Questions: Epistemic Closure and Logical Closure Principles

Question 1

You know you have hands (P). You know that having hands entails you are not a handless brain in a vat (P → ~BIV). A student applies CKE and concludes: 'Therefore I know I'm not a brain in a vat.' What is philosophically significant about this conclusion?

• A. It is a straightforward valid inference — CKE is uncontroversially true and the conclusion follows trivially
• B. The conclusion (~BIV) seems epistemically inaccessible from the inside, creating pressure either to deny ordinary hand knowledge or to deny CKE itself
• C. It commits an informal fallacy by conflating direct knowledge with inferred knowledge
• D. It proves that BIV skepticism is false, since the conclusion is clearly available to ordinary reasoners

Answer: (B)

The philosophical tension is that ~BIV seems like a 'heavyweight' claim you cannot verify from the inside — you would have the same experiences whether or not you were a BIV. So the CKE inference forces a choice: either accept you know ~BIV (the Moorean response), or run the argument backward: since you don't know ~BIV, and CKE says knowing P requires knowing its entailments, you don't know you have hands. Neither horn is comfortable, which is what makes CKE philosophically central.

Question 2

Dretske and Nozick deny closure under known entailment. On their tracking theory, which of the following best explains why you might know you have hands without knowing you are not a brain in a vat?

• A. Ordinary perceptual knowledge is infallible, but BIV knowledge requires a higher epistemic standard
• B. You track 'I have hands' because you would not believe it if it were false (you'd lack the perceptual experience), but you do not track 'I am not a BIV' because you would still believe it even if you were a BIV
• C. The BIV scenario is logically impossible, so the entailment from hands to ~BIV does not hold
• D. CKE only fails for highly technical philosophical claims, not for ordinary knowledge like having hands

Answer: (B)

The tracking theory defines knowledge as a counterfactual sensitivity: you know P iff you wouldn't believe P if P were false. You track 'I have hands' because if you lacked hands, you'd lack the relevant perceptual experience. But if you were a BIV, you'd still believe you weren't one — the BIV scenario is designed to fool you. So you don't track ~BIV even though you (supposedly) know P. This is exactly what Dretske and Nozick use to motivate closure denial: the perceptual connection that gives you ordinary knowledge doesn't extend to ruling out remote skeptical possibilities.

Question 3

The skeptical argument about brains in vats uses modus tollens on CKE: if knowing P requires knowing ~BIV (by CKE), but you don't know ~BIV, then you don't know P.

• T. True
• F. False

Answer: True

This is precisely the logical form of the skeptical argument. CKE says: K(P) ∧ K(P → Q) → K(Q). Contraposing: ¬K(Q) → ¬K(P) ∨ ¬K(P → Q). Since you plausibly know the entailment from having hands to not being a BIV, the skeptic runs: ¬K(~BIV) → ¬K(hands). The skeptic assumes CKE is true and uses your inability to know ~BIV to undermine ordinary knowledge.

Question 4

Epistemic closure under known entailment is universally accepted by epistemologists as correct and unproblematic.

• T. True
• F. False

Answer: False

CKE is explicitly contested. Philosophers Fred Dretske and Robert Nozick denied closure as part of their tracking theory responses to skepticism. While closure is intuitively compelling, its interaction with skeptical scenarios generates significant controversy. The debate is not merely academic: different theories of knowledge (tracking, safety, contextualism, relevant alternatives) make different predictions about whether and when CKE holds.

Question 5

What is the 'odd result' that defenders of epistemic closure level against Dretske and Nozick's closure-denial view?

Model answer: If closure denial is correct, a competent logician who explicitly deduces Q from known premises (knowing P and P → Q, then inferring Q) would thereby know less than an equally situated non-logician who never made the deduction. The non-logician, having never formed the belief Q, avoids the 'untracked' claim and retains knowledge of P. But the logician, by performing valid reasoning, arrives at a belief Q that they don't 'track' — undermining their knowledge of P by CKE's contrapositive. This seems backwards: logical reasoning should not reduce knowledge. Closure defenders argue this consequence makes the tracking theory epistemologically untenable.

This objection, pressed especially by John Hawthorne, captures why closure denial has a high philosophical cost even if it avoids skepticism. The alternative — Moorean responses that simply accept we know ~BIV — carries its own costs, but at least preserves the intuition that deduction is epistemically safe.