Universals are the properties or kinds that many particular things can share. Two red apples have redness in common; the question is what that common possession amounts to.

The positions

Realism holds that universals exist in their own right. Plato gave the strongest form in the theory of forms: the form of redness exists outside space and time, and particular red things participate in it. This explains how the same property can be wholly present in many places and pays for it with an additional realm.

Aristotle held that universals are real and exist only in the particulars that have them. There is no redness apart from red things, and the mind abstracts the universal from the instances. This keeps the explanatory work and drops the separate realm.

Nominalism holds that only particulars exist. "Red" is a name we apply to things that resemble each other, and nothing further is shared. William of Ockham argued that positing universals multiplies entities without need. The objection is that resemblance itself looks like a universal, which threatens a regress.

Conceptualism places universals in the mind as general concepts formed from experience, which explains our ability to classify while leaving open why the world cooperates.

Why the argument matters

The dispute decides what a scientific law describes. If laws relate universals, they state something about the structure of reality. If only particulars exist, a law is a summary of how things have behaved so far, which brings Hume's problem of induction directly into view.

The problem of universals was the central controversy of medieval philosophy and remains a live question in ontology.