The vat argument from lesson two is valid and both its premises are plausible, so a reply has to deny one of them. There are exactly two places to stand, and the interesting fact about the literature is that every major answer of the last century occupies one or the other, usually while insisting it is doing something more subtle.
Recall the argument. You do not know you are not a brain in a vat. If you know you have hands, then since having hands entails not being a vat brain, you know you are not a vat brain. Therefore you do not know you have hands.
Moore: deny the first premise
G. E. Moore gave the British Academy lecture "Proof of an External World" in 1939. He held up one hand, said "here is one hand", held up the other, said "and here is another", and declared the existence of external objects proved.
Read as a rebuttal this is a joke, and it has been received as one by generations of students. Read as what it is, it is a serious argument about the direction of inference. Moore is not claiming to refute the sceptic's reasoning. He is observing that the sceptic's argument and his own share a form, and differ only in which end you start from.
The sceptic runs: I do not know I am not a vat brain, therefore I do not know I have hands. Moore runs it backwards: I know I have hands, therefore I know I am not a vat brain. Both are valid. Both use the closure principle. They cannot both be sound, and the question is which premise is better supported.
Put that way, Moore has a real case. How confident are you that you have hands? Extremely. How confident are you in the epistemological principle that indistinguishable scenarios cannot be ruled out? Rather less, on reflection, since it is an abstract claim in a contested field. Moore's point is that when a valid argument runs from premises you find less certain to a conclusion you find less credible than the denial of those premises, the rational move is to run it the other way. A proof is only as good as its most doubtful premise, and here that is not the hand.
The cost is that this feels like refusing to engage, and in a sense it is. Moore offers no account of how you know you have hands in the face of the vat possibility. He says you do know it, more surely than you know any philosophical premise, and that this is enough.
Example. Someone objects that Moore is begging the question, since the existence of his hand is exactly what the sceptic doubts. Is the objection right?
It is the standard objection and it is weaker than it sounds. Begging the question means assuming your conclusion as a premise, and every argument does assume its premises: the charge only bites if the premise has no support independent of the conclusion. Moore's premise does have such support, namely that it is among the most secure beliefs anyone has. The sceptic's premise likewise has support, namely the indistinguishability of the scenarios. So both arguments assume something, neither assumes its own conclusion outright, and the dispute is about which premise survives comparison. The objection misdescribes a standoff as a fallacy, which is a common way of dressing up a preference as a logical point.
Now you. The sceptic replies to Moore: "You cannot claim to know you have hands, because if you were a vat brain you would say exactly the same thing with the same confidence." Does this rebut him?
Answer
No, though it feels like it should. The observation is true, and what it establishes is that your confidence is not a reliable guide to which situation you are in. But Moore was never claiming that his confidence proves anything to a neutral observer, he was making a claim about what he is entitled to believe given everything he has. The sceptic's reply is an argument that you cannot tell the two cases apart from the inside, which is premise one restated, so it advances the dispute not at all. Notice the general pattern: restating a premise more emphatically when it is challenged looks like argument and is not. The sceptic needs an independent reason to prefer their premise to Moore's, and the real ones are the two replies that follow.
Deny closure
The second place to stand is premise two. Fred Dretske argued in 1970, and Robert Nozick in Philosophical Explanations (1981), that knowledge simply is not closed under known entailment.
Nozick's machinery is sensitivity: you know p only if, had p been false, you would not have believed it. Test it on the two beliefs. Had you not had hands, would you believe you did? No, you would have noticed. So the hand belief is sensitive and counts as knowledge. Had you been a vat brain, would you believe you were not? Yes, necessarily, since that is how the scenario is built. So that belief is not sensitive and does not count. Closure fails, because one belief passes the test and something it entails does not.
This is elegant and the price is high. It licenses saying: I know I have hands, and I do not know I am not a handless brain in a vat. Keith DeRose named these abominable conjunctions, and the name stuck because almost everyone finds them intolerable to assert. Worse, closure is what licenses ordinary deductive reasoning, and a theory that permits knowledge to evaporate across a valid inference has given up something structural to save something local.
Shift the standard
The third reply, developed by DeRose and by David Lewis in "Elusive Knowledge" (1996), says both parties are right because "know" does not express one fixed relation.
On contextualism, how much a speaker must rule out to count as knowing varies with the conversation. In ordinary contexts the vat possibility is not in play and "I know I have hands" is true. In an epistemology seminar, where the possibility has been raised and made salient, the standards rise, and "I do not know I have hands" is also true. The two sentences do not contradict each other any more than "Francisco is tall" said of a jockey and of a basketball player.
The attraction is that it explains the data: why scepticism is compelling while you are reading about it and evaporates when you stand up. The cost is that it makes a metaphysical-sounding dispute into a fact about English. Many find that deflationary in a way that does not fit how the argument feels, and there is a technical worry that the sceptic can simply insist on the high standard and ask whether you know, in that sense, and the answer is still no.
Example. A contextualist and a Nozickian are both told: "In the seminar you said you do not know you have hands, and in the corridor you said you do. One of those is false." How does each answer?
The contextualist says neither is false, because the word changed its meaning between the two rooms, exactly as "flat" does when applied to a table and to Kansas. The Nozickian cannot say that, since for them "know" is univocal and the answer is fixed: you do know you have hands, in every context, and you never know you are not a vat brain, in any context. So the Nozickian is committed to the abominable conjunction being literally true everywhere, while the contextualist avoids it by denying that both conjuncts are ever assertable at once. That is the real division between the two replies, and it shows they are not variants of one idea.
Now you. Which premise of the vat argument does contextualism deny?
Answer
Neither, strictly, and that is the point of the position. Contextualism accepts that in the high-standards context both premises are true and the conclusion follows, so the argument is sound there. What it denies is that the conclusion, established in that context, contradicts the ordinary claims made in low-standards contexts, because the word does not mean the same thing. The sceptic wins the seminar and loses the corridor, and there is no single proposition they have established that survives the trip. Whether that is a solution or a change of subject is precisely what critics and defenders disagree about, and a reader who wants to hold the position should be able to state the objection in that form.
Explain the experience
The fourth reply, and the one this course will lean on, treats the question as an ordinary problem of inference. It goes back to Bertrand Russell in The Problems of Philosophy (1912) and was developed carefully by Jonathan Vogel in 1990.
You have experiences. Two hypotheses explain them: an external world of persisting objects, or a vat and a machine. Both predict your experience equally well, since that is how the vat was built. So they cannot be separated by prediction. They can be separated on the other virtues a hypothesis is judged by, and the real world hypothesis wins on almost all of them. It explains why experience is coherent across senses, why objects behave lawfully when unobserved, why other people report what you would expect, and why the world is so often inconvenient. The vat hypothesis explains none of this by itself: it has to add, for each regularity, that the machine was programmed to produce it. Every regularity is a separate stipulation.
The cost is that this is not a proof and does not pretend to be. It concludes that the external world is the better explanation, not that the vat is impossible. If you demand certainty, it gives you nothing. Lesson one is what makes this acceptable: knowledge does not require certainty, so a conclusion that is merely far better supported than its rival is exactly what knowledge is made of.
Example. A sceptic answers Vogel: "Your objection is that the vat hypothesis needs extra stipulations. But I can state mine in one sentence. The machine simulates a world exactly like the one you believe in. That is simpler than your version, not more complicated, since I get all your physics for free and add one vat." What is wrong with the reply?
It smuggles the complexity into the phrase "a world exactly like the one you believe in", which is not a simple specification but a pointer to the entire content of the rival hypothesis. Unpacked, the vat theory contains all of the real world theory as a description of what the machine computes, plus a vat, plus a machine, plus whoever built it. Length of sentence is not what parsimony measures, and lesson nine makes this precise. Notice the reply is a good one in the sense that it forces the defender to say what simplicity actually means, and that anybody using parsimony as a weapon in the God lessons will need an answer ready.
Now you. Of the four replies, which are compatible with each other?
Answer
Moore and abduction go together naturally, and in fact the abductive reply can be read as supplying the account Moore refused to give: it explains why the hand belief is better supported than the sceptical premise, rather than simply asserting that it is. Contextualism is compatible with either, since it is a claim about the word rather than about the evidence, and a contextualist can hold that in low-standards contexts the abductive case is what makes ordinary knowledge claims true. Denying closure is the outlier. It is incompatible with the abductive reply in spirit, since abduction concludes that you do know you are not a vat brain, while Nozick concludes that you do not and never could. A reader assembling a position should notice that three of the four fit together and one stands apart, which is a good reason to be suspicious of the one that stands apart.
That reply needs a way of saying what "better supported" means, precisely enough to use in harder cases where the answer is not obvious. That is the next lesson, and it is the tool the second half of this course runs on.