Under supervaluationism, John is borderline tall — 'John is tall' is neither true nor false on any single precisification. What is the truth value of 'John is tall or John is not tall'?
AIndeterminate, because the disjunction inherits the indeterminacy of both disjuncts
BFalse, because neither disjunct is true
CSupertrue — true on every precisification, even though neither disjunct has a determinate truth value
DOnly true if we first settle on a single precisification and evaluate the disjunction within it
This is the signature consequence of supervaluationism. On any single precisification, John either counts as tall (making 'John is tall' true) or doesn't (making 'John is not tall' true). So 'John is tall or John is not tall' is true on EVERY precisification — supertrue — even though 'John is tall' and 'John is not tall' are each indeterminate. Classical tautologies are preserved. The cost is that we can have a true disjunction where neither disjunct is true, which violates classical inference rules like disjunction elimination.
Question 2 Multiple Choice
Epistemicism handles the sorites paradox by claiming that vague predicates like 'bald' actually have sharp, precise extensions. What is the epistemicist explanation for why we cannot identify the boundary?
AThe boundary is determined by social convention and shifts depending on context, making it impossible to pin down
BThere is no fact of the matter about where the boundary falls — the predicate is genuinely borderless, but we can pretend there's a boundary for logical purposes
CThe boundary exists and is perfectly sharp, but our concepts and linguistic practices are not fine-grained enough to detect exactly where it falls
DVague predicates refer to continuous physical properties, and boundaries in continuous domains are always physically indeterminate
Williamson's epistemicism holds that 'bald' has a precise extension — there is a specific number of hairs below which someone is bald — but we cannot know where this threshold is because our knowledge of word meanings is limited by how we learned them. Semantic facts outstrip epistemic access. This preserves classical bivalence (every statement is true or false) and classical logic fully, but at a steep cost: it implies that removing a single hair sometimes changes someone from not-bald to bald, we just can't tell when. Many find this counterintuitive.
Question 3 True / False
On the supervaluationist account, a disjunction can be true (supertrue) even when neither of its disjuncts has a truth value.
TTrue
FFalse
Answer: True
This is the defining and controversial feature of supervaluationism. 'P or not-P' is a classical tautology that remains supertrue even when P is borderline (indeterminate), because on every precisification either P or not-P is true. But neither P nor not-P is supertrue when P is indeterminate. This preserves the law of excluded middle as a logical law while creating truth-value gaps for individual borderline sentences. The cost is that classical inference rules like 'from P-or-Q and not-P, infer Q' can fail.
Question 4 True / False
Degree semantics resolves the problem of higher-order vagueness, because assigning a precise numerical degree (like 0.7) to a borderline sentence gives it a determinate truth value.
TTrue
FFalse
Answer: False
Degree semantics faces the higher-order vagueness problem directly. Even if we assign 'John is tall' a degree of 0.7, the boundary between 'clearly tall' (degree ≈ 1) and 'borderline tall' (intermediate degree) is itself vague — there's no sharp line between degree 0.9 (clearly tall) and degree 0.7 (borderline tall). This generates vagueness about the degrees themselves, threatening an infinite regress: vagueness about vagueness, and then vagueness about that, and so on. The numerical assignment appears precise but doesn't eliminate the underlying gradience.
Question 5 Short Answer
Epistemicism fully preserves classical two-valued logic. What does it sacrifice to do so, and why do many philosophers find that cost too high?
Think about your answer, then reveal below.
Model answer: Epistemicism preserves bivalence by positing that vague predicates have perfectly sharp extensions that we simply cannot know. The cost is making meaning radically inaccessible: there is a precise hair-count threshold for baldness, but no amount of linguistic analysis or empirical investigation can identify it. This seems to sever meaning from use — the meaning of 'bald' is fixed by something beyond our grasp, not by the practices and contexts in which we use the word. Many philosophers find it implausible that meaning could be so epistemically opaque to the very speakers who deploy it.
The deeper objection is that epistemicism seems to generate sharp facts from nowhere. If our use of 'bald' is necessarily imprecise — no community ever drew a sharp line at exactly 1,047 hairs — then what could possibly fix such a boundary? Williamson argues that meaning supervenes on use in a way that produces sharp extensions even without explicit boundary-fixing, but this remains contested. The debate connects to broader questions about semantic externalism and the relationship between meaning, use, and knowledge.