The Skeptic’s Master Argument (as given):
1) I can see my two hands, and therefore I reasonably believe that I have two hands.
2) But if I were a brain in a vat (and didn’t have any hands), I could be having exactly the same perceptual experiences as I am now having.
3) Unless I can prove that I am not a brain in a vat, I cannot reasonably believe that I have two hands.
4) I cannot prove that I am not a brain in a vat.
5) Therefore, I cannot reasonably believe that I have two hands.
3’) Unless I know that I am not a (handless) BIV, I cannot know that I have two hands.
4’) I do not know that I am not a (handless) BIV.
5’) Therefore, I cannot know that I have two hands.
The reason for these revisions will be discussed in the essay (see especially footnotes 1 and 13, and the main text of section 1.2). The basic problem is that the given argument is weaker than it could be (due to the illogic of the 3rd premise), so we ought to strengthen it as much as possible in order to avoid attacking a ‘straw man’. The proposed revisions should be sufficient to achieve that end.
The purpose of this preamble is to give a brief analysis of the effect of these revisions, and so convince the reader that they are appropriate (i.e. the argument has indeed been strengthened).
There are two alterations: (a) changing the requirement in 3) from proof to knowledge, and (b) replacing talk of ‘reasonable belief’ with knowledge.
Alteration (b) is fairly trivial, and discussed in footnote 1.
Alteration (a) is more significant, and discussed in section 1.2 (and footnote 13) of the essay. But note that this alteration could not possibly weaken the argument: If the given argument is sound, then the revised argument will also necessarily be sound. This is because 3) implies that proof is necessary for justified belief (and thus knowledge), which in conjunction with 4) guarantees 4’). It should be clear that 3’) is a weaker claim than its original equivalent – because known to be proven propositions are a subset of known propositions, so 3’) has a wider scope than 3) – and will be true at least whenever 3) is.
So the revised argument is no weaker; at the very least my alterations do no harm. Do they help? Well, consider the possibility that although proof is not necessary for knowledge, nevertheless we still fail to know that we’re not BIVs. In this possibility, my revised argument will be sound, but the original argument will not be.
The revised argument is never worse, and indeed is sometimes better, than the original. It has the added advantage of being more consistent with the skeptical arguments commonly discussed in the literature. I have therefore concluded that this essay would benefit from focussing on the revised, rather than original, argument. I hope that after reading the essay to follow, the reader will share my judgement here.
The Skeptic argues that our beliefs about the world are unjustified. The first step is to note that our basic beliefs (e.g. that I have two hands) derive from our sense perceptions, and that it is precisely these perceptions that we appeal to in order to justify such beliefs. The Skeptic then points out that our perceptual experiences could be misrepresenting reality, much like the scenario depicted in The Matrix. I could be a brain-in-a-vat (henceforth, a BIV), being ‘fed’ experiences by a super-computer which electrically stimulates my brain, causing lucid hallucinations which I have mistaken for reality. It is crucial to note that a BIV’s conscious experiences would be entirely indistinguishable from reality. The Skeptic then reasons that: a) the validity of our basic beliefs depends upon the validity of our sense perceptions, and b) a BIV’s sense perceptions misrepresent reality; therefore, c) our beliefs are justified only if we can prove that we are not BIVs. I cannot prove this, so the Skeptic’s stunning conclusion follows: I do not know that I have two hands.
The original third premise, looks initially plausible. The possibility that I might be a BIV implies that I might not have two hands. Thus, I cannot be assured of having two hands unless I can first demonstrate that I am not a BIV. It is further implied that I cannot know an unassured proposition.
However, this implication is blatantly invalid according to any form of epistemic externalism, according to which the strength of our epistemic position is determined primarily by external factors – which we may be unaware of and therefore unable to state as evidence. Rather than mere absence of proof, the Skeptic requires absence of knowledge – a different matter entirely.
Let us instead turn to the defence of the revised premise (3’). Suppose we want to know P, but there is an alternative Q, such that Q implies ~P. If we do not know Q to be false, then for all we know it could be true – and thus (via the material implication), for all we know, P could be false.
Applying this general principle to the present argument (using P = “I have two hands”, and Q = “I am a brain in a vat”) provides us with a powerful argument in support of the Skeptic’s third premise. The reasoning here is a variation of the ‘Closure Principle’: If S knows that P, and S knows that P implies ~Q, then S knows that ~Q. Premise (3’) is simply the contrapositive of this: if we do not know that ~Q, then we do not know that P.
The Closure Principle strikes us as axiomatic. However, it will be denied if we conceive of knowledge as belief which ‘tracks’ the truth through close possible worlds. According to Nozick’s ‘Conditional Theory’, for S’s true belief-that-P to count as knowledge, requires two further conditions: S would believe P if it were true, and S would not believe P if it were false. According to this definition, I can simultaneously know that I have two hands, but not know that I am not a (handless) BIV. This is because the close worlds relevant for tracking the truth of P, differ from the closest worlds necessary to track the truth of ~Q. No facts about those close worlds could be expected to restrict possible outcomes in more distant worlds. This explains why knowledge that P does not imply knowledge that ~Q, even though we know P implies ~Q. Nozick can thus refute the skeptic, but at the cost of some highly counter-intuitive results.
Proving that I am not a BIV – or even that it is unlikely – seems an impossible task. There is no possible evidence that could count against the skeptical hypothesis, because there is no possible real-world experience that could not be emulated exactly in the BIV world. Their empirical equivalence guarantees that there is no possible way, for a mind inside the system, to tell the two worlds apart. One could posit a priori reasons for preferring realism as the default hypothesis, but these tend not to be very convincing.
I believe there is potential for a compelling a priori answer to the Skeptic, but from quite a different direction. It is unproductive to attempt proof that the world of our common experience is objectively real. Instead, we could embrace this hard fact, and clearly delineate between these two conceptual frameworks: the “Common World” (henceforth, CW), and the “Objective World” (OW). It should be clear that truth will be relative to the ‘world’ being used as a frame of reference. Furthermore, we have direct – though not infallible – perceptual access to the CW. We can have knowledge about the CW, and the Skeptic’s present argument cannot deny this. The worst he can do is point out that we do not know whether our CW is identical with the OW. But this seems unimportant. I would suggest that in most contexts, people are seeking knowledge of the CW, not knowledge of the OW.
Those whose intuitions clash with mine in this respect will be unsatisfied by this answer. So for the remainder of this essay I will suppose (contrary to my own inclinations) that we seek knowledge of the OW. Within this framework, we must accept the impossibility of disproving the skeptical hypothesis.
However, as noted in section 1.2, a lack of proof here is insufficient to meet the Skeptic’s needs. Instead, he needs to establish that I do not know that I am not a BIV – premise (4’). Our total lack of proof, or even evidence, provides the Skeptic with strong prima facie support for this premise. However, as previously mentioned, this conflation of proof with knowledge depends on epistemic internalism. Externalism does not necessarily require agents to have internal justification for their knowledge. In the case of Reliabilism, all that is necessary is that the true belief be caused by a reliable process. Most people believe that they are not BIVs. If this belief is true, and caused by a reliable process – even though we cannot prove it – then it follows that we truly do know that we are not BIVs.
When confronted by skepticism, most of us are inclined to agree that, ultimately, we do not know whether we are BIVs. It may seem that externalist responses are simply dismissing the skeptical argument, rather than explaining it. This is where (epistemic) Contextualism comes in. The central thesis of Contextualism is that the epistemic standards required for knowledge vary according to context. The contextualist thus explains the apparent paradox of skepticism by conceding that all our intuitions are correct, but only within certain contexts. We cannot reach the high standards demanded by the Skeptic, but the lower standards required for everyday knowledge are attainable. Skepticism is true, but in a very non-threatening way.
Contextualism is a very plausible theory. We all recognise that the standards for knowledge required by the law courts, for example, differ from those in more casual settings. However, we must be careful not to equivocate between what is appropriate to say, and what is true. And even if we grant contextualism about knowledge, we may still question whether this theory has anything useful to add to the skepticism debate.
Contextualism by itself is unable to respond to the Skeptic. There is no possible evidence against the BIV hypothesis, so no matter how low the standards for knowledge are set, it seems that they cannot be met. To beat this objection, the contextualist will need to appeal to some form of epistemic externalism.
The anti-skeptical worth of contextualism will therefore depend on its ability to augment externalism, perhaps to explain why we find skepticism so convincing. As discussed in section 1.4, the contextualist explains this by suggesting that the skeptic is right – but only according to unusually high standards. But externalism alone can explain the plausibility of skeptical arguments simply by referring to the prevalence of (mistaken) internalist intuitions about knowledge. Thus contextualism appears to be redundant.
Contextualism’s last hope is that it may be of indirect use. It may augment an externalist theory so that the externalist theory itself can better refute skepticism. DeRose’s adaptation of Nozick’s conditional theory achieves exactly that. Let’s say that S’s belief that P is stronger, the more remote are the closest possible worlds which fail the condition: S believes that P iff P is true (in that possible world). DeRose then defines knowledge as (roughly) “strong enough true belief”. Our belief that we are not BIVs is very ‘strong’, so we can truly know it (according to all but the most extreme standards) – thus preserving closure and avoiding ‘abominable conjunctions’. DeRose explains our reluctance to say that we know it, by positing the “Rule of Sensitivity”: discussing knowledge of a proposition P tends to raise epistemic standards to the level necessary to make S’s belief-that-P sensitive. Of course we know next to nothing according to such excessive standards, but that poses no threat to our ordinary knowledge.
I have offered a brief outline of a semantic theory which may provide a compelling a priori solution to skepticism. Failing that, one will need to appeal to some form of epistemic externalism in order to overcome skeptical doubts. The counterintuitive results of denying closure (premise 3’) are too severe – the fourth premise is a much better target. Although contextualism has little to offer directly, it can help subjunctive conditional theories to preserve closure, and thus provide a much more plausible rebuttal of skepticism.
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Cohen, S. ‘Contextualism and Skepticism’ Philosophical Issues vol. 10, pp.94-107.
Cohen, S. ‘Replies’ Philosophical Issues vol. 10, pp.132-139.
Comesana, J. Philosophy from the (617) [http://philosophy617.blogspot.com/].
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Dretske, F. ‘Epistemic Operators’ in K. DeRose & T. Warfield (eds.), Skepticism: A Contemporary Reader, Oxford: Oxford University Press, 1999.
Hill, C. ‘Process Reliabilism and Cartesian Skepticism’ in K. DeRose & T. Warfield (eds.), Skepticism: A Contemporary Reader, Oxford: Oxford University Press, 1999.
Kornblith, H. ‘The Contextualist Evasion of Epistemology’ Philosophical Issues vol. 10, pp.24-32.
Lehrer, K. ‘Sensitivity, Indiscernibility and Knowledge’ Philosophical Issues vol. 10, pp.33-37.
Nozick, R. ‘Philosophical Explanations (selections)’ in K. DeRose & T. Warfield (eds.), Skepticism: A Contemporary Reader, Oxford: Oxford University Press, 1999.
Putnam, H. ‘Brains in a Vat’ in K. DeRose & T. Warfield (eds.), Skepticism: A Contemporary Reader, Oxford: Oxford University Press, 1999.
Sosa, E. ‘Skepticism and Contextualism’ Philosophical Issues vol. 10, pp.1-18.
Stine, G. ‘Skepticism, Relevant Alternatives, and Deductive Closure’ in K. DeRose & T. Warfield (eds.), Skepticism: A Contemporary Reader, Oxford: Oxford University Press, 1999.
 I have taken the liberty of replacing “reasonably believe” with “justifiably believe” throughout the argument, primarily for the sake of clarity, and to avoid any possible equivocation between epistemic and instrumental rationality (note that it could be instrumentally “reasonable” to have a false belief, so long as holding this belief served to help the agent achieve his goals). Furthermore, to avoid begging the question against externalism (as will be discussed more subsequently) I take “justification” to simply refer to whatever criteria are necessary to turn true belief into knowledge (rather than limiting the term to mean the giving of reasons or evidence). “Know” and “justifiably believe” can thus be used interchangeably with regard to true beliefs.
 As C. Hill wrote, “The question of whether one is entitled to hold a belief is logically independent of whether one is in a position to convince others that one is so entitled.” (‘Process Reliabilism and Cartesian Skepticism’, p.124.)
 F. Dretske, ‘Epistemic Operators’, p.134.
 I have consistently substituted “~Q” for the usual “Q” throughout this formulation of the principle, in order to maintain consistency with my previously defined variables. Of course the logic is unchanged. This formulation has the added advantage of clarifying the Skeptic’s reasoning: If we knew P, then we would know ~Q. But we do not know ~Q (by premise 4), therefore we do not know P.
 R. Nozick, ‘Philosophical Explanations (selections)’ p.163. I think these subjunctive conditionals are best interpreted as being in terms of close possible worlds. That is, the odd-sounding “if P were true” asks us to consider the group of close possible worlds where P is true (in addition to the actual world!), and judge whether S would believe that P in all of these close worlds. (How close? Nozick suggests out to the closest not-P world.) Similarly for “if P were false” – we are not considering all possible worlds, but only the close ones.
 Ibid, pp.167-172. Note that to subjunctively assess P, the most distant worlds we consider are the closest ones where P is false. In close ~P worlds, I do not have two hands for a relatively mundane reason (perhaps I was in an unfortunate accident), certainly not because I’m a BIV (that is a much more distant world than those we are concerned with when evaluating P!). However, to assess ~Q we must consider those worlds where ~Q is false (so Q is true), i.e. worlds where I am a BIV.
 His denial of closure leads to some “abominable conjunctions”. It is bad enough that I can know I have two hands but not know that I’m not a (handless) BIV. But it gets worse. For I can also know that “I have two hands and I am not a BIV” (after all, the closest worlds where that is false are those worlds where ‘I have two hands’ is false, rather than worlds where I am a BIV!). Thus, according to Nozick’s theory, I can know that I have two hands and I am not a BIV, whilst not knowing that I am not a BIV. Quite bizarre, to say the least. Thanks to the Juan Comesana, Philosophy from the (617), [entry: Oct 12, 2003] for pointing this out.
 For example, S. Cohen, ‘Contextualism and Skepticism’ pp.104-6. His basic argument is that we think it rational to deny that we are BIVs, yet we have no evidence against it, so to call it a priori rational seems the only (internalist) option left.
 For a full argument in support of this distinction, see my weblog Philosophy, et cetera [entry: 1st April 04]. As a conceptual aid, consider the Matrix movies: In that scenario, the familiar world inside the Matrix would be the CW, whereas the outside world (ruled by machines) would be the OW.
Take care not to confuse this current talk of ‘worlds’ with the ‘possible worlds’ discussed elsewhere in this essay. The latter refers to various possible OWs, only one of which actually exists. In the current treatment, all the worlds under discussion are equally “real” – they are simply different ways of looking at a single reality, from a different ‘frame of reference’, if you will. The various non-objective worlds should all be reducible to the OW in some sense. For example, the world of a fictional story is reducible to the real-world text on a real-world page. In the BIV hypothesis, our CW is reducible to the rules of the computer program that determines the experiences fed to a BIV in any given situation.
 Something may be true within the world of a story that is blatantly false in real life. To preserve the truth value, one must reinterpret the semantics so that the proposition about the story-world becomes a proposition about its reduced equivalent (i.e. what text is written on a real-world page). I propose a similar sort of semantic revision to H. Putnam (‘Brains in a Vat’, p.37), who suggests that a BIV saying “there is a tree in front of me” likely speaks the truth, given what “tree” and “in front of” mean in Vat-English.
It should be noted that I disagree with Putnam’s suggestion that a BIV is incapable of referring to the OW. Such ‘semantic externalism’ strikes me as far less plausible and helpful than the ‘semantic contextualism’ I’ve outlined here. A BIV could refer to the OW if he wanted to, but within most contexts, it simply isn’t appropriate or useful to do so.
To get an intuitive feel for my semantic contextualism, consider the following example (which I owe to conversation with Patrick Kerr): Suppose I say to you “In my dream last night, I was walking down the street…”, it is clearly inappropriate to respond “Liar! You were in bed asleep!”. Instead, we implicitly recognise that the phrase “In my dream last night” alerts the listener to a shift of semantic context: the truth of the subsequent proposition is to be evaluated in terms of the dream world, not the real world.
 The sort of “anti-realism” discussed by J. Dancy, (An Introduction to Contemporary Epistemology, p.19) posits the useful concept of the “recognizable world”, i.e. the world of our perceptual experiences (let’s call it the PW), containing no gap between evidence and truth. (Of course, the anti-realist allows for no other worlds, but we need not follow him so far.) I must emphasise that the CW is distinct from the PW – though there is some overlap. The CW is simply that world which our perceptions are attuned to, what people normally refer to as “reality”, regardless of whether it is the ultimate reality of the OW. I hope my use of the word ‘direct’ is not misleading here.
 See my April 1st weblog post (Philosophy, et cetera) for further justification and examples.
 Note the big “if”. The Skeptic can respond by focussing on internalistic questions, e.g. “Can you provide any reasons to suggest that your belief is true and reliably formed?” The externalist has to concede this point (though no doubt accompanied by a brusque dismissal of its importance). Note then, that although externalism still poses a problem for the Skeptic, he is at least better off now than he was with the original Master Argument (which externalism instantly renders illogical).
 E. Sosa (‘Skepticism and Contextualism’, pp.1-4) makes a roughly similar point, which is then taken up more definitely by K. Lehrer, ‘Sensitivity, Indiscernibility and Knowledge’, pp.33-34. Cf K. DeRose (‘Solving the Skeptical Problem’, pp.213-4), who argues that accusing natural language speakers of “systematic falsehood” surely counts against a semantic theory. S. Cohen (‘Replies’, p.137), in discussing the strangeness of various cross-contextual conjuncts, argues that a) pragmatic implicatures are cancellable, b) the strangeness of cross-contextual conjuncts is not cancellable, therefore c) the strangeness is due to genuine semantic differences, rather than pragmatic factors.
 A popular contextualist response involves “relevant alternatives”, but it should be noted that any successfully anti-skeptical definition of ‘relevance’ will necessarily be externalist in nature – and need not be contextualist at all! For example, Dretske (‘Epistemic Operators’, p.142) anticipates Nozick’s subjunctive conditional theory when he suggests that a relevant alternative is one that “might have been realised in the existing circumstances if the actual state of affairs had not materialised”. He is clearly referring only to close possible worlds, rather than mere logical possibility. Dretske denies closure, but contextualists can avoid this if they take Stine’s approach (‘Skepticism, Relevant Alternatives, and Deductive Closure’, p.154) and insist that we “simply know” non-relevant alternatives to be false. See my paragraph on DeRose’s theory for a much more convincing explanation.
 Cohen, ‘Contextualism and Skepticism’, p.104.
 As H. Kornblith (‘The Contextualist Evasion of Epistemology’, p.27) put it, “the externalist part… is doing the work in combating Full-Blooded Skepticism. Contextualism does no work here”.
Of course, Cohen himself avoid externalism, which is why he is forced into positing implausible a priori reasons (see note 8).
 Kornblith, pp.29-30. See also Lehrer’s discussion (‘Sensitivity, Indiscernibility and Knowledge’, pp.35-36) of the “indiscernibility condition” and why it (falsely) leads us to doubt what is in fact reliable knowledge.
 DeRose, ‘Solving the Skeptical Problem’, p.204. This is a somewhat oversimplified outline of his position.
 DeRose, ‘Sosa, Safety, Sensitivity, and Skeptical Hypotheses’, p.20. Note that the “enough” is where Contextualism comes into the picture – this ‘threshold’ requirement will vary with context.
 DeRose, ‘Solving the Skeptical Problem’, pp.205-6. Sensitivity requires that if P were false, S would not believe it. That is, our epistemic position must be so strong that it extends all the way out to the closest not-P worlds. In the case of the BIV hypothesis, that is a very distant world indeed!