When a physicist describes two electrons as having identical charge, or a chemist notes that multiple samples share the same crystalline structure, they invoke a metaphysical assumption so fundamental it typically escapes notice: that sameness of property is a genuine feature of reality requiring explanation. The problem of universals—perhaps philosophy's oldest metaphysical puzzle—asks what grounds these attributions of shared characteristics. Must there exist abstract entities, universals, that multiple particulars literally instantiate? Or can we account for predication and resemblance through the concrete furniture of the world alone?

This question gains renewed urgency when we examine how contemporary physics deploys property-talk. Quantum field theory describes particles as excitations of underlying fields, each characterized by invariant properties like mass and spin. The Standard Model's explanatory power depends on systematic relationships between these properties—relationships that seem to cry out for ontological grounding. Yet nominalists argue that admitting universals into our ontology creates more problems than it solves, multiplying entities beyond necessity while leaving the deepest questions about instantiation unanswered.

The debate between nominalists and realists about universals is not merely a scholastic exercise. It shapes how we understand natural kinds, laws of nature, and the modal structure of reality itself. If nominalism succeeds, then science's property-attributions reduce to something more metaphysically innocent—class membership, resemblance relations, or tropes. If it fails, we must accept that reality includes abstract entities whose relationship to concrete particulars remains philosophically puzzling. Examining this ancient controversy through the lens of contemporary science reveals unexpected complexities on both sides.

Consider two electrons measured in different laboratories on different continents. Each possesses charge of precisely −1.602176634 × 10⁻¹⁹ coulombs. Not approximately the same charge—exactly the same, to arbitrary precision. What metaphysical fact makes this attribution true? The realist answer posits a universal—negative elementary charge—that both electrons instantiate. The electrons share a property because they stand in the instantiation relation to the same abstract entity.

This realist picture faces immediate challenges. The instantiation relation itself seems to require explanation: what connects a concrete particular to an abstract universal? If we posit another relation to explain this connection, we generate Bradley's regress—an infinite chain of relations relating relations to their relata. Moreover, universals seem causally inert; they exist (if they exist) outside spacetime. How can spatiotemporally located particulars stand in any genuine relation to non-spatiotemporal abstracta?

Yet the alternatives face their own difficulties. If we deny universals exist, we must explain what makes property-attributions true. When we say electrons have the same charge, our predication succeeds or fails—it's not merely verbal. Scientific realism about physics seems to commit us to properties as genuine features of the world, not mere linguistic conveniences. The nominalist must show how to preserve what's right about scientific property-talk while avoiding ontological commitment to universals.

The problem sharpens when we consider natural kinds and laws. Electrons don't merely happen to share charge; they must share it to be electrons. The laws of quantum electrodynamics govern all entities with certain properties, not arbitrary collections of individuals. This modal dimension—the necessity attaching to property-possession—seems difficult to capture without universals serving as the truthmakers for claims about what things could or must be like.

Contemporary physics adds another layer. In quantum field theory, properties like mass emerge from symmetry considerations and the structure of the underlying field. The electron's mass reflects how the electron field couples to the Higgs field. This suggests properties might be derivative rather than fundamental—but derivative on what? The field-theoretic picture may transform the problem of universals rather than dissolving it, relocating the question to what grounds the symmetries and coupling constants themselves.

Takeaway

The problem of universals emerges whenever we take scientific property-attributions seriously—asking what in reality makes true our claims that distinct particulars share characteristics is not optional metaphysical speculation but a demand imposed by our best theories.

Class nominalism offers the most straightforward reduction: to have a property is simply to be a member of the relevant class. Being an electron means belonging to the class of electrons. No universal electronhood exists; there's just the set containing all and only electrons. Property-sharing reduces to class co-membership, predication to set membership. The apparatus of set theory replaces the troublesome ontology of universals.

But class nominalism faces the extensionality problem. The class of creatures with hearts is (on Earth, at present) identical to the class of creatures with kidneys. If properties are classes, then having-a-heart is the same property as having-a-kidney. Yet these seem like genuinely different properties—they figure differently in explanations and could come apart in possible cases. The class nominalist must either accept this counterintuitive identification or retreat to intensional entities like concepts, reintroducing something suspiciously universal-like.

Resemblance nominalism takes a different approach: things share properties in virtue of resembling each other. Red things are red because they belong to a maximal resemblance class—they all resemble each other more than they resemble non-red things. No abstract universal redness exists; there are just concrete particulars standing in concrete resemblance relations. This preserves the intuition that property-sharing is a genuine worldly phenomenon while keeping the ontology nominalist-friendly.

The resemblance nominalist confronts the companionship and imperfect community problems identified by Nelson Goodman. Some properties necessarily accompany others (charge accompanies being-an-electron), making resemblance classes overlap in ways that defeat the analysis. And some classes of pairwise-resembling things don't share any single property—a, b, and c might resemble each other pairwise while having no property in common. More fundamentally, resemblance itself seems to require explanation: in what respect do things resemble? If we answer that they resemble in respect of redness, we've reintroduced the universal.

Trope theory represents the most sophisticated nominalist option. Properties exist, but as particulars rather than universals. Each electron has its own charge trope—a particular property-instance distinct from every other charge trope. These tropes resemble each other exactly, grounding our judgments of property-sameness, but no single entity is shared. This preserves properties as worldly constituents without the problematic abstractness of universals. However, trope theory still requires an account of what grounds exact resemblance between tropes, and the primitive status of this resemblance relation may seem no more satisfying than primitive instantiation.

Takeaway

Each nominalist strategy trades one metaphysical puzzle for another—class nominalism struggles with intensionality, resemblance nominalism with specifying respects of resemblance, and trope theory with explaining why distinct tropes resemble exactly—suggesting that eliminating universals may merely relocate rather than resolve the underlying problem.

Nominalism's primary appeal is ontological parsimony. Ockham's razor counsels against multiplying entities beyond necessity, and universals are paradigmatically mysterious entities—abstract, non-spatiotemporal, yet somehow intimately connected to the concrete particulars that instantiate them. If we can explain everything universals explain without them, we've achieved a genuine theoretical economy. The nominalist bets that property-talk can be paraphrased away or given a deflationary semantics.

But parsimony must be weighed against explanatory power, and here nominalism faces serious challenges. Laws of nature seem to quantify over properties: all objects with mass attract each other, all charged particles generate electromagnetic fields. If properties are just classes or resemblance structures, what grounds the modal force of laws? Why should it be necessary that all members of the mass-having class attract, rather than merely accidental? Armstrong's argument from laws suggests that the nomic connections between properties—connections that obtain of necessity—require properties to be genuine entities capable of standing in necessary relations.

Natural kinds pose a related problem. Electrons constitute a natural kind: there are objective similarities between electrons that make them more alike to each other than to quarks or photons. The realist explains this through shared universals; the nominalist must explain it through class membership or resemblance. But not all classes correspond to natural kinds—the class {my coffee cup, the Eiffel Tower, the number 7} is perfectly legitimate set-theoretically but carves nature at no joints. The nominalist needs a principled distinction between natural and non-natural classes, and it's unclear how to draw this distinction without invoking properties.

Regress problems threaten several nominalist positions. If resemblance grounds property-sharing, resemblance itself seems to be a shared property of resembling pairs—do we need a universal of resemblance? If trope-resemblance is primitive, we've simply pushed the explanatory burden elsewhere. The realist faces analogous regress concerns about instantiation, but at least has a principled stopping point: instantiation is the fundamental relation connecting particulars to universals. The nominalist's stopping points often seem arbitrary.

Contemporary physics may ultimately adjudicate this debate. If fundamental physics requires quantification over properties in its laws and explanations, then properties earn their place in our ontology through indispensability arguments parallel to those for mathematical entities. The nominalist must show either that physics can be reformulated without property-quantification or that property-talk, though useful, isn't genuinely committing. Neither task has been accomplished to most philosophers' satisfaction, suggesting that while nominalism remains a live option, the burden of proof increasingly falls on those who would eliminate universals from our picture of reality.

Takeaway

The nominalist program succeeds in highlighting genuine puzzles about universals but has not yet produced a fully satisfactory alternative—the choice between nominalism and realism may ultimately depend on whether one finds abstract entities or primitive resemblance relations more metaphysically troublesome.

The problem of universals resists easy resolution precisely because both positions capture something important. The realist is right that property-sharing is a genuine worldly phenomenon requiring explanation, that laws and natural kinds involve more than accidental co-extension. The nominalist is right that universals are metaphysically peculiar, that their connection to concrete particulars demands account, that ontological parsimony matters.

Perhaps the deepest lesson is that our pre-theoretical concepts of property and sharing are insufficiently precise to determine which ontology is correct. The debate may require reconceptualization rather than victory for either side. Structural realist approaches that emphasize relations over intrinsic properties, or dispositional essentialist views that ground properties in causal powers, suggest alternative frameworks transcending the traditional dispute.

What remains clear is that the question matters. Our understanding of natural kinds, laws, modality, and scientific explanation depends on getting the metaphysics of properties right. The nominalist challenge forces realists to articulate what universals genuinely contribute; the difficulties facing nominalism demonstrate that we cannot simply talk away the ontological commitments implicit in our best theories.