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Universals: Nominalism and Realism

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universals nominalism realism properties ontology

Core Idea

The problem of universals asks what accounts for objective similarities among particulars. Realism holds that universals (abstract properties shared by many particulars) are real entities that exist in each instance. Nominalism denies universals, explaining similarity through resemblance classes or class membership. This problem remains central because the answer shapes ontology and the theory of properties.

Explainer

From your study of universals and particulars, you understand the basic distinction: a particular is a concrete individual thing (this red apple, that red fire truck), while a universal would be the redness they share. The problem of universals asks: what exactly is being shared? Is there a real entity — redness itself — that is literally present in every red thing, or is the similarity among red things explained some other way?

Realism holds that universals are genuine entities. When two objects are both red, there is a single property, redness, that is wholly present in each. This explains similarity by positing a common constituent. The most radical version — Platonic realism — places universals in a realm of abstract objects that exist independently of any particular instance; redness exists whether or not anything is currently red. A more moderate Aristotelian realism holds that universals are real but only ever exist instantiated in particulars — redness exists only insofar as there are red things. Both versions face the challenge of explaining how an abstract or multiply-located entity can causally interact with the physical world, and how we come to have knowledge of it.

Nominalism denies that universals exist and tries to explain the appearance of shared properties without them. Class nominalism identifies properties with sets: being red just means being a member of the class of red things. Resemblance nominalism says that what makes two things red is that they sufficiently resemble each other and the paradigm cases of red things. The challenge for all nominalisms is to explain objective similarity without invoking the very universals they're trying to eliminate. What grounds the resemblance relation? If we say two red things resemble each other, are we smuggling in a shared property through the back door?

Your study of trope theory offers a third path: tropes are particular instances of properties — the redness of *this apple* is a distinct entity from the redness of *that truck*, even though they resemble each other. Trope theory avoids Platonic abstract universals while still giving properties ontological status. The debate between these positions isn't merely terminological. It shapes questions about natural laws (do laws hold because properties are universals that necessitate causal relations?), mathematics (are numbers universals?), and the metaphysics of science (what are natural kinds?). Choosing between nominalism and realism is one of the first and most consequential decisions in constructing an ontology.

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Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Introduction to Exponents → Order of Operations → Integer Order of Operations → Variable Expressions → The Distributive Property → Variables and Expressions Review → Introduction to Polynomials → Adding and Subtracting Polynomials → Multiplying Polynomials → Factorial → Permutations → Combinations → Counting Principles: Addition and Multiplication Rules → Introduction to Graph Theory → Propositional Logic Foundations → Logical Equivalences → Boolean Algebra → Introduction to Propositional Logic → Introduction to Predicate Logic (First-Order Logic) → First-Order Logic Syntax → Terms and Atomic Formulas in FOL → Variable Binding and Scope → Open and Closed Formulas in First-Order Logic → Variable Substitution and Capture-Avoidance in First-Order Logic → Quantifier Instantiation Rules in First-Order Proof Systems → Universal Quantification: Meaning and Scope → Free Variables and Bound Variables → Substitution and Instantiation in Predicate Logic → Terms and Atomic Formulas → Formulas and Well-Formed Expressions → Structures and Interpretations → Model Interpretation and Satisfaction → Interpretation, Truth, and Satisfaction of Formulas → Logical Consequence and Entailment → Soundness Theorem and Validity of Proof Systems → Deductive Reasoning and Formal Proof Systems → First-Order Resolution → Propositional Resolution → Semantic Tableaux (Propositional) → Semantic Tableaux (First-Order) → Decidable Fragments of First-Order Logic → Gödel's Completeness Theorem for First-Order Logic → Gödel's Incompleteness Theorems → Introduction to Intuitionistic Logic → Introduction to Modal Logic → Modal Semantics: Necessity and Possibility → Intensionality and Possible Worlds Semantics → Event Semantics → Aktionsart (Lexical Aspect) → Tense and Aspect in Formal Semantics → Viewpoint Aspect (Perfective and Imperfective) → Formal Semantics of Tense and Time → Formal Semantics of Modality and Possibility → Possible Worlds Semantics → Modal Realism → Necessity and Contingency → Actualism and the Actuality Thesis → Universals: Nominalism and Realism

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