Nominalism

1. Introduction

Nominalism is the broad family of philosophical views that deny the existence of universals and other robust abstract objects in favor of a world composed fundamentally of particulars. It is usually defined in contrast to various forms of realism about universals, which hold that there are repeatable entities—such as redness, humanity, or triangularity—shared by many individual things.

In its classical and medieval formulations, nominalism emerged in response to the problem of universals, the question of how different things can be of the same kind or share the same properties. Nominalists maintain that sameness in kind and property can be understood without positing a separate ontological category of universals, appealing instead to language, thought, resemblance relations, or particularized properties.

The term “nominalism” covers a range of positions that differ in how they interpret generality:

• Some treat general terms as mere sounds or names without corresponding universal entities.
• Others locate generality in mental acts or concepts rather than in the external world.
• More recent variants reinterpret talk of properties, relations, and mathematical objects to avoid commitment to non-spatiotemporal entities.

Across these versions, several themes recur: a preference for ontological parsimony (“do not multiply entities beyond necessity”), a focus on the linguistic or conceptual mechanisms underlying classification, and an effort to reconcile everyday and scientific discourse with a sparse ontology of individuals.

Historically, nominalism has played a significant role in medieval scholastic debates, influenced strands of early modern empiricism and political theory, and continues to shape contemporary discussions in analytic metaphysics, the philosophy of language, and the philosophy of science. It is not a unified school with a single doctrine, but a recurring strategy for explaining generality, meaning, and lawlike patterns without positing a realm of universals or abstract entities.

2. Historical Origins and Founding Context

Nominalism’s emergence in the Latin West is closely tied to medieval debates over universals that developed after the reintroduction of Aristotle’s logical works in the 11th and 12th centuries. Earlier ancient and late antique sources provided background problems and distinctions, but the systematic formulation of nominalism occurred within scholastic institutions such as cathedral schools and, later, universities.

Late Antique and Early Medieval Background

Ancient Platonism and Aristotelianism had already framed the issue of universals, while Stoic attention to language and predicates provided precedents for a more linguistic orientation. Late antique commentators and early medieval thinkers like Boethius transmitted these debates, especially through commentaries on Porphyry’s Isagoge, which explicitly raised the problem of universals without resolving it.

High Medieval Context

With the growth of the University of Paris and other centers of learning, Aristotelian logic became central to the curriculum. The question of whether genera and species exist outside the mind became a focal point of logical and metaphysical discussion. Within this environment:

• Early figures such as Roscelin of Compiègne (late 11th c.) were reported to treat universals as mere flatus vocis, although historical evidence is fragmentary.
• In the 12th century, Peter Abelard developed a sophisticated account that rejected real universals while emphasizing the role of signification and mental acts.

The institutional setting of disputations, commentaries, and quaestiones encouraged increasingly fine-grained positions. Nominalism appeared not as a freestanding movement with formal membership, but as a recognizable tendency within scholastic logic and metaphysics.

Later Medieval Developments

By the 14th century, figures such as William of Ockham, John Buridan, and Nicholas of Autrecourt articulated influential nominalist systems. Their work occurred against the backdrop of:

• Tensions between scholastic realism (including Thomism and Scotism) and dissenting approaches.
• Theological concerns about divine omnipotence, grace, and the status of theological propositions.
• Institutional conflicts within the church and universities, which sometimes shaped the reception and condemnation of certain doctrines.

Nominalism thus took shape in an environment where logical analysis, theological orthodoxy, and university politics intersected.

3. Etymology of the Name "Nominalism"

The term “nominalism” derives from the Medieval Latin nominalismus, based on nomen (“name”). It signals the central idea that what are called “universals” are, in some sense, names rather than things.

Medieval Latin and Scholastic Usage

In medieval scholastic discourse, nominales or nominalistae were contrasted with reales (realists) and, in some taxonomies, with conceptualists or terminists. The label emphasized:

• The status of general terms (nomina communia) as linguistic items.
• The denial that such terms correspond to real, mind-independent universals.

The associated slogan, reported for some early figures, was:

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Universalia sunt nomina, non res (“Universals are names, not things”).

The expression flatus vocis (“breath of the voice”) was used polemically to characterize more radical positions that treated universal terms as mere sounds without corresponding universal entities.

Later Vernacular and Philosophical Adoption

In later German scholastic and early modern discussions, the Latin term was rendered as Nominalismus, from which modern European languages derived their versions (e.g., French nominalisme, English nominalism). These terms came to denote:

• Historical movements within medieval thought (e.g., “Ockhamist nominalism”).
• A broader metaphysical stance regarding universals and abstract objects.

In contemporary philosophy, “nominalism” often has an expanded usage, applying not only to medieval debates about universals but also to modern positions that deny the existence of abstracta such as sets, propositions, or numbers. Despite this broader application, the etymological core remains: nominalists, in one way or another, explain generality and abstraction by appeal to names, language, or conceptual practices rather than to independently existing universal entities.

The etymology thus tracks both a historical faction within scholasticism and a more general philosophical orientation characterized by anti-realist attitudes toward universals and abstract objects.

4. The Problem of Universals

The problem of universals is the central theoretical issue that nominalism addresses. It concerns how to account for the apparent sameness or repeatability found in the world: many different things are red, many individuals are human, and different events instantiate the same law. The question is what, if anything, these items literally share.

Classical Formulation

A standard medieval formulation, inherited from Porphyry’s Isagoge and Boethius’s commentaries, asks whether genera and species:

1. Exist or are mere concepts;
2. If they exist, whether they are corporeal or incorporeal;
3. Whether they exist separately from sensibles or only in them.

Realists answer by positing universals—entities that can be wholly present in many different particulars (e.g., the universal “humanity” present in each human). Nominalists, in contrast, seek to explain classification and predication without such entities.

Dimensions of the Problem

Different aspects of the problem have been distinguished:

Nominalists typically address all three dimensions simultaneously, proposing accounts of meaning and knowledge that do not require universals.

Nominalist Challenges

Nominalists argue that positing universals raises difficulties:

• How can a single entity be wholly present in multiple locations at once?
• How are universals themselves individuated and related to particulars?
• Do universals introduce unnecessary complexity into our ontology?

In response, they develop alternative explanations: treating general terms as devices for grouping individuals, construing general thoughts as mental acts directed at many particulars, or appealing to resemblance and relational structures rather than shared natures.

The problem of universals thus provides the primary backdrop against which the various forms of nominalism define themselves and from which they derive many of their distinctive strategies.

5. Core Doctrines and Central Maxims

While nominalist views vary, historians and theorists commonly identify several core doctrines and maxims that structure the family of positions.

Denial of Real Universals

Nominalists deny that there are mind-independent universals—entities such as “humanity,” “redness,” or “justice” that exist over and above individual humans, red things, and just acts. Instead, they hold that:

• Only particulars (individual concrete entities, events, and, for some, particularized properties) fundamentally exist.
• Generality is to be explained without invoking shared universal natures.

Priority of Language and/or Thought

A second core idea is that language or cognition underlies the appearance of universals:

• General terms (e.g., “cat,” “triangle”) are features of languages.
• General concepts or acts (e.g., thinking of “cat” in general) are features of minds.
• Apparent reference to universals is often reinterpreted as talk about words, concepts, or sets of individuals.

This emphasis is expressed in the traditional maxim:

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Universalia sunt nomina, non res
Universals are names, not things.

Ontological Parsimony

Nominalists typically appeal to ontological economy. A slogan widely associated with William of Ockham is:

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Entia non sunt multiplicanda praeter necessitatem.
Entities are not to be multiplied beyond necessity.

Proponents use this principle to argue that if we can explain phenomena (such as predication and similarity) without universals, we should refrain from positing them.

Extensional and Particularist Orientation

Many nominalists favor extensional accounts: to understand a predicate, one looks to the collection of individuals it applies to, rather than to an intensional content identified with a universal. They also tend to prioritize:

• Singular terms and propositions about specific individuals;
• The construction of general statements as quantifications over individuals.

Diversity Within a Shared Framework

Within this shared framework, nominalists diverge over:

• Whether generality is primarily linguistic (names), mental (concepts), or ontological (tropes, resemblance relations).
• How much metaphysical structure—such as relations or particularized properties—they are willing to admit.

Despite such differences, the rejection of robust universals, the stress on language or thought, and a commitment to parsimonious ontology form the central, recurring themes of nominalist doctrine.

6. Metaphysical Views: Individuals and the Denial of Universals

Nominalist metaphysics is characterized by a commitment to individuals as the basic constituents of reality and a corresponding denial of universals as distinct entities.

Ontological Commitment to Particulars

Nominalists typically maintain that:

• The world is fundamentally composed of individual substances (such as particular people, trees, or electrons) and, in some versions, individual events or tropes (particularized property-instances).
• Any adequate ontology should be expressible, at least in principle, as a domain of such particulars and their relations.

This commitment is often articulated as an anti-Platonic stance: there is no separate realm of Forms, and no need to posit common natures existing “in” or “over” particulars in a realist sense.

Strategies for Denying Universals

Different nominalist metaphysics handle properties and kinds in alternative ways:

Despite differences, these views converge in rejecting repeatable, shareable universals as fundamental.

Individuation and Identity

Without universals, nominalists face questions about individuation and identity conditions:

• Some hold that individuals are primitively distinct;
• Others ground individuation in spatiotemporal location, causal history, or qualitative patterns of tropes or relations.

Realists often charge that universals are needed to account for qualitative identity and difference; nominalists instead appeal to detailed configurations of individuals, tropes, or resemblance structures.

Laws, Dispositions, and Modal Structure

Nominalist metaphysics also addresses laws of nature and modal properties (possibility, necessity) without invoking universals such as “being a law” or “mass.” Approaches include:

• Reducing laws to regularities among particular events;
• Treating modal claims as about what particular configurations could obtain, sometimes grounded in powers understood as particularized dispositions.

Proponents argue that these accounts avoid populating the ontology with abstract, multiply-exemplifiable entities while still capturing the patterns and structures that scientific and everyday discourse describe.

7. Epistemological Views and Theories of Knowledge

Nominalist epistemology tends to align knowledge of general truths with our dealings with individual cases, rather than with intellectual apprehension of universals.

Priority of Singular Cognition

Many medieval nominalists distinguish between:

• Intuitive cognition: direct awareness of existing individuals and their states;
• Abstractive or general cognition: mental acts that can apply to many individuals.

They often claim that knowledge begins with intuitive cognition of singulars, upon which the mind forms general ways of thinking that do not require grasping real universals. For example, Ockham maintains that we first know individual substances and qualities, then perform mental acts that can stand indifferently for many such individuals.

General Knowledge Without Universals

Nominalists interpret universal propositions (“All humans are mortal”) in ways that avoid commitment to universals:

• As quantified statements about many individuals (“For every x, if x is human, then x is mortal”);
• As rules for the correct application of terms (“‘Human’ is correctly applied only to mortals”).

In both readings, the epistemic task is to track patterns among particulars—whether through observation, inference, or scientific theorizing—rather than to discern a universal nature.

Empiricism and Experience

Modern nominalists often adopt or influence empiricist views:

• Sensory experience provides data about particular objects and events.
• Inductive and abductive reasoning identifies regularities and constructs explanatory theories.
• General concepts are formed by abstracting or schematizing from multiple experiences, without positing universals as objects of knowledge.

Some argue that positing universals adds nothing to our explanatory or epistemic resources, since what we know are regularities in the behavior of individuals.

Mental Language and Concept Formation

Medieval nominalists like Ockham develop a theory of mental language (lingua mentalis). On this view:

• Thought proceeds in a structured internal language whose basic units are mental terms.
• These mental terms naturally signify individuals but can be used in a general way (i.e., one mental term can be intended to stand for many individuals).

Knowledge is then analyzed in terms of relations between mental signs and individuals, rather than in terms of relations between minds and universals.

Limits and Skeptical Tendencies

Some nominalists, especially in the later Middle Ages and early modern period, display skeptical or fallibilist tendencies, emphasizing:

• The provisional status of generalizations based on finite experience;
• The difficulty of claiming necessity or strict universality in empirical knowledge without appealing to controversial metaphysical entities.

These epistemological attitudes dovetail with nominalist suspicions about robust metaphysical commitments.

8. Ethical Implications and Moral Theories

Nominalism as a metaphysical stance does not mandate a single ethical theory, but historical connections and conceptual implications have led to characteristic patterns in moral philosophy.

Divine Command and the Status of Moral Properties

In late medieval theology, some nominalists, notably William of Ockham, develop strong forms of divine command theory:

• Moral goodness and obligation are grounded in God’s will, rather than in participation in an objective universal such as “the Good” or a fixed human essence.
• Acts are right or wrong because God commands or forbids them, not because they instantiate or fail to instantiate moral universals.

Proponents argue that this approach coheres with nominalist metaphysics by avoiding robust moral universals. Moral predicates like “good” or “just” are understood as reflecting divine legislation, individual states of affairs, or evaluative attitudes, rather than real, mind-independent moral essences.

Particularism and Case-Sensitivity

Nominalist emphasis on individuals can encourage ethical attention to particular cases:

• Moral reasoning is often framed as applying or interpreting norms in light of specific, concrete circumstances.
• Some later thinkers influenced by nominalism and empiricism highlight context-sensitive judgment over deduction from abstract moral forms.

This can be associated with ethical particularism or with more flexible casuistry, though not all nominalists explicitly endorse these approaches.

Conventionalism and Social Norms

Without objective universals such as “human nature” or “natural end,” some nominalist-influenced ethics locate normativity in:

• Divine law (for theologically oriented nominalists);
• Positive law and social conventions;
• The contingent features of human psychology and shared practices.

In this perspective, moral terms may track socially constructed standards or collectively recognized rules rather than metaphysically grounded moral natures.

Universalizability Without Universals

Many nominalists nonetheless accept universalizable moral principles (e.g., “Treat like cases alike”) while denying that such principles correspond to ontological universals. They can interpret these as:

• Generalizations about individual actions and their consequences;
• Rules of discourse or rational endorsement;
• Features of rational choice among individuals.

Critics contend that without real moral universals or essences, it is harder to explain strong notions of moral objectivity. Nominalists respond by appealing to divine will, rational consensus, or stable features of human life, while maintaining their metaphysical economy.

9. Political Philosophy and Social Ontology

Nominalist ideas have influenced views about political authority, institutions, and the nature of collective entities.

Individuals and Corporate Bodies

In social ontology, nominalists are often inclined to treat entities such as states, churches, or universities as:

• Aggregates of individuals plus relationships, rather than as independent metaphysical wholes with their own substantial existence.
• Products of agreements, customs, and legal constructions.

This orientation is sometimes described as an aggregate theory of social entities. It stands in contrast to views that treat such bodies as real “moral persons” or as having a kind of substantial form.

Late Medieval Political Thought

Some late medieval nominalists contribute to theories emphasizing:

• The role of consent and covenant in legitimizing political power;
• The priority of individual rights and duties over the supposed intrinsic rights of corporate entities.

For example, certain nominalist thinkers argue that the Church is a collection of believers or office-holders organized by divine and human law, not a single metaphysical substance. This has implications for debates about papal versus conciliar authority, though scholars differ on how direct the causal relation is between nominalist metaphysics and these political stances.

Early Modern Contractualism

In early modern political philosophy, figures influenced by nominalism and empiricism, such as Thomas Hobbes, conceptualize the commonwealth in contractual terms:

• The state is understood as an artificial person constituted by the authorization and agreement of individuals.
• Legal and political norms are treated as human creations, backed by sovereign power, rather than as expressions of a natural political essence.

While interpretations vary, some commentators see in these theories a continuation of the nominalist tendency to avoid metaphysically robust collective substances.

Social Kinds and Classification

In contemporary social ontology, nominalist inclinations often manifest as skepticism about:

• Natural kinds in the social domain (e.g., “race,” “gender”) as metaphysically fixed categories.
• Objective, universal essences of social roles or institutions.

Alternative accounts emphasize historical construction, institutional facts, and norm-governed practices. Social categories are then understood as dependent on human activities—classifications, rules, and interactions among individuals—rather than on independent social universals.

Proponents maintain that this approach allows for rigorous analysis of social structures while adhering to an ontology centered on individuals and their relations, in line with nominalist commitments.

10. Major Figures and Intellectual Lineages

Nominalism has been articulated and reformulated by a range of thinkers across periods. The following overview highlights major figures and the lines of influence among them.

Medieval Precursors and Early Nominalists

• Roscelin of Compiègne (late 11th c.) is often cited as an early nominalist, sometimes associated with the “flatus vocis” view that universals are mere sounds. Surviving evidence is limited, and interpretations are contested.
• Peter Abelard (1079–1142) develops a sophisticated semantics and logic that denies real universals while emphasizing signification and mental acts. He plays a key role in shaping later discussions.

Fourteenth-Century Developments

• William of Ockham (c. 1287–1347) is the most influential medieval nominalist. He advances:
  • A denial of universals outside the mind;
  • A theory of mental language;
  • Strong use of ontological parsimony (often linked to “Ockham’s Razor”).
• John Buridan (c. 1300–c. 1360) develops an elaborate nominalist system in logic and natural philosophy, including his theory of supposition and analyses of motion.
• Nicholas of Autrecourt (c. 1300–after 1350) combines nominalist tendencies with skeptical arguments about causation and substance.

These figures contribute to a recognizable late medieval nominalist movement, especially in Paris and Oxford.

Later Medieval and Renaissance Transmission

Ockhamist thought is carried forward by various “moderni” (moderns) in the 14th–16th centuries, including nominalist theologians and philosophers in German and Central European universities (e.g., Cologne, Heidelberg, Erfurt). Their influence on late scholasticism and early Protestant thought has been widely discussed.

Early Modern and Enlightenment Figures

• Thomas Hobbes (1588–1679) adopts an overtly nominalist theory of names and universals, integrated into a materialist metaphysics and contractual political philosophy.
• Some historians also identify nominalist elements in John Locke’s theory of abstract ideas and general terms, though Locke’s classification is debated.

These thinkers help translate medieval concerns about universals into early modern frameworks of empiricism and scientific naturalism.

Modern Analytic Nominalists

In the 20th and 21st centuries, nominalism reappears in analytic metaphysics:

• W.V.O. Quine advocates a naturalistic ontology limited to the entities required by our best scientific theories, expressing skepticism about many abstract objects.
• Nelson Goodman develops a nominalist project aimed at constructing science without sets or universals.
• Other contemporary philosophers (e.g., David Armstrong as a critical interlocutor, various trope theorists, and anti-realist logicians) refine or contest nominalist positions.

These figures constitute overlapping lineages rather than a single continuous school, but they share a family of concerns and strategies that define nominalism across historical contexts.

11. Variants of Nominalism: Conceptualism, Resemblance, and Tropes

Nominalism encompasses diverse strategies for handling generality. Three prominent variants are conceptualism, resemblance nominalism, and trope theory.

Conceptualism

Conceptualism maintains that universals exist only as mental entities—concepts or acts of thought—not in an external realm.

• General terms correspond to general concepts, which the mind can apply to many individuals.
• No common nature exists outside the mind; the external world is composed of individuals.
• Medieval figures such as Abelard and some 14th-century nominalists are often read as conceptualists.

Proponents argue that conceptualism preserves the psychological reality of general thought while avoiding metaphysical commitment to universals. Critics question whether mental items themselves function as universals or whether such views collapse into realism or pure nominalism.

Resemblance Nominalism

Resemblance nominalists explain property-sharing via similarity relations among particulars:

• There is no universal “redness”; instead, red things resemble one another in certain respects.
• Higher-order resemblance (resemblance among resemblance classes) can ground more complex classifications.

This view seeks to explain generality wholly in terms of individuals and their interrelations. It faces challenges such as:

• The need to account for objective standards of resemblance without invoking universals;
• The “companionship” and “imperfect community” problems—cases where resemblance patterns are messy or overlapping.

Advocates respond by refining accounts of resemblance networks or by combining resemblance with other nominalist tools.

Trope Theory

Trope theory posits tropes—particularized property-instances—as basic:

• This redness of this apple, that exact mass of that stone, are individual tropes.
• Objects are bundles or compresences of tropes, rather than substances instantiating universals.
• Generality arises from resemblance or other relations among tropes (e.g., all red tropes resemble each other).

Trope theory is often considered “moderately” nominalist: it admits entities that are property-like but insists they are non-repeatable and fully particular. It aims to combine the intuitive appeal of properties with nominalist anti-universalism.

Comparative Overview

These variants illustrate the internal diversity of nominalism while sharing its core rejection of mind-independent, repeatable universals.

12. Nominalism in Medieval Scholasticism

In medieval scholasticism, nominalism appears as a set of positions within logic, metaphysics, and theology, articulated primarily in university contexts.

Institutional and Doctrinal Landscape

By the 13th century, dominant schools such as Thomism and Scotism defended versions of moderate realism, affirming real common natures in things. Nominalists arose as dissenting voices, proposing alternative accounts of:

• The status of genera and species;
• The structure of propositions and inference;
• The nature of theological and scientific knowledge.

Debates were conducted in commentaries on Aristotle, Porphyry, and Peter Lombard’s Sentences, as well as in disputed questions.

Ockham and the “Moderni”

William of Ockham systematized a nominalist approach that influenced many later scholastics:

• He denied real universals outside the mind and offered a detailed theory of mental language.
• He reinterpreted categories such as substance, quality, and relation in terms of individuals and their mental or linguistic representation.

Followers and sympathizers (often called “moderni” in contrast to older “antiqui”) circulated nominalist teachings across universities, particularly in England and the German-speaking regions.

Areas of Application

Medieval nominalists contributed to multiple areas:

• Logic: development of theories of supposition, connotation, and syncategorematic terms, explaining how language can function without universals.
• Natural philosophy: analyses of motion, change, and causation using individual-based frameworks; Buridan’s work on impetus is a notable example.
• Theology: reformulations of doctrines about God’s attributes, grace, and predestination, guided by concerns about divine omnipotence and parsimonious ontology.

Controversy and Condemnation

Nominalist views were sometimes subject to ecclesiastical scrutiny and condemnation, especially when perceived as threatening traditional doctrines or realist metaphysics. The Condemnation of 1277 at Paris is often cited as background, though it predated the most systematic nominalism. Later disputes involved accusations of:

• Undermining the intelligibility of sacraments or the church as a corporate body;
• Excessive skepticism or voluntarism in theology.

Historians debate the extent and uniformity of “medieval nominalism” as a movement; nonetheless, by the late Middle Ages it had become a recognizable and influential current within scholastic thought.

13. Nominalism in Early Modern and Enlightenment Thought

In the early modern and Enlightenment periods, nominalist themes were integrated into broader projects of scientific reform, empiricism, and political theory.

Hobbes and Materialist Nominalism

Thomas Hobbes is a paradigmatic early modern nominalist:

• He holds that names are the basic units of language, with universals being nothing more than general names applied to many things.
• Only bodies and their motions fundamentally exist; abstract entities are products of naming and reasoning.
• His political theory in Leviathan builds a contractual state out of individual agents, reflecting both nominalist social ontology and materialism.

Hobbes argues that disputes about universals are often verbal and that clear definition of terms can dissolve many philosophical confusions.

Locke and Ideas

John Locke’s theory of general ideas and nominal essences in the Essay Concerning Human Understanding has been read by some as a form of nominalism:

• General terms stand for abstract ideas formed by leaving out individuating details.
• The “essence” of a species (e.g., gold) is a nominal essence, a complex idea associated with a term, rather than a real metaphysical nature.

However, Locke’s position is complex, and scholars differ on whether he should be classified as a nominalist, a conceptualist, or a moderate realist about real essences in some domains.

Enlightenment and Scientific Taxonomy

Nominalist tendencies also appear in debates about classification in natural history:

• Some thinkers stress that species and genera are human groupings based on observable similarities, not discoveries of fixed natural universals.
• Others maintain that there are objective “natural systems,” though they may avoid strong metaphysical claims about universals.

This period sees increased sensitivity to the pragmatic and conventional components of scientific categories, even among those who do not explicitly endorse nominalism.

Skepticism about Abstract Entities

Early modern empiricists such as George Berkeley and David Hume raise doubts about abstract ideas and metaphysical universals:

• Berkeley criticizes abstract notions of extension, matter, and being.
• Hume treats general ideas as habits of association, not as apprehensions of separate abstract entities.

While not all these positions are straightforwardly nominalist, they contribute to an intellectual climate in which appeals to universals and abstract objects are treated with increasing suspicion, paving the way for later, more formal nominalist doctrines.

14. Nominalism in Contemporary Analytic Metaphysics and Philosophy of Science

In contemporary analytic philosophy, nominalism primarily concerns abstract objects—universals, sets, numbers, propositions—and their role in science and mathematics.

Quine, Naturalism, and Ontological Commitment

W.V.O. Quine reframes ontological questions through the lens of quantification and naturalism:

• We are ontologically committed to whatever entities our best scientific theories quantify over.
• He is wary of many traditional abstracta but accepts some (e.g., sets) as indispensable for science, leading to a nuanced position rather than pure nominalism.

Quine’s methodology nevertheless shapes later nominalist projects, which seek to show that successful science does not require commitment to problematic abstract entities.

Nominalism About Properties and Universals

Contemporary nominalists in metaphysics develop detailed accounts of:

• Resemblance nominalism and trope theory, aiming to reconstruct theories of properties, laws, and causation without universals.
• The ontology of relations, dispositions, and causal powers, often treating them as particularized or reducible.

Opponents, such as David Armstrong, defend realism about universals, arguing that universals are needed to account for laws of nature and objective resemblance. This realism–nominalism debate is a central strand in late 20th-century metaphysics.

Mathematical and Logical Nominalism

Nominalism has also been influential in the philosophy of mathematics:

• Field’s program (Science Without Numbers) attempts to reconstruct portions of physics in a nominalistic language free of reference to numbers and sets, arguing that mathematics is a conservative extension not needed for physical explanation.
• Other nominalists explore fictionalist or deflationary accounts of mathematical discourse, treating mathematical entities as useful fictions rather than real objects.

In logic and semantics, some nominalists propose substitutional quantification or alternative formal systems that avoid explicit commitment to sets or propositions.

Philosophy of Science and Theories of Law

Nominalists in the philosophy of science typically:

• Resist ontological commitment to laws of nature as governing universals;
• Propose regularity or best-system analyses of laws, grounded in patterns among particular events.

They also often interpret theoretical entities (e.g., fields, forces) in ways that minimize or reinterpret abstract commitments, while still acknowledging the empirical success of scientific theories.

Contemporary Landscape

Contemporary nominalism is diverse:

Debates continue over whether nominalistic reconstructions can match the explanatory, predictive, and unifying power of realist accounts while preserving a more austere ontology.

15. Criticisms and Rival Positions

Nominalism faces a range of objections from realists about universals, Platonists, and others who defend abstract entities. Rival positions offer alternative frameworks that seek to address perceived shortcomings of nominalist views.

Realist Objections About Similarity and Predication

Realists argue that nominalism struggles to explain:

• Objective similarity: Why do red things resemble each other in a way they do not resemble blue things?
• Predication: What makes the statement “Socrates is wise” true, if there is no universal wisdom that Socrates instantiates?

They contend that universals provide a straightforward account: properties and kinds are shared entities, grounding similarity and truth-making. Nominalist appeals to resemblance or classes, critics suggest, either implicitly rely on universals or face regress and arbitrariness problems.

Laws of Nature and Modal Facts

Opponents such as David Armstrong maintain that nominalists cannot adequately account for:

• Laws of nature as more than accidental regularities;
• Modal truths about what could or must happen.

Realists propose universals and their necessary connections (e.g., a universal relation between mass and force) as the grounds for nomic and modal structure. Nominalist accounts based on Humean regularities or best-system analyses are criticized as too weak to capture the apparent necessity of laws.

Mathematical Indispensability

In the philosophy of mathematics, indispensability arguments (associated with Quine and Putnam) challenge nominalism:

• Mathematics appears indispensable to our best scientific theories.
• Therefore, we should be committed to the existence of mathematical entities.

Nominalists who deny numbers and sets must either show that science can be reformulated without them (as in Field’s program) or accept some form of fictionalism, which critics argue undermines the explanatory role of mathematics.

Internal Coherence and Conceptual Problems

Critics also allege that some nominalist positions risk:

• Reintroducing universals under other names (e.g., mental contents that play the role of universals in conceptualism; resemblance relations that seem universal-like).
• Inflating the ontology with tropes or other particulars in ways that may be less parsimonious than realist theories.

Questions arise about whether nominalism truly delivers on its promise of ontological economy and whether it can avoid circularity in analyzing generality.

Rival Positions

Major rival positions include:

These alternatives propose different ways of reconciling our linguistic, cognitive, and scientific practices with a robust ontology of universals or abstract structures, in contrast to nominalist austerity.

16. Methodological Themes: Ontological Parsimony and Logical Analysis

Nominalism is not only a set of metaphysical theses but also a methodological orientation emphasizing parsimony and logical scrutiny.

Ontological Parsimony

A hallmark of nominalist method is the preference for sparse ontologies:

• Avoid positing new kinds of entity unless required to explain phenomena.
• Seek reductive analyses of discourse apparently referring to universals, sets, or other abstracta.

This is encapsulated in the principle associated with Ockham:

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Entia non sunt multiplicanda praeter necessitatem.
Entities are not to be multiplied beyond necessity.

While the principle itself is subject to interpretation, nominalists use it to favor theories that:

• Quantify only over individuals (and, for some, particularized properties or relations);
• Treat many abstract-seeming expressions as paraphrasable into talk of particulars.

Logical and Semantic Analysis

Nominalists historically rely on careful logical analysis to reveal hidden ontological assumptions. In different periods this has taken various forms:

• Medieval nominalists developed sophisticated theories of terms, supposition, and mental language to explain meaning and inference without universals.
• Modern analytic nominalists use formal logic, model theory, and semantic tools to:
  • Diagnose where ontological commitment arises (e.g., via quantification);
  • Propose alternative formulations (e.g., free logics, substitutional quantification, nominalistic reconstruals of set-theoretic language).

The general strategy is to show that many apparently ontologically loaded statements can be reinterpreted in ways that commit us only to individuals and their arrangements.

Reconstruction and Paraphrase

A common nominalist methodology involves reconstruction:

1. Identify a domain of discourse that seems to involve abstract objects (e.g., mathematics, properties).
2. Analyze the inferential and explanatory roles of that discourse.
3. Provide a paraphrase or alternative theory in a more austere language that preserves those roles as far as possible.

This method is visible, for example, in Field’s attempt to reaxiomatize physics without numerical quantification and in trope-theoretic reconstructions of property talk.

Empirical and Scientific Orientation

Many contemporary nominalists adopt a naturalistic or science-guided methodology:

• Ontological commitments should be constrained by the needs of empirical science.
• Philosophical theories are evaluated partly by how well they integrate with, or economize upon, scientific practice.

This reinforces the focus on individuals, spatiotemporal relations, and causal structures, while encouraging suspicion of entities that do not feature explicitly in scientific theorizing.

Trade-offs and Methodological Debates

Methodologically, nominalism faces choices:

• How much theoretical simplicity to trade against explanatory power;
• Whether certain abstract entities might be justified as indispensable despite a general preference for parsimony.

These debates are internal as well as external to nominalism, shaping the diversity of nominalist projects and their ongoing revision.

17. Legacy and Historical Significance

Nominalism’s legacy spans multiple domains—metaphysics, logic, theology, political theory, and the philosophy of science—shaping both historical and contemporary thought.

Transformation of Medieval Thought

In the medieval period, nominalism contributed to:

• The pluralization of scholastic metaphysics, challenging the dominance of realist systems (Thomism, Scotism).
• Refinements in logical theory (supposition, mental language, analysis of terms) that influenced later developments in logic and semantics.
• Reorientations in theology, including emphases on divine omnipotence and the contingency of created orders.

These shifts played a role in the gradual transformation of late medieval intellectual life and its transition toward early modern forms of inquiry.

Influence on Early Modern Philosophy and Science

Nominalist ideas about universals, language, and classification fed into:

• Empiricism, with its stress on experience of particulars and suspicion of innate or abstract ideas.
• Scientific methodology, encouraging focus on observable regularities and laws rather than on metaphysical essences.
• Political theory, where individual-centered, contractual, and legalistic conceptions of the state found conceptual support in nominalist social ontology.

Although the causal pathways are complex, many scholars see nominalism as one of the currents contributing to the intellectual climate of the Scientific Revolution and the Enlightenment.

Contributions to Analytic Philosophy

In the 20th century, nominalism helped shape central debates in analytic metaphysics and the philosophy of mathematics:

• Disputes between nominalists and realists about properties and laws clarified the stakes of ontological commitment.
• Nominalist programs in the philosophy of mathematics prompted detailed analyses of the role of mathematics in science and the nature of indispensability.
• The focus on parsimony, logical form, and reconstruction influenced broader methodological norms in analytic philosophy.

Continuing Relevance

Nominalist themes remain active in contemporary discussions about:

• The status of abstract objects across domains (from mathematics to morality).
• The nature of social kinds and the construction of categories in social and natural sciences.
• The relationship between language, thought, and ontology.

Through these influences, nominalism has played a significant role in shaping how philosophers conceive the structure of reality, the aims of theory, and the relationship between our representations and the world.