According to Nozick's tracking theory, why do you know you have hands but NOT know that you are not a brain in a vat?
ABecause the brain-in-a-vat scenario is logically impossible, so the question is meaningless
BBecause your belief that you have hands tracks the truth (if you lacked hands you'd notice), but your belief that you're not a brain in a vat does not track (a vat would produce the same experiences)
CBecause knowledge requires certainty, and you are only certain about your own hands
DBecause the brain-in-a-vat scenario is not known to entail that you lack hands
Nozick's tracking condition requires: if P were false, you would not believe P. For 'I have hands': if you lacked hands, you would notice — the condition is met, so you know it. For 'I am not a brain in a vat': even in the counterfactual where you ARE in a vat, the vat would produce exactly the same experiences, so you would still believe you're not — the condition fails. This asymmetry is what allows Nozick to deny closure: you can know P without knowing the known consequences of P.
Question 2 Multiple Choice
The epistemic closure paradox rests on three propositions that cannot all be true together. Which of the following is NOT one of the three?
AI know I have hands
BI know that having hands entails I am not a brain in a vat
CI cannot know I am not a brain in a vat
DKnowledge requires absolute certainty that cannot be undermined by any hypothesis
The three propositions forming the paradox are: (1) I know I have hands, (2) I know that having hands entails I am not a brain in a vat, and (3) I cannot know I am not a brain in a vat. Option D is not part of the paradox's structure — it is a separate (and disputed) claim about the nature of knowledge. The paradox's force comes from the fact that (1), (2), and (3) are each individually plausible but jointly inconsistent given the closure principle.
Question 3 True / False
Denying epistemic closure means rejecting modus ponens as a valid logical inference rule.
TTrue
FFalse
Answer: False
Denying closure is a claim about the epistemic concept of *knowledge*, not about logical validity. Modus ponens (if P, and P entails Q, then Q) remains logically valid. What Nozick denies is that the *epistemic status* of knowledge transfers across known entailments — you can know P without knowing Q, even when you know P entails Q. Logic and epistemology are different domains: the inference is still valid, but knowledge is a property that doesn't automatically propagate along valid inferences.
Question 4 True / False
On Nozick's tracking theory of knowledge, it is possible to know a proposition P without knowing all the propositions that logically follow from P.
TTrue
FFalse
Answer: True
This is precisely what denying closure entails. For Nozick, knowledge requires that your belief tracks the truth — a local, sensitivity-based condition that need not hold for every consequence of what you know. You know you have hands (tracking condition met), but you don't know you're not a brain in a vat (tracking condition fails). The entailment from having-hands to not-being-in-a-vat is valid, yet knowledge does not transmit across it. This is counterintuitive — and its cost is what makes the debate live.
Question 5 Short Answer
What makes the epistemic closure paradox philosophically significant? Why can't we simply accept all three propositions simultaneously?
Think about your answer, then reveal below.
Model answer: The three propositions — (1) I know I have hands, (2) I know that having hands entails I am not a brain in a vat, and (3) I cannot know I am not a brain in a vat — jointly violate the closure principle, which says that knowledge is closed under known entailment. Accepting all three requires either that closure fails (Nozick's move) or that ordinary knowledge claims like (1) are false (skepticism), or that we contextualize when standards for knowledge apply (contextualism). Each option has a significant cost, which is why the paradox is productive: it forces a decision about the structure of knowledge itself.
The paradox matters because each proposition seems independently plausible. (1) is what common sense says. (2) is just logic — having hands obviously means you're not handless. (3) feels undeniable — no experience could rule out a perfect simulation. But closure says (1) + (2) gives you (3), contradicting (3). Something has to go, and each candidate response (deny closure, accept skepticism, contextualize) commits you to a substantive theory of knowledge. The paradox thus maps the entire landscape of contemporary epistemology.