View source for Nominalism

{{Short description|Philosophy emphasizing names and labels}}
[[File:William_of_Ockham.png|thumb|[[William of Ockham]]]]

In [[metaphysics]], '''nominalism''' is the view that [[Universal (metaphysics)|universals]] and [[abstract object]]s do not actually exist other than being merely names or labels.<ref>{{Cite dictionary |url=http://www.lexico.com/definition/nominalism |archive-url=https://web.archive.org/web/20210826005738/https://www.lexico.com/definition/nominalism |url-status=dead |archive-date=August 26, 2021 |title=nominalism |dictionary=[[Lexico]] UK English Dictionary |publisher=[[Oxford University Press]]}}</ref><ref>Mill (1872); Bigelow (1998).</ref> There are two main versions of nominalism. One denies the existence of universals—that which can be instantiated or exemplified by many particular things (e.g., strength, humanity). The other version specifically denies the existence of abstract objects ''as such''—objects that do not exist in space and time.<ref>Rodriguez-Pereyra (2008) writes: "The word 'Nominalism', as used by contemporary philosophers in the Anglo-American tradition, is ambiguous. In one sense, its most traditional sense deriving from the Middle Ages, it implies the rejection of universals. In another, more modern but equally entrenched sense, it implies the rejection of abstract objects" (§1).</ref>

Most nominalists have held that only physical [[Particular|particulars]] in space and time are real, and that universals exist only ''post res'', that is, subsequent to particular things.<ref>Feibleman (1962), p. 211.</ref> However, some versions of nominalism hold that some particulars are abstract entities (e.g., [[number]]s), whilst others are concrete entities – entities that do exist in space and time (e.g., pillars, snakes, and bananas). Nominalism is primarily a position on the [[problem of universals]]. It is opposed to [[Philosophical realism|realist]] philosophies, such as [[Platonic realism]], which assert that universals do exist over and above particulars, and to the [[Hylomorphism|hylomorphic]] substance theory of Aristotle, which asserts that universals are [[Immanent realism|immanently real]] within them; however, the name "nominalism" emerged from debates in medieval philosophy with [[Roscellinus]].

The term ''nominalism'' stems from the [[Latin]] ''nomen'', "name". [[John Stuart Mill]] summarised nominalism in his [[aphorism]] "there is nothing general except names".<ref>[[John Stuart Mill|Mill, J.S.]] (1865/1877). [https://books.google.com/books?id=5HBEAQAAMAAJ ''An Examination of Sir William Hamilton's Philosophy'', Volume II], Chapter XVII, p. 50.</ref> In [[philosophy of law]], nominalism finds its application in what is called '''constitutional nominalism'''<!--boldface per WP:R#PLA-->.<ref>An overview of the philosophical problems and an application of the concept to a case of the Supreme Court of the State of California, gives Thomas Kupka, 'Verfassungsnominalismus', in: ''Archives for Philosophy of Law and Social Philosophy'' 97 (2011), 44–77, [https://ssrn.com/abstract=2343741 PDF].</ref>

==History==
{{see also|Anti-realism}}

===Ancient Greek philosophy===

[[Plato]] was perhaps the first writer in [[Western philosophy]] to clearly state a [[Realism (philosophy)|realist]], i.e., non-nominalist, position:
<blockquote>... We customarily hypothesize a single form in connection with each of the many things to which we apply the same name.&nbsp;... For example, there are many beds and tables.&nbsp;... But there are only two forms of such furniture, one of the bed and one of the table.  ([[The Republic (Plato)|''Republic'']] 596a–b, trans. Grube) </blockquote>

<blockquote>What about someone who believes in beautiful things, but doesn't believe in the beautiful itself&nbsp;...? Don't you think he is living in a dream rather than a wakened state? (''Republic'' 476c)</blockquote>

The Platonic universals corresponding to the names "bed" and "beautiful" were the [[Theory of Forms|Form]] of the Bed and the Form of the Beautiful, or the ''Bed Itself'' and the ''Beautiful Itself''.  Platonic Forms were the first universals posited as such in philosophy.<ref name="Penner 1987, p. 24">Penner (1987), p. 24.</ref>

Our term "universal" is due to the English translation of [[Aristotle]]'s technical term ''katholou'' which he coined specially for the purpose of discussing the problem of universals.<ref>Peters (1967), p. 100.</ref>  ''Katholou'' is a contraction of the phrase ''kata holou'', meaning "on the whole".<ref>[http://archimedes.fas.harvard.edu/cgi-bin/dict?name=lsj&lang=el&word=kaqo%2flou&filter=GreekXlit "katholou"] in [[Harvard]]'s Archimedes Project online version of [[Henry Liddell|Liddell]] & [[Robert Scott (philologist)|Scott]]'s ''[[A Greek-English Lexicon]]''.</ref>

Aristotle famously rejected certain aspects of Plato's Theory of Forms, but he clearly rejected nominalism as well:

<blockquote>... 'Man', and indeed every general predicate, signifies not an individual, but some quality, or quantity or relation, or something of that sort.  (''[[Sophistical Refutations]]'' xxii, 178b37, trans. Pickard-Cambridge)</blockquote>

The first philosophers to explicitly describe nominalist arguments were the [[Stoics]], especially [[Chrysippus]].<ref>John Sellars, ''Stoicism'', Routledge, 2014, pp. 84–85: "[Stoics] have often been presented as the first nominalists, rejecting the existence of universal concepts altogether.&nbsp;... For Chrysippus there are no universal entities, whether they be conceived as substantial [[Platonic Forms]] or in some other manner."</ref><ref>{{cite web| url = https://www.iep.utm.edu/chrysipp/| title = Chrysippus (Internet Encyclopedia of Philosophy)}}</ref>

===Medieval philosophy===
In [[medieval philosophy]], the French philosopher and [[Theology|theologian]] [[Roscellinus]] (c. 1050 – c. 1125) was an early, prominent proponent of nominalism. Nominalist ideas can be found in the work of [[Peter Abelard]] and reached their flowering in [[William of Ockham]], who was the most influential and thorough nominalist. Abelard's and Ockham's version of nominalism is sometimes called [[conceptualism]], which presents itself as a middle way between nominalism and realism, asserting that there ''is'' something in common among like individuals, but that it is a concept in the mind, rather than a real entity existing independently of the mind. Ockham argued that only individuals existed and that universals were only mental ways of referring to sets of individuals. "I maintain", he wrote, "that a universal is not something real that exists in a subject&nbsp;... but that it has a being only as a thought-object in the mind [objectivum in anima]". As a general rule, Ockham argued against assuming any entities that were not necessary for explanations.  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. Critics argue that conceptualist approaches answer only the psychological question of universals. 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). If resemblances between individuals are asserted, conceptualism becomes moderate realism; if they are denied, it collapses into nominalism.

===Modern and contemporary philosophy===
In [[modern philosophy]], nominalism was revived by [[Thomas Hobbes]]<ref name=SEP>{{cite book| chapter-url = http://plato.stanford.edu/entries/hobbes/| title = Thomas Hobbes (Stanford Encyclopedia of Philosophy)| chapter = Thomas Hobbes| date = 2022| publisher = Metaphysics Research Lab, Stanford University}}</ref> and [[Pierre Gassendi]].<ref>{{cite book| chapter-url = https://plato.stanford.edu/entries/gassendi/| title = Pierre Gassendi (Stanford Encyclopedia of Philosophy)| chapter = Pierre Gassendi| date = 2014| publisher = Metaphysics Research Lab, Stanford University}}</ref>

In [[contemporary philosophy|contemporary]] [[analytic philosophy]], it has been defended by [[Rudolf Carnap]],<ref name=:0>{{cite web| url = https://ndpr.nd.edu/news/resemblance-nominalism-a-solution-to-the-problem-of-universals/| title = "Review of Gonzalo Rodriguez-Pereyra, ''Resemblance Nominalism: A Solution to the Problem of Universals''" – ndpr.nd.edu| date = 7 February 2004| last1 = MacBride| first1 = Fraser}}</ref> [[Nelson Goodman]],<ref>{{cite web| url = https://plato.stanford.edu/entries/goodman/supplement.html| title = "Nelson Goodman: The Calculus of Individuals in its different versions", Stanford Encyclopedia of Philosophy}}</ref>  [[H. H. Price]],<ref name=:0/> and [[D. C. Williams]].<ref>[https://plato.stanford.edu/entries/williams-dc/ Donald Cary Williams, Stanford Encyclopedia of Philosophy].</ref>

Lately, some scholars  have been questioning what kind of influences nominalism might have had in the conception of [[modernity]] and contemporaneity. According to [[Michael Allen Gillespie]], nominalism profoundly influences these two periods. Even though modernity and contemporaneity are secular eras, their roots are firmly established in the sacred.<ref name="gillespie">{{cite book |last1=Gillespie |first1=Michael Allen |title=The Theological Origins of Modernity |date=2008 |publisher=University of Chicago Press |location=Chicago |isbn=978-0226293516}}</ref> Furthermore, "Nominalism turned this world on its head," he argues. "For the nominalists, all real being was individual or particular and universals were thus mere fictions."<ref name="gillespie"/>

Another scholar, Victor Bruno, follows the same line. According to Bruno, nominalism is one of the first signs of rupture in the medieval system. "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. The result of this fissure will be the essays to establish the [[nation state]]."<ref name="Bruno">{{cite book |last1=Bruno |first1=Victor |date=2020 |title=A Imagem Estilhaçada: Breve Ensaio sobre Realismo, Nominalismo e Filosofia |publisher=Editora ViV |location=Rio de Janeiro |isbn=978-6588972021}}</ref>

===Indian philosophy===
{{See also|Difference (philosophy)}}
[[Indian philosophy]] encompasses various realist and nominalist traditions. 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. According to Indian realism, both the individual and the universal exist objectively, with the second underlying the former.

Buddhists take the nominalist position, especially those of the [[Sautrāntika]]<ref>{{cite web|author=Sonam Thakchoe|editor=Edward N. Zalta|title=The Theory of Two Truths in India|url=https://plato.stanford.edu/entries/twotruths-india/|website=Stanford Encyclopedia of Philosophy|date=2022 }}</ref> and [[Yogācāra]] schools;<ref>{{cite book |last1=Chatterjee |first1=A. K. |title=The Yogācāra Idealism |date=1975 |publisher=Motilal Banarsidass |location=Delhi |isbn=8120803159 |edition=2d, rev.}}</ref><ref name="Bruno" /> they were of the opinion that words have as referent not true objects, but only concepts produced in the intellect. These concepts are not real since they do not have efficient existence, that is, causal powers. Words, as linguistic conventions, are useful to thought and discourse, but even so, it should not be accepted that words apprehend reality as it is.

[[Dignāga]] formulated a nominalist theory of meaning called ''apohavada'', or ''theory of exclusions''. The theory seeks to explain how it is possible for words to refer to classes of objects even if no such class has an objective existence. Dignāga's thesis is that classes do not refer to positive qualities that their members share in common. On the contrary, universal classes are exclusions (''[[apoha]]''). As such, the "cow" class, for example, is composed of all exclusions common to individual cows: they are all non-horse, non-elephant, etc.

==The problem of universals==

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. One wants to know by virtue of ''what'' are Fluffy and Kitzler both cats, and ''what'' makes the grass, the shirt, and Kermit green.

The [[Platonic realism|Platonist]] answer is that all the green things are green in virtue of the [[existence]] of a universal: a single [[Abstraction|abstract]] thing that, in this case, is a [[part (mathematics)|part]] of all the green things. With respect to the color of the grass, the shirt and Kermit, one of their parts is identical. In this respect, the three parts are literally one. Greenness is repeatable because there is one thing that [[exemplification|manifests]] itself wherever there are green things.

Nominalism denies the existence of universals. The motivation for this flows from several concerns, the first one being where they might exist. [[Plato]] famously held, on one interpretation, that there is a realm of abstract forms or universals apart from the physical world (see [[theory of the forms]]). Particular physical objects merely exemplify or instantiate the universal. But this raises the question: Where is this universal realm?  One possibility is that it is outside space and time. A view sympathetic with this possibility holds that, precisely because some form is immanent in several physical objects, it must also transcend each of those physical objects; in this way, the forms are "transcendent" only insofar as they are "immanent" in many physical objects. In other words, immanence implies transcendence; they are not opposed to one another. (Nor, in this view, would there be a separate "world" or "realm" of forms that is distinct from the physical world, thus shirking much of the worry about where to locate a "universal realm".) However, [[metaphysical naturalism|naturalists]] assert that nothing is outside of space and time. Some [[Neoplatonists]], such as the pagan philosopher [[Plotinus]] and the Christian philosopher [[Augustine of Hippo|Augustine]], imply (anticipating [[conceptualism]]) that universals are contained within the ''mind'' of God. To complicate things, what is the nature of the [[instantiation principle|instantiation]] or [[exemplification]] [[logic of relatives|relation]]?

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

[[Moderate realism|Moderate realists]] hold that there is no realm in which universals exist, but rather there universals are located in space and time however they are manifest. Suppose that a universal, for example greenness, is supposed to be a single thing. Nominalists consider it unusual that there could be a single thing that exists in multiple places simultaneously. The realist maintains that all the instances of greenness are held together by the exemplification relation, but that this relation cannot be explained. Additionally, in lexicology there is an argument against color realism, namely the subject of the [[Blue–green distinction in language|blue-green distinction]]. In some languages the equivalent words for blue and green may be [[Colexification|colexified]] (and furthermore there may not be a straightforward translation either – in Japanese "青", which is usually translated as "blue", is sometimes used for words which in English may be considered as "green" (such as green apples).)<ref>{{cite journal |last1=Conlan |first1=Francis |date=January 2003 |title=Searching for the semantic boundaries of the Japanese colour term 'AO' |url=https://www.jbe-platform.com/content/journals/10.1075/aral.26.1.06con |journal=Australian Review of Applied Linguistics|volume=26 |issue=1 |pages=71–86 |doi=10.1075/aral.26.1.06con |access-date=April 17, 2022|url-access=subscription }}</ref>

Finally, many philosophers prefer simpler [[ontology|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.'" They try to express everything that they want to explain without using universals such as "catness" or "greenness."

==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.

==Criticisms==
===Historical origins of the term===
As a category of late medieval thought, the concept of 'nominalism' has been increasingly queried. Traditionally, the fourteenth century has been regarded as the heyday of nominalism, with figures such as [[John Buridan]] and [[William of Ockham]] viewed as founding figures. However, the concept of 'nominalism' as a movement (generally contrasted with 'realism'), first emerged only in the late fourteenth century,<ref>The classic starting point of nominalism has been the edict issued by [[Louis XI]] in 1474 commanding that realism alone (as contained in scholars such as [[Averroes]], [[Albert the Great]], [[Aquinas]], [[Duns Scotus]] and [[Bonaventure]]) be taught at the University of Paris, and ordering that the books of various 'renovating scholars', including Ockham, [[Gregory of Rimini]], Buridan and [[Peter of Ailly]] be removed. The edict used the word 'nominalist' to describe those students at Paris who 'are not afraid to imitate' the renovators. These students then made a reply to Louis XI, defending nominalism as a movement going back to Ockham, which had been persecuted repeatedly, but which in fact represents the truer philosophy.  See Robert Pasnau, ''Metaphysical Themes, 1274-1671'', (New York: OUP, 2011), p. 85.</ref> and only gradually became widespread during the fifteenth century.<ref>For example, when [[Jerome of Prague]] visited the [[University of Heidelberg]] in 1406, he described the nominalists as those who deny the reality of universals outside the human mind, and realists as those who affirm that reality. Also, for instance, in a 1425 document from the [[University of Cologne]] that draws a distinction between the via of Thomas Aquinas, Albert the Great, and the via of the 'modern masters' John Buridan and Marsilius of Inghen. See Robert Pasnau, ''Metaphysical Themes, 1274-1671'', (New York: OUP, 2011), p84.</ref> The notion of two distinct ways, a ''via antiqua'', associated with realism, and a ''via moderna'', associated with nominalism, became widespread only in the later fifteenth century – a dispute which eventually dried up in the sixteenth century.<ref name="See Robert Pasnau 2011 p84">See Robert Pasnau, ''Metaphysical Themes, 1274-1671'', (New York: OUP, 2011), p84.</ref>

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. While one might speak of family resemblances between Ockham, Buridan, Marsilius and others, there are also striking differences. 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.<ref>See Robert Pasnau, ''Metaphysical Themes, 1274-1671'', (New York: OUP, 2011), p86.</ref> This makes it difficult, it has been argued, to follow the twentieth century narrative which portrayed late scholastic philosophy as a dispute which emerged in the fourteenth century between the ''via moderna'', nominalism, and the ''via antiqua'', realism, with the nominalist ideas of [[William of Ockham]] foreshadowing the eventual rejection of scholasticism in the seventeenth century.<ref name="See Robert Pasnau 2011 p84"/>

===Nominalist reconstructions in mathematics===
A critique of nominalist reconstructions{{clarification needed|date=January 2023}} in mathematics was undertaken by Burgess (1983) and Burgess and Rosen (1997). Burgess distinguished two types of nominalist reconstructions.  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.&nbsp;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 [[infinitesimal]]s; the [[constructivism (mathematics)|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.<ref>{{cite journal | last1 = Usadi Katz | first1 = Karin | author-link2 = Mikhail Katz | last2 = Katz | first2 = Mikhail G. | year = 2011 | title = A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography | journal = [[Foundations of Science]] | volume = 17 | pages = 51–89 | doi = 10.1007/s10699-011-9223-1 | arxiv = 1104.0375 | s2cid = 119250310 }}</ref>

== See also ==
{{cols|colwidth=16em}}
* [[Abstraction]]
* [[Abstract object]]
* [[Conceptualism]]
* [[Concrete (philosophy)]]
* [[Idea]]
* ''[[Ideas Have Consequences]]''
* [[Linguistic relativity]]
* [[Literary nominalism]]
* [[Object (philosophy)|Object]]
* [[Problem of universals]]
* [[Psychological nominalism]]
* [[Realism (philosophy)]]
* [[School of Names]]
* [[Substantial form]]
* [[Universal (metaphysics)]]
* [[William of Ockham]]
{{colend}}

== Notes ==
{{Reflist}}

== References and further reading ==
* [[Marilyn McCord Adams|Adams, Marilyn McCord]].  ''[[William of Ockham]]'' (2 volumes) Notre Dame, IN:  Notre Dame University Press, 1987.
* ''[[American Heritage Dictionary]] of the English Language'', Fourth Edition, 2000.
* [[Borges, Jorge Luis]] (1960). "De las alegorías a las novelas" in ''Otras inquisiciones'' (pg 153–56).
* Burgess, John (1983). Why I am not a nominalist. Notre Dame J. Formal Logic 24, no. 1, 93–105.
* [[John P. Burgess|Burgess, John]] & Rosen, Gideon. (1997). ''A Subject with no Object''. Princeton University Press.
* Courtenay, William J.  ''[[Adam Wodeham]]:  An Introduction to His Life and Writings'', Leiden:  E. J. Brill, 1978.
* [[James Feibleman|Feibleman, James K.]] (1962). "Nominalism" in ''Dictionary of Philosophy'', Dagobert D. Runes (ed.). Totowa, NJ: Littlefield, Adams, & Co. ([http://www.ditext.com/runes/index.html link])
* [[Nelson Goodman|Goodman, Nelson]] (1977) ''The Structure of Appearance'', 3rd ed. Kluwer.
* Hacking, Ian (1999). ''The Social Construction of What?'', Harvard University Press.
* Karin Usadi Katz and [[Mikhail Katz|Mikhail G. Katz]] (2011) A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography. [[Foundations of Science]]. {{doi|10.1007/s10699-011-9223-1}} See [https://doi.org/10.1007%2Fs10699-011-9223-1 link]
* [[John Stuart Mill|Mill, J. S.]], (1872). ''An Examination of William Hamilton's Philosophy'', 4th ed., [http://oll.libertyfund.org/index.php?option=com_staticxt&staticfile=show.php%3Ftitle=240&layout=html#chapter_40884 Chapter XVII].
* [[Heiko Oberman|Oberman, Heiko]].  ''The Harvest of Medieval Theology:  [[Gabriel Biel]] and Late Medieval Nominalism'', Grand Rapids, MI:  [[Baker Academic]], 2001.
* Penner, T. (1987). ''The Ascent from Nominalism'', D. Reidel Publishing.
* Peters, F. (1967). ''Greek Philosophical Terms'', New York University Press.
* Price, H. H. (1953). "Universals and Resemblance", Ch. 1 of ''Thinking and Experience'', Hutchinson's University Library.
* [[W. V. O. Quine|Quine, W. V. O.]] (1961). "On What There is," in ''From a Logical Point of View'', 2nd/ed. N.Y: Harper and Row.
* [[W. V. O. Quine|Quine, W. V. O.]] (1969). ''Set Theory and Its Logic'', 2nd ed. Harvard University Press. (Ch. 1 includes the classic treatment of virtual sets and relations, a nominalist alternative to set theory.)
* Robson, John Adam, ''[[Wyclif]] and the Oxford Schools:  The Relation of the "Summa de Ente" to [[Scholasticism|Scholastic]] Debates at Oxford in the Late Fourteenth Century'', Cambridge, England:  [[Cambridge University Press]], 1961.
* Utz, Richard, "Literary Nominalism." ''Oxford Dictionary of the Middle Ages''. Ed. Robert E. Bjork. Oxford: Oxford University Press, 2010. Vol. III, p.&nbsp;1000.
* [[Bertrand Russell|Russell, Bertrand]] (1912). "The World of Universals," in ''The Problems of Philosophy'', Oxford University Press.
* Williams, D. C. (1953). "On the Elements of Being: I", ''Review of Metaphysics'', vol. 17, pp.&nbsp;3–18.

==External links==
{{NIE Poster}}
* {{cite SEP |url-id=nominalism-metaphysics |title=Nominalism in Metaphysics |last=Rodriguez-Pereyra |first=Gonzalo}}
* {{cite SEP |url-id=tropes |title=Tropes |last=Maurin |first=Anna-Sofia}}
* {{IEP|/mathematical-nominalism/}}
* [https://www.iep.utm.edu/universa/ Universals], entry by Mary C. MacLeod and Eric M. Rubenstein in the [http://www.iep.utm.edu/ ''Internet Encyclopedia of Philosophy'']
* {{cite SEP |url-id=universals-medieval |title=The Medieval Problem of Universals |last=Klima |first=Gyula}}
* [https://www.newadvent.org/cathen/11090c.htm Nominalism, Realism, Conceptualism], from ''The Catholic Encyclopedia''.
* [https://books.google.com/books?id=GU3lV1xoWC8C  Rosen, Burgess: Nominalism Reconsidered] in The Oxford Handbook of Philosophy of Mathematics and Logic (2007)
* ''[https://www.uni-due.de/imperia/md/content/perspicuitas/nominalism_medieval.pdf Medieval Nominalism and the Literary Questions: Selected Studies]'' by Richard Utz, with the assistance of Terry Barakat ''Perspicuitas'', (2004)

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