominalism'''<!--boldface per WP:R#PLA--> believe that 'cat' applies to both cats because Fluffy and Kitzler [[Similarity (philosophy)|resemble]] an [[wikt:exemplar|exemplar]] cat closely enough to be classed together with it as members of its [[natural kind|kind]], or that they differ from each other (and other cats) quite less than they differ from other things, and this warrants classing them together.<ref>MacLeod & Rubenstein (2006), §3b.</ref> Some resemblance nominalists will concede that the resemblance relation is itself a universal, but is the only universal necessary. Others argue that each resemblance relation is a particular, and is a resemblance relation simply in virtue of its resemblance to other resemblance relations. This generates an infinite regress, but many argue that it is not [[virtuous circle and vicious circle|vicious]].<ref>See, for example, H. H. Price (1953).</ref>

'''Class nominalism'''<!--boldface per WP:R#PLA--> argues that class membership forms the metaphysical backing for property relationships: two particular red balls share a property in that they are both members of classes corresponding to their properties – that of being red and of being balls. A version of class nominalism that sees some classes as "natural classes" is held by [[Anthony Quinton, Baron Quinton|Anthony Quinton]].<ref>{{Cite journal|title=Properties and Classes|first=Anthony|last=Quinton|journal=Proceedings of the Aristotelian Society|volume=58|year=1957|pages=33–58|doi=10.1093/aristotelian/58.1.33|jstor=4544588}}</ref>

[[Conceptualism]] is a philosophical theory that explains universality of particulars as conceptualized frameworks situated within the thinking mind.<ref>Strawson, P. F. "Conceptualism." Universals, concepts and qualities: new essays on the meaning of predicates. Ashgate Publishing, 2006.</ref> 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.<ref>"Conceptualism." ''The Oxford Dictionary of Philosophy. Simon Blackburn. Oxford University Press'', 1996. Oxford Reference Online. Oxford University Press.</ref>

Another form of nominalism is [[trope nominalism]].  A trope is a particular instance of a property, like the specific greenness of a shirt.  One might argue that there is a primitive, [[Objectivity (science)|objective]] resemblance relation that holds among like tropes.  Another route is to argue that all apparent tropes are constructed out of more primitive tropes and that the most primitive tropes are the entities of complete [[physics]].  Primitive trope resemblance may thus be accounted for in terms of causal [[indiscernibility]]. Two tropes are exactly resembling if substituting one for the other would make no difference to the events in which they are taking part. Varying degrees of resemblance at the macro level can be explained by varying degrees of resemblance at the micro level, and micro-level resemblance is explained in terms of something no less robustly physical than causal power.  [[David Malet Armstrong|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.<ref>{{cite web |last1=Rodriguez-Pereyra |first1=Gonzalo |title=Nominalism in Metaphysics |url=https://plato.stanford.edu/entries/nominalism-metaphysics/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=22 December 2024 |date=2019}}</ref><ref>{{cite journal |last1=Imaguire |first1=Guido |date=2022 |title=What Is the Problem of Universals About? |url=https://www.pdcnet.org/pdc/bvdb.nsf/purchase_mobile?openform&fp=philosophica&id=philosophica_2022_0030_0059_0071_0089 |journal=Philosophica: International Journal for the History of Philosophy |volume=30 |issue=1 |pages=71–89 |doi=10.5840/philosophica20229135 |access-date=22 December 2024|url-access=subscription }}</ref>

[[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.  For this reason, he claims, scientists and constructionists tend to "shout past each other".<ref>Hacking (1999), pp. 80–84.</ref>

Mark Hunyadi characterizes the contemporary Western world as a figure of a "libidinal nominalism." He argues that the insistence on the individual will that has emerged in medieval nominalism evolves into a "libidinal nominalism" in which desire and will are conflated.<ref> Mark Hunyadi, ''Le second âge de l'individu'' (Paris: Presses Universitaires de France, 2023). </ref>

===Mathematical nominalism<!--'Mathematical nominalism' redirects here-->===
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. Collections of individuals likewise exist, but two collections having the same individuals are the same collection. 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 (mathematics)|singleton]] was identical to the individual inside it. Classes corresponding to what are held to be species or genera are concrete sums of their concrete constituting individuals. For example, the class of philosophers is nothing but the sum of all concrete, individual philosophers.

The principle of [[extensionality]] in set theory assures us that any matching pair of curly braces enclosing one or more instances of the same individuals denote the same set. Hence {''a'', ''b''}, {''b'', ''a''}, {''a'', ''b'', ''a'', ''b''} are all the same set. For Goodman and other proponents of '''mathematical nominalism'''<!--boldface per WP:R#PLA-->,<ref name=SEP-Nom>Bueno, Otávio, 2013, "[https://plato.stanford.edu/entries/nominalism-mathematics/ Nominalism in the Philosophy of Mathematics]" in the [[Stanford Encyclopedia of Philosophy]].</ref> {''a'', ''b''} is also identical to {''a'', {''b''}{{spaces}}}, {''b'', {''a'', ''b''}{{spaces}}}, and any combination of matching curly braces and one or more instances of ''a'' and ''b'', as long as ''a'' and ''b'' are names of individuals and not of collections of individuals. Goodman, [[Richard Milton Martin]], and [[Willard Quine]] all advocated reasoning about collectivities by means of a theory of ''virtual sets'' (see especially Quine 1969), one making possible all elementary operations on sets except that the [[Universe_(mathematics)|universe]] of a quantified variable cannot contain any virtual sets.

In the [[foundations of mathematics]], nominalism has come to mean doing mathematics without assuming that [[Set (mathematics)|sets]] in the mathematical sense exist. In practice, this means that [[Quantifier (logic)|quantified variables]] may range over [[Universe_(mathematics)|universes]] of [[number]]s, [[point (geometry)|points]], primitive [[ordered pair]]s, and other abstract ontological primitives, but not over sets whose members are such individuals. Only a small fraction of the corpus of modern mathematics can be rederived in a nominalistic fashion.