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Determinate and Determinable Properties

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Intrinsic and Extrinsic PropertiesSubstance and Property→→Scalar and Vectorial Properties
properties determinates determinables

Core Idea

Properties exist at different levels of specificity: determinable properties are general categories (like color) while determinate properties are specific instances (like crimson red). Understanding this distinction proves crucial for metaphysical theories of properties and predication, as causes typically cite determinate rather than determinable properties.

How It's Best Learned

Compare concrete color examples—analyze how specific hues relate to general color categories—and work through why this distinction matters for causal explanation and property attribution.

Common Misconceptions

Treating determinables and determinates as entirely separate properties rather than as different levels of generality. Confusing this distinction with the type/token distinction or with the distinction between abstract and concrete properties.

Explainer

From intrinsic and extrinsic properties, you know that properties can be categorized by their dependence on other things — whether a property belongs to an object in isolation or only in relation to something else. The determinate/determinable distinction cuts along a different axis entirely: it organizes properties by their level of specificity. Rather than a flat list of properties, properties form hierarchies from the general to the particular, and understanding where a property sits in this hierarchy matters for both metaphysics and the theory of causation.

A determinable is a general property that can be realized in multiple, more specific ways. Color is a paradigm determinable: it can be realized as red, blue, green, and so on. Red is itself a determinable relative to its own determinates — crimson, scarlet, vermilion are all more specific reds. A determinate is a fully specific way of instantiating a determinable — a particular shade that cannot be further refined within that dimension of variation. The key logical feature of this relationship: if something instantiates a determinate, it necessarily instantiates the corresponding determinable (being crimson entails being colored), but the reverse does not hold (being colored does not determine which color).

There is a striking constraint on how determinates relate to each other: a thing can instantiate only one determinate under a given determinable at a time. An object can be crimson or cerulean but not both simultaneously — those are incompatible determinates of color. This incompatibility is not merely empirical (it happens to be that way) but metaphysically necessary (it's built into the nature of the determinable structure). This is why determinables aren't reducible to disjunctions of their determinates: having "color" doesn't mean having crimson OR cerulean OR scarlet as a disjunctive property; it means having some fully specific color, exactly one.

The determinate/determinable distinction connects directly to questions about causal explanation. When something happens — a ball breaks a window — what is the causally relevant description of the event? The window-breaking was caused by impact: but was the cause "physical contact" (a highly determinable description) or "the specific force, angle, and material properties of the ball" (a much more determinate one)? Philosophers of causation generally argue that causes are determinate events, not determinable ones. If a doctor's loud shout startled a patient with a heart condition, what caused the heart attack — "sound" (determinable) or the specific decibels, frequency, and shock of that particular shout (determinate)? The distinction structures debates about causal exclusion, mental causation, and the question of whether higher-level properties (like psychological states) can genuinely cause anything when more determinate physical properties are always available.

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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 → ZFC Axioms Overview → Axiom Schema of Separation → Axiom Schema of Replacement → Von Neumann Ordinals → Hereditarily Finite Sets → Recursive Definitions on Finite Sets → Well-Founded Relations and Transfinite Recursion → The Axiom of Choice and Equivalent Formulations → Axiom of Choice → Well-Ordering Theorem → Infinite Cardinal Numbers → Cantor's Theorem → Set-Theoretic Cardinality → Universals and Particulars → Intrinsic and Extrinsic Properties → Determinate and Determinable Properties

Longest path: 88 steps · 467 total prerequisite topics

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