A philosopher argues: 'There IS a precise number of grains that separates a heap from a non-heap — we simply cannot know what that number is.' Which response to the sorites paradox does this represent?
ADegree-theoretic (fuzzy logic) — truth comes in gradations rather than sharp cutoffs
BContextualism — the threshold shifts depending on the conversational context
CSemantic indeterminacy — 'heap' has no determinate extension in borderline cases
DEpistemicism — sharp thresholds exist but are unknowable in principle
This is epistemicism (associated with Tim Williamson). It preserves classical logic by insisting that every predicate has a precise extension — including vague ones. The vagueness is in our epistemic access, not in reality or meaning. This is the only response that leaves classical logic fully intact, but at the cost of postulating precise thresholds that seem metaphysically arbitrary and permanently unknowable.
Question 2 Multiple Choice
What makes the sorites paradox a genuine paradox rather than just a bad argument?
AThe conclusion is obviously false, so the premises must also be false
BThe argument is logically valid and the premises seem plausible, yet the conclusion is absurd
CThe argument relies on circular reasoning that most people fail to notice
DThe paradox only applies to physical objects, not abstract predicates
A paradox is a valid argument with apparently true premises that yields an unacceptable conclusion. The sorites has valid logical form (modus ponens applied repeatedly) and both premises seem reasonable: 10,000 grains is a heap, and removing one grain cannot make the difference. Yet the conclusion — that one grain is a heap — is clearly false. The paradox forces us to reject at least one premise or classical logic itself, but none of the options is obviously wrong. That tension is what makes it genuinely paradoxical.
Question 3 True / False
Epistemicism preserves classical logic by accepting that vague predicates have sharp, determinate extensions even if those boundaries cannot be known.
TTrue
FFalse
Answer: True
Epistemicism (Williamson) holds that 'bald' has a precise threshold — some exact hair count — but that this threshold is unknowable, even in principle. This lets epistemicists keep the law of excluded middle and bivalence intact: every person is either bald or not bald. The cost is metaphysical: it requires postulating precise thresholds that nothing in our linguistic practices seems to fix.
Question 4 True / False
Vagueness and ambiguity are the same phenomenon: both arise when a word's meaning is unclear.
TTrue
FFalse
Answer: False
Vagueness and ambiguity are distinct. Ambiguity means a word has multiple distinct meanings (e.g., 'bank' means river bank or financial institution). Vagueness means a word has ONE meaning that lacks a sharp boundary between cases where it applies and cases where it doesn't. 'Bald' is vague — it has one meaning, but no precise cutoff. 'Bank' is ambiguous — it has two meanings. The philosophical problems they pose are entirely different.
Question 5 Short Answer
Why is the sorites paradox philosophically troubling, and what does it reveal about the classical semantic picture of language?
Think about your answer, then reveal below.
Model answer: The sorites paradox is troubling because it forces a choice between rejecting a plausible premise (the tolerance principle: one hair cannot make the difference between bald and not bald) and accepting an absurd conclusion (a single grain is a heap). The classical semantic picture assumes every predicate has a sharp extension and every statement is determinately true or false (bivalence). Vagueness challenges this: natural language predicates seem to genuinely lack sharp boundaries, yet the classical picture cannot accommodate borderline cases without either positing unknowable thresholds or abandoning bivalence.
Each response to the paradox pays a cost: epistemicism gets unknowable thresholds; semantic indeterminacy gives up bivalence; degree theory must explain why accumulated tiny truth-value drops eventually license a clearly false conclusion; contextualism must explain whether threshold shifts are principled. No response is cost-free, which reveals that the classical framework may simply not fit the structure of natural language vague predicates.