Nominalism is the philosophical position that universals - general terms such as redness, humanity, or triangularity - have no existence independent of the particular things to which they apply. Nominalists hold that only individual, concrete particulars exist; what we call universals are, at most, names, concepts, or mental habits imposed on a world that contains nothing genuinely shared among distinct objects. The position has been defended across the history of philosophy by logicians, empiricists, and analytic philosophers who regard the postulation of abstract universal entities as ontologically extravagant and explanatorily unnecessary.

Nominalists invoke Ockham's Razor as a foundational methodological commitment: entities should not be multiplied beyond necessity. If ordinary language and science can be fully accounted for without positing a realm of abstract universals - a Platonic heaven of forms, or Aristotelian immanent universals inhering in matter - then such entities should be rejected. Nominalists argue that particular red things are fully explained by their individual physical properties; there is no further need to posit Redness Itself as a shared constituent.

Nominalists press the question of how a universal relates to its instances. If the universal humanity is somehow present in each human being, it must either be wholly present in each (which seems to require mysterious multiplication of a single entity) or only partially present (which seems to contradict what it means to be a universal). This regress worry, sometimes associated with the Third Man Argument pressed against Plato, is taken by nominalists as evidence that universal-positing theories generate more problems than they solve.

Many nominalists, especially those in the empiricist tradition, argue that we have no credible account of how finite, embodied minds could acquire knowledge of abstract, non-spatiotemporal universals. John Locke's account of abstract ideas, and later David Hume's attack on abstract general ideas, reflect the broadly nominalist suspicion that purported acquaintance with universals reduces, on examination, to familiarity with particular ideas used as representatives of a class.

Nominalists contend that the semantic work allegedly done by universals can be handled by other means: by resemblance relations among particulars, by predicates treated as primitive linguistic devices, by classes or sets of particulars, or by tropes (particular property-instances, themselves individuals). On this view, the sentence “Socrates is wise” is true in virtue of Socrates being a certain kind of particular, not in virtue of his instantiating a separately existing entity called Wisdom.

Nominalists are not unanimous about what does ground general truths, and several distinct programs exist within the broadly nominalist camp.

• Predicate Nominalism holds that what makes a particular an F is simply that the predicate “F” applies to it. Critics charge this makes truth depend on linguistic convention; defenders argue it merely refuses to inflate ontology.
• Resemblance Nominalism, associated especially with H. H. Price and developed rigorously by Gonzalo Rodriguez-Pereyra, holds that particulars fall under a common general term because they sufficiently resemble a paradigm or resemble one another in the relevant respect. No universal mediates the resemblance; resemblance itself is a primitive relation among particulars.
• Trope Theory (sometimes called property nominalism or abstract particulalism) holds that properties exist but are themselves particulars - this particular redness, not Redness. Tropes can resemble one another; what look like universals are simply classes of exactly resembling tropes. D. C. Williams and Keith Campbell are canonical trope theorists.
• Class Nominalism identifies a property with the class of all its instances. It faces the coextension problem: if exactly the same things happen to be renates and cordates, the view seems to imply that being a renate and being a cordate are the same property.
• Mereological Nominalism, explored by Nelson Goodman and W. V. O. Quine, attempts to replace set-theoretic constructions with the part-whole relation, avoiding commitment to abstracta.

The nominalist position is classically associated with the medieval philosopher William of Ockham (c. 1287-1347), though earlier figures such as Roscelin of Compiègne (c. 1050-1125) had raised related doubts. Ockham argued that universals are termini - signs in the mind or in language - that stand for many things simultaneously without any corresponding shared nature in the world. His position, often called terminism, was developed by followers such as Jean Buridan and Gabriel Biel and became a significant force in late medieval scholasticism, sometimes labeled the via moderna in contrast to the realist via antiqua.

Early modern empiricism renewed nominalist themes. Locke's critique of innate ideas and his account of general ideas formed by abstraction, Hume's insistence that all genuine ideas trace to particular impressions, and Berkeley's rejection of Locke's abstract general ideas all contributed to an empiricist climate broadly hostile to Platonic realism.

In the twentieth century, nominalism became a central concern of analytic ontology. W. V. O. Quine and Nelson Goodman published their landmark joint paper “Steps Toward a Constructive Nominalism” in 1947, attempting to reconstruct mathematics without appeal to classes or abstracta. Quine later retreated from strict nominalism under pressure from the indispensability argument for mathematical entities, while Goodman maintained a more consistently nominalist program. The debate was sharpened by the realist responses of David Armstrong, whose Universals and Scientific Realism (1978) provided what many regard as the most systematic contemporary defense of immanent realism, prompting in turn more sophisticated nominalist replies.

• William of Ockham (c. 1287-1347) - Franciscan philosopher whose terminism established nominalism as a major scholastic program and whose methodological razor remains nominalism's most famous slogan.
• W. V. O. Quine (1908-2000) - American logician who, especially in “On What There Is” (1948) and Word and Object (1960), made ontological parsimony and the rejection of abstracta central to analytic philosophy, even as he qualified his nominalism regarding mathematical entities.
• Nelson Goodman (1906-1998) - Maintained a thoroughgoing nominalism, refusing to admit classes as genuine entities, and developed mereological alternatives in works including The Structure of Appearance (1951).
• H. H. Price (1899-1984) - Oxford philosopher whose Thinking and Experience (1953) developed an influential version of resemblance nominalism.
• D. C. Williams (1899-1983) - Defended trope theory as a nominalist-friendly alternative to Platonic universals in “The Elements of Being” (1953).
• Keith Campbell (b. 1938) - Australian philosopher whose Abstract Particulars (1990) provided a thorough development and defense of trope theory.
• Gonzalo Rodriguez-Pereyra (b. 1968) - Contemporary defender of resemblance nominalism whose Resemblance Nominalism: A Solution to the Problem of Universals (2002) offers a systematic modern formulation.

Nominalists disagree significantly about which positive account should replace realism. Resemblance nominalists and trope theorists dispute whether resemblance can be treated as a primitive without illicitly importing something universal-like. Class nominalists face the coextension problem and the question of whether classes are themselves abstracta. Predicate nominalists are accused by their colleagues of offering no real explanation at all. Some nominalists accept tropes but dispute whether tropes require resemblance primitives or whether exact resemblance can be analyzed further.

A further internal tension concerns mathematics. Quine's indispensability argument - that scientific theories quantify over mathematical entities and therefore commit us to their existence - has forced nominalists either to accept mathematical abstracta as an exception (as Quine did), to develop nominalistic reformulations of science (as Hartry Field attempted in Science Without Numbers, 1980), or to argue that mathematical language does not carry genuine ontological commitment. Field's program of fictionalism - the view that mathematical statements are useful fictions, not truths about abstracta - is embraced by some nominalists as the correct resolution; see mathematics-fictionalism-viewpoint.

There is also disagreement about whether nominalism should be understood as a thesis about language, about ontology, or about both. Metalinguistic nominalists hold that sentences apparently about universals can be paraphrased into sentences about words; ontological nominalists make the stronger claim that the world simply contains no universals; the two programs do not always coincide. Some philosophers occupy an intermediate position, holding that general concepts are real as mental constructions without requiring mind-independent abstract entities; this view, known as conceptualism, is treated at Universals - Conceptualism Viewpoint.

• Universals - Main topic overview
• Universals - History - History of the problem of universals
• Universals - Debate - The broader debate between realists and nominalists
• Universals - Realism Viewpoint - The opposing realist position
• universals-platonism-viewpoint - Platonic realism regarding universals
• Universals - Aristotelian Realism Viewpoint - Immanent realist position
• Universals - Trope Theory Viewpoint - Trope-theoretic approaches
• Universals - Conceptualism Viewpoint - The intermediate conceptualist position
• abstract-objects-debate - Broader debate on the existence of abstracta
• mathematics-fictionalism-viewpoint - Fictionalist approach to mathematical entities

1. William of Ockham, Summa Logicae, ed. Philotheus Boehner, Gedeon Gál, and Stephen Brown (St. Bonaventure, NY: Franciscan Institute, 1974). Part I contains the canonical statement of Ockham's terminism.
2. W. V. O. Quine, “On What There Is,” Review of Metaphysics 2, no. 5 (1948): 21-38. Reprinted in From a Logical Point of View (Cambridge, MA: Harvard University Press, 1953).
3. Nelson Goodman and W. V. O. Quine, “Steps Toward a Constructive Nominalism,” Journal of Symbolic Logic 12, no. 4 (1947): 105-122.
4. Nelson Goodman, The Structure of Appearance (Cambridge, MA: Harvard University Press, 1951).
5. H. H. Price, Thinking and Experience (London: Hutchinson, 1953), chaps. 1-2.
6. D. C. Williams, “The Elements of Being,” Review of Metaphysics 7, nos. 1-2 (1953): 3-18, 171-192.
7. Keith Campbell, Abstract Particulars (Oxford: Blackwell, 1990).
8. Gonzalo Rodriguez-Pereyra, Resemblance Nominalism: A Solution to the Problem of Universals (Oxford: Oxford University Press, 2002).
9. David Armstrong, Universals and Scientific Realism, 2 vols. (Cambridge: Cambridge University Press, 1978). The principal contemporary realist target that nominalist responses engage.
10. Hartry Field, Science Without Numbers: A Defence of Nominalism (Oxford: Blackwell, 1980). The most influential attempt to reformulate physics without abstract mathematical entities.
11. Michael J. Loux, Universals and Particulars: Readings in Ontology (Notre Dame, IN: University of Notre Dame Press, 1976). A standard anthology covering the full range of positions.
12. Michael J. Loux, Metaphysics: A Contemporary Introduction, 3rd ed. (New York: Routledge, 2006), chap. 2. A useful survey of the problem of universals.