Determinate and Determinable Properties

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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

Counting to 10Counting to 20Understanding ZeroThe Number ZeroCounting to FiveOne-to-One CorrespondenceCombining Small Groups Within 5Addition Within 10Addition Within 20Two-Digit Addition Without RegroupingTwo-Digit Addition with RegroupingAddition Within 100Repeated Addition as MultiplicationMultiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Two-Digit by One-Digit DivisionDivision with RemaindersRemainders and Quotients in DivisionDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueReading and Writing DecimalsComparing and Ordering DecimalsAdding and Subtracting DecimalsMultiplying DecimalsDividing DecimalsDividing FractionsMixed Number ArithmeticOrder of OperationsInteger Order of OperationsVariable ExpressionsThe Distributive PropertyVariables and Expressions ReviewIntroduction to PolynomialsAdding and Subtracting PolynomialsMultiplying PolynomialsFactorialPermutationsCombinationsCounting Principles: Addition and Multiplication RulesDefining Finite Sets RigorouslyRecursive Definitions on Finite SetsWell-Founded Relations and Transfinite RecursionThe Axiom of Choice and Equivalent FormulationsAxiom of ChoiceWell-Ordering TheoremInfinite Cardinal NumbersCantor's TheoremSet-Theoretic CardinalityUniversals and ParticularsIntrinsic and Extrinsic PropertiesDeterminate and Determinable Properties

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