Questions: Determinate and Determinable Properties

Question 1

A rose is crimson. How does the determinate/determinable framework describe the relationship between 'crimson' and 'colored'?

• A. Crimson and colored are entirely separate, unrelated properties that happen to co-occur
• B. Crimson is a determinate of the determinable 'colored' — a maximally specific instance of the general property
• C. Colored is a determinate of crimson — a broader version of a more specific property
• D. Crimson and colored are the same property, just described at different levels of linguistic abstraction

Answer: (B)

Crimson is a specific shade — a determinate — that instantiates the more general determinable 'colored.' The relationship is hierarchical: being crimson necessarily entails being colored (you can't be crimson without being colored), but being colored does not determine which color (you could be crimson, cerulean, or any other shade). Note that 'red' sits in between: it's a determinable relative to crimson but a determinate relative to colored. The hierarchy runs from most general to most specific.

Question 2

A philosopher argues that 'color' is just shorthand for the disjunctive property 'is crimson OR is cerulean OR is scarlet OR …' — that determinables reduce to disjunctions of their determinates. What is the best objection?

• A. This is correct — determinables are just convenient abbreviations for long disjunctions
• B. Determinables cannot be defined at all since there are infinitely many possible determinates
• C. The disjunction analysis fails because having 'color' is not merely having one or more options from a list — it means having some fully specific shade, and the determinates under a determinable are mutually exclusive in a way that a bare disjunction does not capture
• D. The disjunction analysis works, but only for color; other determinables like shape or mass resist it

Answer: (C)

The mutual exclusivity of determinates is the key problem for the disjunction analysis. A thing can instantiate only one determinate per determinable at a time — an object cannot be both crimson and cerulean simultaneously. A bare disjunction (A OR B OR C) doesn't capture this exclusivity; it would allow all three to be true at once. Moreover, determinables carry structure that mere disjunctions lack: the determinates are organized along a dimension of variation (hue, in the case of color) with a specific incompatibility built in. This structure is why 'determinable' is a distinct metaphysical category, not just an abbreviation.

Question 3

If an object instantiates the determinate property 'scarlet,' it necessarily also instantiates the determinable property 'colored.'

• T. True
• F. False

Answer: True

This is the fundamental logical relationship between determinates and determinables: instantiating a determinate entails instantiating the corresponding determinable. Being scarlet is a way of being colored, so any scarlet object is also colored — by necessity, not contingency. The reverse does not hold: being colored does not determine which color. This one-way entailment (determinate → determinable, but not vice versa) defines the determinate/determinable relationship.

Question 4

A single object can instantiate two different determinates of the same determinable at the same time — for example, being both crimson and cerulean simultaneously.

• T. True
• F. False

Answer: False

Mutual exclusivity of co-instantiation is a defining feature of determinates under a common determinable. A thing can have exactly one determinate per determinable at any moment. This incompatibility is metaphysically necessary, not just empirically observed: it's built into the structure of the determinable. This is precisely why determinables can't be reduced to disjunctions — a disjunction would permit multiple disjuncts to be true simultaneously, but the determinate/determinable structure forbids it.

Question 5

Why do philosophers of causation typically hold that causes must cite determinate rather than determinable properties?

Model answer: Causes must cite the specific properties that actually made the difference — the determinate level of description. A highly determinable description (e.g., 'sound caused the heart attack') underdetermines the causal mechanism: many different sounds with different frequencies, volumes, and timing would satisfy 'sound,' but only the specific determinate properties of this particular sound did the causal work. Citing only the determinable leaves open the question of what specifically caused the effect. Moreover, if causes were determinable, we'd face a problem of causal overdetermination: both the determinable property and its specific determinate property would each cause the same effect, which is metaphysically problematic.

The connection to causal exclusion debates is central here. In philosophy of mind, if mental states are determinable descriptions of more determinate neural states, the worry is that the mental level never actually causes anything — the more determinate physical level always does the real causal work. This is why the determinate/determinable distinction matters beyond abstract metaphysics: it structures debates about whether higher-level properties (psychological, biological, social) can be genuinely causally efficacious.