This is an abbreviated version of a very famous radical sceptical challenge to knowledge. It is known by various names. Most famously it is called "Cartesian Scepticism", after Rene Descartes who initiated modern sceptical thought with his "method of doubt". He hypothesized that for all he knew, all of his experiences might be deceptions provided by an evil demon. More recently, drawing upon the popularity of science fiction and technology, Descartes'evil demon has been replaced by evil scientists or ingenious aliens who steal your brain and place it in a vat of nutrients. In this scenario all of your experiences are provided by a super computer wired to the sensory nerves of your brain. By hypothesis, no experience that we might possibly have can discern whether or not we are a brain in a vat. (There have been Star Trek episodes and the Matrix trilogy of movies that have popularized this scenario.) This form of scepticism is also known as "The Problem of Under-Determination" or "The Problem of the External World". The "Problem of Error" is also associated with this form of scepticism.
The sceptic argues that all of our beliefs about the existence of an external world are unjustified because all of the evidence (perceptual experience) we have in support of those beliefs cannot rule out the sceptical alternative that we are a brain in a vat. All of our experiences are fully compatible with both the hypothesis of an external world and the sceptical alternative that we are but a brain in a vat. Hence our beliefs about the external world are unjustified. And since all our beliefs about the external world are unjustified, none can qualify for the honour of "knowledge".
This sceptical argument depends for its impact on its apparent paradox -- the argument seems intuitively reasonable, yet at the same time intuitively false. It seems quite obvious that we do in fact have a lot of knowledge about the external world. Yet it also seems obvious that the sceptical argument is at least comprehensible. Once the possibility is pointed out, it seems reasonable to suppose that I don't in fact know that I am not a brain in a vat. And it also seems reasonable to conclude from this that I therefore don't know what I think I know. To see where the problem lies, we need to examine the argument in greater depth.
In order to be comprehensible, the short-form argument provided in the title requires the necessary addition of a number of premises. Some of these are rather obvious additions required to turn the argument into a valid deductive format. But some of these necessary additional premises are buried. Both the obvious and hidden missing premises open up opportunities for responding to the sceptic, either by negating his argument or by demonstrating that his argument is incoherent. Making clear what these unmentioned premises are makes clear that the sceptical argument is not as intuitively reasonable as first supposed. Thus, at the very least, desolving the apparent paradox.
To begin with the obviously necessary additions, a more formally framed version of the argument proceeds as follows:
(a) If (I know things about the external world,
I know that knowing things about the external world implies that I am not a BIV),
then - (I know that I am not a BIV).
(b) Things may not really be as they appear.
(c) Despite appearances, I may really be a BIV. [From (b)]
(d) I cannot prove (I do not know) that I am not a BIV. [From (c)]
Therefore (e) I do not know things about the external world. [From (a) and (d)]
Now let's explore some of the implications of the necessary missing premises -
(1) Things may not be as they appear. This premise is necessary in order to separate the way that things appear from the way that things are in fact. If there is no such separation, then I could prove that I am not a BIV by simply observing that it does not appear to me that I am a BIV. In order for the sceptical argument to have any force, it must assume that it is possible that I might in fact be a BIV despite the fact that it does not appear to me that I am. "Folk" philosophy comes freighted with the baggage of Cartesian mind/body dualism, so it is natural for us to expect that there is a gap between how our minds "see" things, and how they really are. Hence, from the perspective of folk philosophy, it is quite intuitively acceptable that things may not be as they appear.
One way to challenge the BIV argument, therefore, is the alternative of a direct realist theory of perception. Direct realism would deny the premise that things might not be as they appear. Another way to mount the same sort of challenge is the alternative of an anti-realist conception of truth. Anti-realism would also deny the premise that things might not be as they appear.
(2) An infallibilist model of knowledge. In order to move from the mere suggestion of the BIV alternative to the conclusion that I therefore do not know (cannot prove) that I am not a BIV, the sceptical reasoning must demand that my justification for my beliefs about whether or not I am a BIV rule out all potential defeaters, including the BIV hypothesis. In other words, the BIV argument is based on the assumption that the justification required to make my belief (that I am not a BIV) into knowledge must be infallible. This infallibilist premise is reinforced by the particular form in which the BIV argument is posed in the title variation. The title asserts the premise that "I cannot prove that I am not a brain in a vat" (emphasis added). Employing the word "prove" reinforces the presumption of infallibilism, since "prove" in contexts such as this is usually understood to imply something like "logical proof", or "deductive proof" -- a sense of guaranteeing the truth of, rather than simply providing evidence in support of. This is nicely consistent with the common "folk philosophy" understanding of knowledge as a belief about which we are "certain". Hence the infallibist assumption appears quite reasonable.
The way to challenge the BIV argument here is the alternative of a fallibilist conception of knowledge. A fallibilist conception of knowledge would allow that I could know a lot of things about the external world because those beliefs are adequately justified, and yet never-the-less that justification might be mistaken about the truth of those beliefs. The justification required for my beliefs to qualify for the honorific "knowledge" would not have to rule out all logically possible alternatives. The process of justification could permit some errors. It is possible (if I am indeed a BIV) that I do not in fact know anything about the external world. But the fact that I cannot prove that I am not a BIV is not a defeater for any of my claims to have such knowledge. Fallibilism draws upon the distinction between a first-person (internal) view of justification, and a third-person (external or God's Eye") view of justification.
(3) A foundationalist model of knowledge. The BIV argument is based on the premise that knowledge is to be understood from a foundationalist perspective. The argument is based on the premise that experiential awareness of perceptual evidence has some form of intrinsic epistemic priority. The justification necessary to elevate beliefs into knowledge has to be fundamentally based on perceptual knowledge, not on other beliefs. Otherwise, the required possibility that things might not be as they appear would have no epistemic weight. On some alternative models of knowledge, my belief that I am not a BIV (and my beliefs about the external world) would be sufficiently justified (proven) by the coherence of a set of beliefs. Similarly for the various externalist models of knowledge, my beliefs about the external world could qualify as knowledge without my even considering the BIV alternative -- let alone proving that I am not a BIV. But we are all intuitive empiricists, so we naturally feel quite comfortable with the assumption that perceptual/evidentiary propositions have some special epistemic status -- the basis of foundationalism.
As a result, any of the non-foundationalist models of knowledge would provide a way to challenge the BIV argument. They have been specifically constructed to do so.
(4) A prior grounding model of justification. As a consequence of the premises that assume that knowledge demands an infallible foundationalist justification of one's beliefs, the BIV argument can also be seen to assume the "prior grounding" model of justification. The BIV argument demands that the subject be aware of the "proof" that infallibly justifies the belief that one is not a BIV before allowing that one knows that one is not a BIV. The sceptic cannot admit either (a) the possibility that the subject might in fact be appropriately justified and yet not be aware of that fact; or (b) the possibility that some of the subject's beliefs about the external world might be default justified. Otherwise, the subject might properly be said to know that he is not a BIV without being able to prove it. When folk philosophy thinks about "knowledge", it normally thinks in terms of asking and giving reasons for one's beliefs. So it is natural to assume a "prior grounding" model of justification. Knowing that one is not a BIV requires having reasons for believing that one is not a BIV. Which, of course, the BIV hypothesis denies is possible ex hypothesi.
There are two kinds of challenging alternatives here, or rather two ways in which one can adopt a non-prior-grounding model of justification. One is to adopt an externalist theory of knowledge that denies that knowledge involves justification at all (such as pure reliablism, a causal theory, or Nozick's truth-tracking theory). The other option is to adopt the "default and challenge" model of justification (as is incorporated in the contextualist theory of knowledge, for example). From this latter alternative, I am prima facie justified in believing all sorts of things about the external world until and unless the sceptic can provide a context that challenges that default justification. Since the mere mention of the BIV alternative does not provide the necessary context, the burden is shifted to the sceptic to provide justification for believing the BIV alternative. With a default prima facie justification in play, it is irrelevant that I cannot prove that I am not a BIV.
(5) Knowledge is closed under known entailment. (This is the "closure principle" employed in step (a) above.) In order to reason from the premise that "I cannot prove that I am not a BIV" to the conclusion that "I know nothing", the sceptic is drawing upon the premise that knowledge is closed under known entailment. The sceptic is drawing upon a modus tollens deductive argument that proceeds from the premise "I know that P" (I know some thing about the external world) through the closure principle (if I know that P, and I know that P implies Q, then I know that Q), to the interim conclusion "I know that Q" (I know that I am not a BIV), and then denying this interim conclusion (I do not know that I am not a BIV) to reach the ultimate objective of denying P (I do not know any thing about the external world). We are all familiar with deductive reasoning, and the closure principle for knowledge seems to be a simple matter of deductive logic and therefore seems obviously true.
However, an easy challenge to the BIV argument would be to deny that knowledge is closed under known entailment. There are many theories of knowledge that do exactly that (Nozick and Dretske most famously). And when considering the context within which the BIV argument operates (a Foundationalist JTB theory of knowledge) it is rather easy to show that the closure principle does not in fact hold for knowledge. The truth of Q obviously holds across the entailment. And so does justification for Q. But for knowledge to hold across the entailment, it would be necessary that belief holds as well. Yet it is quite easily conceivable that I might believe that P, and believe that P entails Q, without believing that Q. We all of us hold at least some beliefs that are mutually inconsistent. I might not believe Q because it conflicts with some other beliefs of mine (that are in fact false). Or I might not believe Q simply because I am epistemicly irrational on this subject.
When the hidden premises behind the apparent intuitive reasonableness of the sceptic's argument are made clear, it becomes obvious that the BIV argument relies for its comprehensibility on a concatenation of highly questionable premises about the nature of knowledge. Each of those premises has been challenged by criticisms presented by many philosophers. There are numerous theories of knowledge available in the literature that provide alternatives for each premise. While the image of "knowledge" that underlies the seeming reasonableness of the BIV sceptical argument might be recognized as the "traditional" or "paradigmatic" notion, it is no longer considered the "best" model of knowledge available.
There is one theory of knowledge, Contextualism, that challenges all of the premises relied upon by the BIV argument. Contextualism is a Justified-True-Belief theory of knowledge that incorporates a fallibilist "default and challenge" model of justification. Such a model allows me to claim prima facie justification for my belief that things are indeed exactly as they seem. The sceptic's assumption of foundationalism implies the necessary presumption of an intrinsic (objective) property that distinguishes basic beliefs from non-basic beliefs. Contextualism denies that there is any such intrinsic property of beliefs. Within Contextualism, all differences between kinds of beliefs are determined contextually -- within the context of other beliefs (such as second-level epistemic beliefs). Contextualism would therefore also deny that there is any intrinsic characteristic that would differentiate "knowledge of the world" from any other kind of knowledge -- such as knowledge of my experiences, or knowledge of the meaning of the sceptic's arguments. For the sceptic to claim that I can understand his arguments is to claim that I have knowledge of the world. If there is no intrinsic property that can distinguish between the knowledge necessary to understand the sceptical argument and "knowledge of the external world", the sceptic must be drawing upon an incoherent theory. One does not defeat an argument about UFO propulsion methods by arguing about engineering details. One defeats such arguments by pointing out that there are no such things as UFOs. From the perspective of contextualism, then, the BIV argument is simply incoherent. Not only is the title argument invalid because its conclusion does not follow from its premises, it is also unsound because its premises are false.
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