Nominalist Tradition

Historical Background and Core Thesis

The nominalist tradition is a long-running current in Western philosophy centered on skepticism about the existence of universals and other abstract entities. Its core thesis is that what appear to be shared natures—such as redness, triangularity, or humanity—do not exist as independent, mind‑ or language‑independent entities. Instead, nominalists typically explain such commonalities in terms of names, concepts, or similarities among individual things.

Historically, nominalism emerges within the medieval problem of universals, a debate over how to understand general terms and shared properties. Medieval realists (drawing on Plato and Aristotle) maintained that universals in some sense exist: either ante rem (independently of things, as in strong Platonism) or in re (in the things themselves, as in moderate Aristotelian realism). Nominalists, by contrast, denied that universals enjoy such robust ontological status.

Early precursors are sometimes found in Roscelin of Compiègne (11th century), who is reported to have argued that universals are mere flatus vocis—a “breath of voice.” The tradition becomes more systematic in the 14th century with William of Ockham, often regarded as the paradigmatic medieval nominalist. Ockham argues that only individuals exist in the most fundamental sense; universal terms refer to many individuals by signifying them, but there is no distinct universal entity corresponding to the term.

The nominalist tradition reappears and transforms in early modern philosophy, especially in Thomas Hobbes, John Locke, and later empiricists, many of whom reject innate abstract entities and treat general ideas as products of mental operations. In contemporary analytic metaphysics, nominalism re-emerges as a series of sophisticated positions opposing Platonism about universals, numbers, sets, and other abstract objects.

Despite historical shifts, a recurring slogan captures the tradition’s spirit: “Only individuals exist.” What differs across nominalists is how they analyze generality, similarity, and mathematics without invoking independently existing abstracta.

Varieties of Nominalism

Over time, the nominalist tradition has diversified into multiple, sometimes competing, positions. Philosophers often reserve “nominalism” broadly for all anti‑realist views about universals and abstract objects, while distinguishing more precise sub‑views.

1. Predicate nominalism

Predicate nominalists claim that there is nothing more to a property like being red than the fact that a predicate—“is red”—is correctly applied to certain objects. On this view, explaining why two things are both red simply appeals to the linguistic fact that we use the same word for them. Critics argue this risks circularity: if the predicate is correct, it seems so because the objects already share some feature, which the explanation pretends to avoid.

2. Class (or set) nominalism

Class nominalists propose that properties are identical with sets or classes of individuals: the property being red is just the set of all red things. This view replaces universals with collections of particulars. Realists respond that sets themselves look like abstract entities, so class nominalism may simply relocate, rather than resolve, the metaphysical commitment.

3. Resemblance nominalism

Resemblance nominalists explain universality by appealing to patterns of similarity among individuals. Two objects are both red, on this view, because they resemble each other in certain respects, and because those resembling relations form complex resemblance networks. This avoids invoking universals, but invites questions: is resemblance itself a universal relation, or must it also be nominalized? Elaborate resemblance nominalisms attempt to address this by appealing to primitive resemblance facts or by carefully structuring resemblance classes.

4. Concept nominalism (or conceptualism)

Sometimes grouped under nominalism is conceptualism, the view that universals exist only as concepts in minds rather than as mind‑independent entities. Medieval thinkers such as Peter Abelard and later early modern philosophers develop conceptualist accounts of general ideas. Some historians distinguish conceptualism from strict nominalism (which tends to be more austere), while others treat it as one strand within the broader nominalist tradition.

5. Nominalism about mathematical objects

In modern philosophy of mathematics, nominalism is extended to objects such as numbers, sets, and functions. Here, nominalists deny the existence of abstract mathematical entities while attempting to preserve the usefulness and apparent truth of mathematics.

Prominent strategies include:

• Fictionalism: mathematical statements are treated analogously to statements about fictional characters. They are systematically useful and internally coherent, though not literally about existing abstract objects.

• Figurative or paraphrase nominalism: some seek to reformulate (“paraphrase away”) mathematical claims into statements about concrete structures, physical systems, or modal facts, avoiding commitment to abstracta.

• Structuralism with nominalist leanings: some positions treat mathematics as describing structures or patterns that can, in principle, be instantiated by concrete systems, thereby diminishing the need for standalone abstract objects.

These mathematical forms of nominalism continue the traditional nominalist impulse—minimizing ontological commitments—under the highly formalized conditions of modern science and logic.

Influence and Criticisms

The nominalist tradition has exerted widespread influence in several domains of philosophy.

In metaphysics, nominalism motivates ontological parsimony—the idea that one should not multiply entities beyond what is necessary. Ockham’s formulation, often called Ockham’s Razor, is frequently interpreted as favoring nominalist views against realist ones, though historians debate how explicitly Ockham intended this tool to support nominalism. Many contemporary metaphysicians weigh the cost of positing universals or abstract objects against the explanatory benefits, often describing this as a trade‑off between parsimony and explanatory power.

In epistemology and philosophy of language, nominalism shapes accounts of how general knowledge and reference work. Proponents argue that grounding universality in language, concepts, or resemblance avoids mysterious entities and aligns better with empirical accounts of concept formation. Realists, however, contend that some kind of objective common nature is needed to underwrite successful reference, induction, and scientific classification.

In philosophy of science, nominalist ideas intersect with empiricist and anti‑metaphysical attitudes. Certain logical empiricists, for example, sought to eliminate or minimize reference to abstract entities in scientific theories. More recent debates in the philosophy of physics and ontology of theories revisit nominalist concerns: whether theoretical entities should be interpreted as concrete, as merely instrumental, or as belonging to some attenuated ontological category.

Criticisms of nominalism are correspondingly diverse. Realist opponents argue that:

• Explanatory insufficiency: Nominalist accounts of similarity, generality, and lawlike regularities often appear to presuppose what they seek to explain (for instance, resemblance itself may function as an unacknowledged universal).

• Mathematical indispensability: Some philosophers contend that the indispensability of mathematics to empirical science supports belief in mathematical objects, challenging nominalist projects that attempt to excise these commitments without loss.

• Semantic challenges: There are concerns about how general terms, counterfactuals, and modal statements retain objective truth‑conditions if there are no universals or abstract structures for them to latch onto.

Nominalists reply that realists overpopulate ontology with entities that go beyond what explanatory practice truly requires, and that carefully constructed nominalist theories can match realist accounts in explanatory reach while remaining more austere. In contemporary discussions, the debate is often framed in terms of competing theoretical virtues—parsimony, clarity, coherence with scientific practice, and intuitive appeal—rather than straightforward refutations on either side.

As a result, the nominalist tradition is best understood not as a single doctrine but as a recurrent stance: a persistent skepticism toward abstract and universal entities, accompanied by a continuing effort to reconstruct logic, language, science, and mathematics using as lean an ontology as possible. Its evolving forms chart a central fault line within Western metaphysics, one that continues to structure debates about what there is and how we should talk about it.