Nominalism: Universals, Ockham, and the Realist Reply

Nominalism is the philosophical view that universals, such as redness or humanity, do not exist as real things, so that only particular things exist and our general words and concepts are ways of naming them. It took its classic form in the medieval dispute over universals, where William of Ockham became its most influential defender, and today the same name covers the denial of abstract objects such as numbers and propositions. For a Christian the question reaches God: realism risks setting eternal things beside Him, while nominalism risks making the kinds He created into labels. The Many Beings Framework traces the stalemate to one move both sides share.

Key takeaways

• Nominalism denies universals, abstract objects, or both. Only particulars exist; likeness, meaning and mathematical truth must be explained without shared entities.
• Four answers compete. Platonic realism, Thomist moderate realism, conceptualism and nominalism give four accounts of what makes many things one kind.
• Ockham's razor is misremembered. The famous slogan appears nowhere in his writings, and he rejected universals because he judged realist theories incoherent.
• The theological stakes are contested. Nominalism defended God's freedom, and scholars still dispute whether it set modernity in motion.
• Frame-Indexed Classical Theism offers a third way. Against Platonic realism and Ockham's nominalism, it treats universals as the finite frame's true reading of a created order grounded in God's simple nature.

What is nominalism?

Nominalism, from the Latin nomen, "name," is the family of views holding that general terms do not stand for general things. The Stanford Encyclopedia of Philosophy calls it "an exclusionary thesis in ontology" and distinguishes its two main forms in its 2025 entry. The older form denies universals, entities that can be wholly present in many things at once. The newer form denies abstract objects, entities outside space and time such as numbers, sets and propositions. John Stuart Mill compressed the older view into a phrase: "there is nothing general except names."

Take two apples of the same red. A realist says one thing, redness, is present in both. A trope theorist says each apple has its own redness, two particulars that resemble each other exactly. A strict nominalist says there are two red apples and the word "red" is true of each, with no further entity required. All three agree the apples are red. They disagree about what makes the sentence true.

The two forms of the position can also come apart. A trope theorist rejects universals, yet a theory that builds properties out of sets of tropes accepts sets, which most philosophers count as abstract objects, and so it keeps the older denial while giving up the newer one.

The cost of denying universals is a set of explanations the realist gets for free. The encyclopedia's entry states the burden directly: nominalists "must therefore find a credible way to explain how things can be similar without sharing universals, have linguistic meaning without expressing propositions, or be truths of mathematics without the existence of any mathematical entities." How well a given version meets that burden decides whether the position is an economy or an evasion, and the answer differs from one version to the next.

What is the problem of universals?

The problem of universals asks what makes many things one kind, and what our general words and general knowledge are about. Gyula Klima opens the Stanford entry on the medieval problem of universals with a geometry proof. A demonstration about one drawn triangle holds for every triangle in every semicircle, yet the drawn triangle is jagged and particular, and a universal triangle would have to be isosceles and scalene at once. Universal knowledge seems to concern something that cannot exist as described.

The medieval form of the question came from Porphyry's Isagoge, an introduction to Aristotle's logic. Porphyry asked whether genera and species subsist or exist only in the mind, whether they are bodily or incorporeal, and whether they are separate from sensible things or in them. He declined to answer, and Boethius took up the questions in his commentaries, passing them to the Latin West.

Three places were available for a universal. It could exist before things, as an exemplar; in things, as their shared nature; or after things, as a concept formed by the mind. Klima reports that nearly all medieval thinkers affirmed universals before things, in the form of divine ideas existing in the divine mind, while all of them denied Plato's free-standing Forms. For Christian thinkers, then, the problem of universals was a question about God before it was a question about apples.

Nominalism vs realism: what are the main positions?

Four positions compete: Platonic realism, moderate realism, conceptualism and nominalism, and each answers differently where a universal is and what makes a general word true. Platonic realism holds that universals exist in their own right, independent of minds and of the things that share in them. Its strength is explanatory reach: it says why things resemble each other and why a proof about the triangle holds of every triangle. Its weakness is location. Plato raised the difficulties himself in the Parmenides, and a realm of eternal Forms sits uneasily with the confession that God alone is uncreated. Augustine kept the Forms and moved them, calling the Ideas the stable and immutable reasons of things, which "are contained in the divine understanding."

Boethius had given the Latin West the outline of a middle course, holding that genera and species subsist in one way and are understood in another. Moderate realism, the view of Aristotle and of Thomas Aquinas, holds that a common nature is real but exists only in individual things, and that its universality comes from the way the intellect grasps it. Aquinas puts it with precision in the Summa Theologiae (I, q. 85, a. 2): "the nature itself to which it occurs to be understood, abstracted or considered as universal is only in individuals; but that it is understood, abstracted or considered as universal is in the intellect." Humanity is real in Socrates. Humanity considered as a universal is in the mind that knows him. The Thomism article sets this inside Aquinas's wider system.

For conceptualism, universals exist only as concepts, general acts of the mind that apply to many things. Abelard and Ockham are often filed here. Its critics press a dilemma: if the concept applies correctly because the things really resemble one another, conceptualism has granted what moderate realism asserts; if nothing in the things grounds the concept, it collapses into strict nominalism.

The family proper has several branches. Predicate nominalism says things are red because "red" applies to them, and critics have named it "Ostrich Nominalism" for declining to explain further. Resemblance nominalism grounds kinds in resemblance among particulars. Class nominalism grounds them in membership of natural classes. Trope theory, named by D. C. Williams in 1953, grants each thing its own particular qualities and explains sameness of kind by exact resemblance among them.

David Armstrong, the best-known contemporary defender of universals, grants that trope theory has promise but argues that it cannot account for the laws of nature as a theory of universals can. Klima adds a caution for history: the three tidy labels are "rather crude" for the medieval authors they sort.

Who were the nominalists? From Roscelin to William of Ockham

Roscelin of Compiègne (about 1050 to 1121) is often regarded as the founder of nominalism. He left almost nothing in writing, and his teaching reaches us mainly through Anselm and Abelard, who opposed it. He is remembered for calling a universal a flatus vocis, a breath of the voice. The first test of the theory was theological: Roscelin reasoned that the three divine Persons were three things, and a council at Soissons in 1092 or 1093 charged him with tritheism. From its first appearance, then, the theory of universals was tried on the doctrine of the Trinity.

Peter Abelard (1079–1142), Roscelin's pupil, argued that only universal words count as universals, since only words are predicated of many. He then asked what makes a common word fit many things, and answered with the status of those things, what Klima calls "a cause which is a non-thing," comparable to the way "the pilot was absent" can cause a shipwreck without being an object.

William of Ockham (about 1287–1347), an English Franciscan, gave the position its most influential medieval form. In his mature view a universal concept is a single act of a single mind that represents many things indifferently. His universals, in Klima's summary, "are just our common terms and our common concepts." He reduced the categories of created being to substances and qualities, and admitted distinct relations only where the Trinity, the Incarnation and the Eucharist required them.

The Stanford entry on William of Ockham corrects the best-known fact about him. The slogan that entities must not be multiplied beyond necessity is, in the entry's words, "nowhere to be found in his texts." His own fullest version allows an entity to be posited on three grounds: reason, experience, and the authority of Scripture. His case against universals rested on coherence: he held that the realist theories of his day were incoherent, a stronger charge than needless complexity.

His successors, John Buridan above all, built the via moderna, the "modern way" of logic and theology, and it spread through the universities of the fifteenth century. Domingo Soto (1494–1560), who described himself as born among nominalists and raised by realists, judged realism harder to understand and nominalism harder to believe. Historians now add their own caution: the paired labels of via antiqua and via moderna spread only in the later fifteenth century, and Robert Pasnau has questioned whether a coherent fourteenth-century school of nominalism existed at all.

Volume Four takes up divine simplicity and the question of whether God has properties in Resolving Immutability & Interaction.

Why did nominalism matter to theology?

Ockham's case against universals drew on theology from the start. Sharon Kaye's entry on William of Ockham in the Internet Encyclopedia of Philosophy sets out one of his arguments: if a single universal humanity were really present in each man, God could not annihilate one man without destroying the humanity in the others, and with it the others themselves. God is omnipotent and can do whatever involves no contradiction, so a theory that ties His hands in this way must be mistaken. The Stanford entry also finds "a strong dose of divine command theory" in his ethics, alongside a strand of natural law. At its strongest this is a Christian conviction: God answers to nothing outside Himself. Readers who want the doctrine of divine rule in its own right will find it in the article on the sovereignty of God.

The medieval realists had an answer that located universals inside the divine mind, and it raised its own question. If God has many ideas, is God many? Aquinas replied in the Summa (I, q. 15, a. 2) that "it is not repugnant to the simplicity of the divine mind that it understand many things; though it would be repugnant to its simplicity were His understanding to be formed by a plurality of images." God knows His one essence in all the ways creatures can share in it. Ockham and his followers doubted that the plurality could be kept so harmless, and the argument over simplicity has continued ever since.

A larger claim now travels with the word. Michael Allen Gillespie's The Theological Origins of Modernity (2008) opens with a chapter titled "The Nominalist Revolution and the Origin of Modernity." Brad Gregory's The Unintended Reformation (2012), as Matthew Lundin summarizes it in Christian Scholar's Review, argues that Scotus and Ockham came to treat God as existing in the same way other things exist, a turn that later made God dispensable to a mechanized picture of nature. The Scotist half of that story, and its critics, are traced in the articles on univocity and Duns Scotus.

The genealogy has serious critics. David Burrell, reviewing Gillespie in Notre Dame Philosophical Reviews, praised the history and concluded that it loses much by tracing its story "to an ill-defined singularity like 'nominalism,' as crucial as that sea-change has been." Pasnau's doubts about a unified fourteenth-century school cut the same way. Protestant writers, among them Seth Snyder in the journal Ad Fontes, reject the common claim that Reformation theology is basically nominalist. The modernity thesis is a live argument, and a fair reader holds it as one.

Volume One lays out the framework's single diagnosis of the classical dilemmas; download it free.

What is modern nominalism? Tropes, numbers and Hilbert's formalists

Modern nominalism runs on two tracks. About universals, trope theory, traced above to D. C. Williams, became the leading form; about abstract objects, the argument turned to numbers. In 1947 W. V. O. Quine and Nelson Goodman began a paper with a declaration the Stanford entry quotes: "We do not believe in abstract entities." They continued: "We renounce them altogether." The motives have stayed stable since. Paul Benacerraf argued in 1973 that knowledge of numbers is hard to explain if numbers are causally inert and nowhere, and others add the appeal to economy.

The strongest reply is the indispensability argument associated with Quine and Hilary Putnam. Our best physical theories quantify over numbers and functions throughout; we are committed to what our best theories require; so we are committed to mathematical objects. Mathematical nominalism took up the challenge directly. In Science Without Numbers (1980) Hartry Field argued that mathematics need only be conservative, adding no new claims about the physical world, and he recast Newtonian gravitational theory in comparative terms with no quantification over real numbers, extending David Hilbert's axiomatization of geometry, as Otávio Bueno's Stanford entry explains.

John Burgess, later with Gideon Rosen, pressed a sharper question about such projects. Is the claim that science, properly read, already does without mathematical objects, or is it a proposal to replace our theories with ones that do? He called the first reading hermeneutic and the second revolutionary, and subjected both to a sustained critique.

Hilbert himself stands nearby. His formalist program treated mathematics as a formal system and sought to prove its consistency using only finitary reasoning, a part of arithmetic chosen because it was philosophically uncontroversial, until Gödel's incompleteness theorems of 1931 showed that a consistent system of that strength cannot prove its own consistency.

Christian philosophers have joined the argument from the side of aseity. William Lane Craig's God Over All (2016) holds that uncreated abstract objects would compromise God's standing as the sole ultimate reality. As Graham Oppy's review reports, Craig weighs divine conceptualism, which places abstract objects in God's mind, and concludes that theists "need to take a good look at anti-realist alternatives to Platonism." His own preference, in Oppy's summary, is a "combinatorial approach" that reads talk of numbers, properties and propositions as figurative or as pretence, while leaving room to say that there really are no uncreated abstract objects.

Volume Five, still in draft, gives Hilbert, Gödel and the indispensability debate a chapter each; follow its progress.

Where is nominalism strongest, and where do realists press it?

Nominalism is strongest at three points. It keeps the inventory of reality small. It escapes the access problem, since it posits nothing the mind would need to reach outside space and time. And for the Christian it draws a clean line: God is the uncreated one, and the world He made is a world of particular things He knows. Scripture speaks of that knowledge one creature at a time:

"He determines the number of the stars and calls them each by name." (Psalm 147:4, NIV)

The realist presses back, and the first pressure is resemblance. Bertrand Russell argued in 1912 that anyone who groups particulars by their likeness has admitted at least one universal, likeness itself. The resemblance view also struggles to build its classes without circularity, since two things can resemble each other in many respects. Trope theory answers both charges better than its siblings, and the Internet Encyclopedia of Philosophy's entry on universals reports that this has convinced many it is a serious contender against realism, but the resemblance among tropes is still left as a primitive fact.

Mathematics supplies the realist's second argument. Field's program covers Newtonian gravitation, and the Stanford entry notes that it is unclear whether the same strategy extends to quantum mechanics. Realists add that if mathematics is a useful fiction, its close fit to the physical world is left without an explanation.

The last objection is theological. Scripture describes a creation ordered in kinds, and Genesis reports the kinds as God's own work:

"God made the wild animals according to their kinds, the livestock according to their kinds, and all the creatures that move along the ground according to their kinds. And God saw that it was good." (Genesis 1:25, NIV)

The text is consistent with real kinds in creation. A theory on which "livestock" names only a grouping we find useful has to explain why the text reports God's approval of the kinds themselves.

How does Frame-Indexed Classical Theism answer the problem of universals?

Frame-Indexed Classical Theism (FICT) is a research program in analytic theology that resolves classical theological dilemmas by diagnosing them as artifacts of a single formal error, and it is the position of the Many Beings Framework. Platonic realism holds that likeness needs something real, Ockham's nominalism holds that nothing necessary stands beside God, and Thomist moderate realism holds that natures are real in things and universal in the mind. Frame-Indexed Classical Theism grants each of those claims and holds that the dispute stalls on one shared move: treating universal, instance and property as a single inventory that must apply to God as it applies to creatures.

There is one reality. God knows it in His own perceptual frame, which is atemporal, simple and a se. We know the same reality in ours, which is sequential, composite and contingent. Terms whose content involves time, possibility, agency, freedom or value are said of God and of us analogically and never univocally. Treating such a term as though it meant the same thing in both frames is the error the framework names the Many Beings Fallacy.

Apply that to universals. The apparatus of kinds, instances, properties and bearers is the finite frame's true way of reading a world of composite creatures. The kinds are real in creation, as the realist insists, since God made the wild animals according to their kinds. The apparatus that sorts them is ours, as Ockham insisted, since we form the concepts and give the names. Both claims hold because they describe one created order from inside the frame of a creature who belongs to it.

John names the ground of that order:

"In the beginning was the Word, and the Word was with God, and the Word was God. … Through him all things were made; without him nothing was made that has been made." (John 1:1, 3, NIV)

The likeness among creatures is God's one simple nature reflected in what He made. This places the framework near divine conceptualism while holding to the limit Aquinas set: God understands the many ways creatures share His essence in one act of understanding, so the plurality lies on the side of what is understood.

The realist who sets universals beside God has carried the creature's inventory into God's frame. So has the reasoning that treats an order grounded in God's own nature as a limit on His freedom, as though God stood toward His nature the way a creature stands toward a law it did not make. Freedom and possibility are frame-sensitive terms, and they carry their frame. Ockham himself held that singular things are really and essentially similar in themselves, which is the realist's datum; the framework adds where that likeness is grounded. Alvin Plantinga's objection that a simple God would be a property makes the same move from the other side, and Volume Four answers it.

Mathematics follows the same pattern. Quine and Putnam are right that physics cannot do without it, and the reason is that physicist and mathematician read one created order God sustains, with no realm of abstract objects required. Field is right that the symbols and systems are our instruments. His further claim that mathematics is false goes beyond what his conservativeness results establish. Volume Five, still in draft, makes that argument in full.

Critics will press from both sides. A nominalist will say this is realism with a theological name, and the framework accepts the realism about creation while denying any uncreated abstract object. A realist will ask what "expressed in creation" means, and that is a fair demand. The books make the argument step by step. The statement of Frame-Indexed Classical Theism sets out the framework in one place.

Volume One carries the framework from its foundations to the Many Beings Fallacy; get your free copy.

How the positions compare

Each position keeps a truth the others need, and the comparison turns on what each leaves open.

Frequently asked questions

Was William of Ockham a nominalist or a conceptualist?

Both labels are used, and both fit parts of his view. Ockham denied that universals exist outside the mind, which makes him a nominalist about things. He held that universals are concepts, in his mature view single acts of a mind representing many things, which is why many historians call his position conceptualism. Gyula Klima warns that the three standard labels are crude for medieval thinkers, and Ockham is a case in point.

Did Ockham say "Ockham's razor"?

The formula that entities must not be multiplied beyond necessity is a later summary, and the Stanford Encyclopedia reports that it appears nowhere in his texts. The sentiment is Ockham's, and his own fullest statement allows an entity to be posited when reason, experience or the authority of Scripture requires it. His rejection of universals rested on a different argument, that the realist theories of his day were incoherent.

Is nominalism compatible with Christianity?

Christians have held it, Ockham among them, and William Lane Craig defends anti-realism about abstract objects today on grounds of God's aseity. The worry runs the other way as well: nominalism can seem to make created kinds and God's attributes into names. Frame-Indexed Classical Theism answers with a third option, set between Platonic realism and Ockham's nominalism: created kinds are real, and their ground is God's simple nature.

What is the difference between nominalism and conceptualism?

Nominalism holds that only particular things exist and that general terms name them. Conceptualism holds that universals exist, but only as concepts in the mind. The difference is whether the mind's general concept counts as a universal in its own right. Critics argue that conceptualism must either admit real resemblance in things, which moves it toward moderate realism, or deny it, which returns it to nominalism.

Are numbers real?

Mathematical platonists say numbers exist as abstract objects outside space and time. Fictionalists such as Hartry Field say they do not, and that mathematics is a useful, conservative instrument. Frame-Indexed Classical Theism holds that mathematical structure is real as the order of God's sustained creation, and that the objects we build to describe it are the finite frame's instruments.

Where to go from here

Ockham guarded the right border. Nothing uncreated stands beside God, and a Christian account of universals has to honor that. He drew it in the wrong place, around the created kinds themselves, when the line that matters runs between the frame of the Creator and the frame of the creature. Draw it there, and the realist keeps his kinds while the nominalist keeps his aseity.

Volume One sets out the framework and names the fallacy, and it is free to download. Volume Four, Resolving Immutability & Interaction, takes up divine simplicity and the question of God's properties, and it is available now in every format. The rest of the series carries the same diagnosis through time, evil, infinity and providence.

Related reading

• Apophatic Theology
• Kenoticism and Kenosis
• Haecceity