Questions: Property Exemplification and Instantiation

Question 1

Suppose exemplification is treated as a genuine two-place relation E that holds between object a and property F whenever a has F. What problem immediately arises?

• A. It makes predication a purely linguistic matter with no metaphysical implications
• B. It requires a further relation to connect a, F, and E — which in turn requires another relation, and so on without end (Bradley's regress)
• C. It prevents properties from being abstract objects distinct from their instances
• D. It makes the distinction between particulars and universals collapse

Answer: (B)

If exemplification is a relation, then for a to exemplify F, the relation E must hold between a and F. But relations themselves must be exemplified — so E must hold between a, F, and E via a further relation E', which requires E'' to connect E' to its relata, and so on infinitely. This is Bradley's regress. It motivates treating exemplification as a primitive non-relational tie — something that just binds object to property, with no further story to tell — rather than as a standard relation that generates new regress problems.

Question 2

Consider the property P* = 'the property of not exemplifying itself.' If P* does exemplify itself, then by definition it doesn't; if it doesn't, then by definition it does. This puzzle is most closely analogous to:

• A. Zeno's paradox of motion, which requires mathematical limits to resolve
• B. Russell's paradox about the set of all sets that do not contain themselves
• C. The sorites paradox about vague predicates and borderline cases
• D. Hume's problem of induction about generalizing from finite observations

Answer: (B)

The self-exemplification paradox is a direct analogue of Russell's paradox, applied to properties rather than sets. Just as the set R = {x : x ∉ x} is contradictory (R ∈ R ↔ R ∉ R), the property P* leads to P* ∈ P* ↔ P* ∉ P*. Both paradoxes are resolved by similar means — type-theoretic restrictions that prevent unrestricted self-reference. In property theory, this means preventing properties from ranging freely over all properties, including themselves.

Question 3

On a deflationary account of exemplification, the truth of 'The apple is red' is fully accounted for by the apple being red — there is no additional metaphysical relation of exemplification that further explains or grounds this fact.

• T. True
• F. False

Answer: True

Deflationists hold that talk of 'exemplification' is a logical device for formal representation of predication, not a substantive metaphysical relation. On this view, asking 'what makes it the case that the apple exemplifies redness?' is a pseudo-question — the apple's being red is the basic fact, and nothing further grounds it. This contrasts with the realist view that exemplification is a genuine relation or tie that must be posited to explain object-property connections.

Question 4

Because exemplification relates an object to a property, it is expected to itself be a property — and therefore should exemplify itself.

• T. True
• F. False

Answer: False

This inference is invalid on most developed accounts. Many property theorists deny that exemplification is itself a property; instead, they treat it as a primitive ontological connector — a non-relational tie — precisely to avoid regresses and paradoxes. Even those who grant that exemplification is a relation need not accept that it exemplifies itself; type-theoretic frameworks restrict self-exemplification to block the resulting paradoxes. Assuming all relations are properties, and all properties self-exemplify, leads directly to the self-exemplification paradox.

Question 5

What is Bradley's regress, and why does it motivate treating exemplification as a primitive 'non-relational tie' rather than as a standard two-place relation?

Model answer: Bradley's regress arises when exemplification is treated as a relation: a having F via relation E requires E to hold between a and F, which requires another relation E' connecting a, F, and E, which requires E'', and so on infinitely. The regress never terminates. Treating exemplification as a primitive non-relational tie — something that simply binds object to property without itself being an additional entity — stops the regress by refusing to ask 'what connects them to this connection?' The tie is not a further item in the ontology; it is just what it is for an object to have a property.

The non-relational tie response says: the question 'what makes a related to F by E?' is malformed — exemplification is not itself the kind of thing that gets exemplified. The cost is accepting a primitive that resists further analysis. The benefit is escaping an infinite regress that would undermine any account of object-property relations. Different metaphysical positions (trope theory, Armstrongian states of affairs, nominalism) offer different ways of resolving this tension.