A universal is a property, relation, or quality that can be instantiated by more than one particular thing - for example, the redness shared by two red apples, or the triangularity shared by all triangles. The problem of universals is one of the oldest and most persistent questions in philosophy, asking whether universals exist independently of the things that instantiate them, exist only in those things, or are merely names and concepts with no existence beyond language and thought. The debate shapes foundational questions in metaphysics, epistemology, philosophy of language, and the philosophy of mathematics.

The problem was given its classical formulation in ancient Greek philosophy. Plato argued that universals - what he called Forms or Ideas - exist in a non-physical realm independent of any particular instance. Aristotle challenged this, holding that universals exist only in and through the particulars that have them. These two positions established the broad poles of the debate that continued through medieval Scholastic philosophy, where the dispute between realists and nominalists became one of the defining intellectual controversies of the era. Figures such as William of Ockham, John Duns Scotus, and Thomas Aquinas each developed distinctive positions. The problem did not dissolve with the decline of Scholasticism; it re-emerged in early modern philosophy and remains a live topic in analytic metaphysics.

The major historical lines of the debate are surveyed in Universals - History.

Several distinctions structure the debate:

• Ante rem realism holds that universals exist prior to and independently of their instances - a position associated with Platonic Forms.
• In re realism holds that universals exist, but only in the particulars that instantiate them, not in some separate realm.
• Nominalism denies that universals exist at all as real entities; only individual particulars exist, and what we call universals are names or predicates applied to resembling particulars.
• Conceptualism holds that universals exist as mental concepts or categories, but not as mind-independent entities.
• Bundle theory holds that particulars are nothing over and above bundles of properties - universals or tropes - with no bare substratum underlying them. On this view, what we call a thing is simply a cluster of co-instantiated properties.

Within nominalism, further distinctions arise between predicate nominalism, resemblance nominalism, and trope theory, each offering a different account of why we correctly apply the same term to multiple things.

The problem of universals remains unresolved and is actively debated in contemporary analytic metaphysics. No dominant consensus has emerged across philosophy as a whole; different positions continue to attract serious defense. Realist positions have seen renewed attention through the work of philosophers such as David Armstrong, whose immanent realism attempts to ground universals in the natural world without positing a Platonic realm. Trope theory - which replaces universals with particular instances of properties - has become an influential alternative to both traditional realism and nominalism. The debate intersects with philosophy of mathematics (particularly debates over mathematical Platonism), philosophy of language (theories of predication and reference), and philosophy of science (debates over natural kinds and laws of nature).

• Platonic Realism - Universals exist as abstract entities independent of both mind and matter.
• Aristotelian (Immanent) Realism - Universals exist, but only as they are instantiated in particular things.
• Nominalism - Only particulars exist; universals are names or linguistic conventions applied to groups of similar things.
• Conceptualism - Universals exist as mental constructs rather than as features of mind-independent reality.
• Trope Theory - Properties are particular rather than universal; what appear to be shared universals are resemblances among distinct property-instances.

• Universals - History
• Universals - Debate
• Scholasticism
• Metaphysics
• Philosophy of Mathematics
• Nominalism
• Platonic Forms
• Natural Kinds
• Trope Theory

1. Plato, Phaedo, Republic (Book VI-VII), Parmenides. Standard editions: Oxford Classical Texts.
2. Aristotle, Categories, Metaphysics Books Z and H. Standard editions: Oxford Classical Texts.
3. William of Ockham, Summa Logicae (c. 1323). Trans. Michael Loux, Ockham's Theory of Terms (University of Notre Dame Press, 1974).
4. David Armstrong, Universals and Scientific Realism, 2 vols. (Cambridge University Press, 1978).
5. David Armstrong, Universals: An Opinionated Introduction (Westview Press, 1989).
6. D.C. Williams, “The Elements of Being,” Review of Metaphysics 7, nos. 1-2 (1953): 3-18, 171-192. (Foundational paper for trope theory.)
7. Michael Loux, Metaphysics: A Contemporary Introduction, 3rd ed. (Routledge, 2006). Chapter 1 provides an accessible survey.
8. E.J. Lowe, The Four-Category Ontology (Oxford University Press, 2006).