1. Since I don't know who you are, dear reader, and since I know that some people don't have hands, I don't know whether you have hands. Probably you do, but knowing that something is probable is rarely, if ever, a way of knowing that thing. By contrast, I know that I have hands. Let me check. Yes, here is one of my hands; and here is another. Since I know that here is one of my hands and that here is another, and since I know that it follows from those two claims that I have hands, I can deduce that I have hands. So, I know that I have hands.

Despite the seeming obviousness to me of my conclusion, some people will be willing to question it. Although you may know who I am, you may never have had the sort of proximity with me, or with photographs or videos of me, that would be required for determining by sight that I have hands. Further, you may lack the sort of intimacy with me that might be required for trusting me, and so for coming to know that I have hands by believing me when I say that I do. In that case, it might be reasonable for you to remain open-minded: perhaps I have hands; perhaps I don't. And if you were to keep an open mind about whether I have hands, then you would fail to know that I have hands. But you know that if someone knows something, then what they know must be so. So, you know that if I know that I have hands, then I have hands. Because you know that, if you also knew that I know that I have hands, you would be in a position to deduce, and so know, that I have hands. Since you aren't in a position to know that I have hands, it seems to follow that you aren't in a position to know that I know that I have hands. Just as it can be reasonable for you to remain open-minded as to whether I have hands, it can be reasonable for you to remain open-minded as to whether I know that I have hands.

Such considerations seem to show that you might fail to know that I have hands, and that you might fail to know that I know that I have hands. However, the circumstances that give rise to those considerations seem to be easily rectifiable. We agree to meet. Seeing my hands, you come to know that I have hands. Alternatively, we undertake a correspondence. Overcoming your initial distrust, you come to believe me when I tell you that I have hands, and thereby come to know that I do. More problematic would be considerations that seemed to show that neither you nor I can know that I have hands, and where the circumstances that gave rise to our ignorance are not easily rectifiable. Notoriously, some philosophers have tried to present such considerations. In doing so, they have tried to support the sceptical conclusion that I can't know that I have hands by developing arguments for that conclusion. Insofar as the conclusion of these sceptical philosophers’ arguments seems to conflict with something that we ordinarily take to be obvious, it is worth considering how we might respond to those arguments.

In what follows, I want to consider a sort of response to the argument of such a sceptical philosopher that was developed in the first half of the twentieth century by the philosopher G. E. Moore. In rough, Moore claimed that my conclusion – that I know that I have hands – is obviously correct. Indeed, it is so obviously correct that its correctness is more obvious than is the correctness of the premises of the sceptical philosophers’ arguments that it is incorrect. Where claims conflict, as the claim that I know that I have hands conflicts with the claim that I don't know that I have hands, our obligation is to accept the more obviously correct of those claims and to reject the less obviously correct one. Following that procedure, Moore argues, will lead me to hold on to the claim that I know that I have hands and to give up at least one of the sceptical philosophers’ premises. (This is in broad accord with a reading of Moore's discussions of scepticism proposed in Lycan Reference Lycan, Nuccetelli and Seay2007.)

I'll begin, in section 2, by setting out an argument, of the sort a sceptical philosopher might present, to the conclusion that it's not the case that I know that I have hands. In section 3, I'll set out the basic form of Moore's response to that argument. In section 4, I'll begin to develop Moore's response to the charge that his basic response begs the question against the sceptical philosopher. Finally, in section 5, I'll suggest that one way in which the claim that I know that I have hands is more obviously correct than the sceptical philosopher's various counter-claims derives from the fact that our knowledge of the former claim is distinctively intelligible.

2. To fix ideas, it will be useful to have before us an example of the sort of argument that might be offered by a sceptical philosopher. Let's begin by setting out some general principles that play important roles in the argument.

Earlier, we were willing to accept two principles, Modus Ponens and Modus Tollens, set out immediately below. One way in which the two principles are related is the following. Modus Ponens tells us that if some premise were true, and if some conclusion followed from that premise, then that conclusion would be true too. Modus Tollens records that in that case, if the conclusion would be true too if the premise were true, and if the conclusion were not in fact true, then it must be that the premise is not in fact true either.

(For example, that (I have hands) and that (if (I have hands), then (I'm not handless)) together entail that (I'm not handless). Here, and throughout, ‘p’ and ‘q’ stand in for declarative sentences of English.)

(For example, that it's not the case that (I have hands) and that it is the case that (if (I have hands and feet), then (I have hands)) together entail that it's not the case that (I have hands and feet).)

We were also willing to accept that we can know things on the basis of competent deduction from other things that we know, via principles like Modus Ponens and Modus Tollens. For one instance, we were willing to accept that if someone knows that here is one hand, knows that here is another hand, and knows that it follows from those facts that here are hands, and if they competently deduce, on that basis, that here are hands, then they can know that here are hands. For another instance, we were willing to accept that if someone knows that I know that I have hands, and knows that it follows from my knowing that I have hands that I do have hands, and if they competently deduce, on that basis, that I have hands, then they can know that I have hands. We can see these examples as instances of a more general principle:

(The principle is called ‘Closure’ because it says that knowledge is closed under competent deduction on the basis of known entailment. This just means that every case of competent deduction on the basis of a known entailment from a piece of knowledge is itself a piece of knowledge.) The Closure principle seems plausible insofar as we ordinarily think that we can know things through competently deducing them from other things that we know.

Putting two of these principles together (with the operative principles labelled in parentheses), and adding in two premises (labelled as such in parentheses), we can develop the following skeletal argument form:

1. I. S knows that if p, then q. (Premise.)

2. II. If S knows that p, and S knows that if p, then q, and if S competently deduces that q on the basis of what she knows, then S can know that q. (Closure.)

3. III. If S knows that p, and if S competently deduces that q on the basis of what she knows, then S can know that q. (From I, II.)

4. IV. It's not the case that S can know that q, even on the basis of competent deduction from what S knows. (Premise.)

5. V. It's not the case that S knows that p. (From III, IV, by Modus Tollens.)

That gives the skeletal form of an argument. Putting some flesh on the bones, consider the following instance of that form.

1. I. Guy knows that if Guy has hands, then Guy is not a handless Brain-in-a-Vat. (Premise.)

The operative idea behind Premise I is that of a handless Brain-in-a-Vat, a seemingly imaginable case in which a human's brain is removed from their body, including their hands and their sense organs, and kept alive in a vat. If I were in that situation, then I would not have hands. It seems to follow that if I have hands, then I am not in that situation. The argument continues as follows, replacing ‘p’ and ‘q’ in our skeletal argument form with appropriate sentences:

1. II. If Guy knows that Guy has hands, and Guy knows that if Guy has hands, then Guy is not a handless Brain-in-a-Vat, and if Guy competently deduces that Guy is not a handless Brain-in-a-Vat on the basis of what Guy knows, then Guy can know that Guy is not a handless Brain-in-a-Vat. (Closure.)

2. III. If Guy knows that Guy has hands, and if Guy competently deduces that Guy is not a handless Brain-in-a-Vat on the basis of what he knows, then Guy can know that Guy is not a handless Brain-in-a-Vat. (From I, II.)

3. IV. It's not the case that Guy can know that Guy is not a handless Brain-in-a-Vat, even on the basis of competent deduction from what Guy knows. (Premise.)

The operative idea behind Premise IV is an expansion of the seemingly conceivable case of the handless Brain-in-a-Vat, according to which the brain is not only kept alive, but is also hooked up to a super-computer in a way that gives rise to a series of experiences that the brain would be unable to tell apart from the ordinary experiences its one-time possessor would have had if their brain had not been preserved in the vat. If I were in that situation, then it seems plausible that I would have a series of experiences much like the experiences I am in fact having. Certainly, it seems that I would not be able to tell that the experiences I was then having were not the ordinary experiences I am now having. In that case, it would seem to me that I had hands even though I wouldn't have hands. Further, given that my circumstances would seem much the same to me if I were a handless Brain-in-a-Vat, it is unclear how I can know that I am not one. I seem to raise my hand, and to scrutinize it, but things might seem that way to me even if I had no hand to raise, and no sense organs with which to scrutinize, if I were induced to have sufficiently similar experiences while trapped in a vat. Hence, it seems plausible that I have no way of knowing that I am not a handless Brain-in-a-Vat. On the basis of premises I–IV, we can deduce the conclusion:

1. V. It's not the case that Guy knows that Guy has hands. (From III, IV, by Modus Tollens.)

The premises of this argument are apt to seem initially plausible. And the conclusion of the argument is that, despite what had seemed to be its obvious correctness, the claim that I know that I have hands is incorrect. How can we defend what seems obvious here, that I know that I have hands?

One response would be to revisit the two principles that figure in the argument, Modus Tollens and Closure. For those two principles seem essential to the argument, so that if we were able to give them up, we might thereby avoid the conclusion that I don't know that I have hands. However, Modus Tollens seems to be an obviously correct principle of logic. And Closure also seems obviously correct. Furthermore, rejecting Closure would mean rejecting some of what we take ourselves to know on the basis of competent deduction from other things we know. Much of what we take ourselves to know seems to depend in that way on competent deduction from other things we know. Rejecting Closure is therefore liable to have consequences for what we can know, and for what we take it to be obvious that we can know, which are more or less as damaging as the claim that I can't know that I have hands.

A different response would be to revisit the two operative premises, I – that I know that if I have hands, then I am not a handless Brain-in-a-Vat – and IV – that it's not the case that I can know that I am not a handless Brain-in-a-Vat, even on the basis of competent deduction from what I know. However, premise I is apt to seem obviously correct, given that having hands seems obviously to exclude being handless. And it is not at all clear how we can respond to the sorts of considerations that make premise IV seem plausible. So, it remains unclear how we can respond.

3. Enter Moore. Although Moore doesn't consider precisely the argument that we've constructed on behalf of the sceptical philosopher, we can reconstruct his likely reaction from what he says about a closely related argument. Rather than defending my knowledge that I have hands, Moore seeks to defend his knowledge that the pencil he is holding exists. And he is defending that piece of knowledge in the face of an argument of Hume's, resting on two main principles, to the conclusion that he couldn't have that knowledge. (It won't matter for our purposes what those principles are. For our purposes, they might be either of the principles that figured in our argument, or any of the further considerations we offered in support of premises I and IV.) He writes:

Moore takes it upon himself to attempt to prove that at least one of the principles on which Hume's argument depends is not true. Similarly, in the face of our argument, he would take it upon himself to prove that at least one of the principles or premises on which it depends is not true. In what sort of way? Moore continues:

Moore's thought here is really quite simple. If a set of premises and principles lead to a conclusion that is absurd – for example, if they lead to a contradiction – then we would ordinarily take their doing so to indicate that at least one of the premises and principles leading to that conclusion must be false. Similarly, Moore claims here that Hume's argument leads to an absurd conclusion, and so that at least one of the premises and principles on which that conclusion depends must be rejected. What is the absurd conclusion to which those premises and principles lead? Moore claims that it is absurd to conclude that he does not know that the pencil he is holding exists. And he claims that that is absurd because it conflicts with what is obviously correct: that he knows that the pencil he is holding exists. Likewise, with respect to our argument, an advocate of Moore's strategy would claim that the conclusion that I do not know that I have hands is absurd. And it is absurd because it conflicts with what is obviously correct: that I know that I have hands. In that case, and following Moore's lead, we would take it that we had discovered that it's not the case that V. Since we had accepted that if I–IV were correct, then V would also be correct, we can reason by Modus Tollens that, since V is incorrect, at least one of premises I–IV must be incorrect. And that is so whether or not we can either identify the culprit or explain why it is incorrect.

4. Is that cheating? It is apt to seem as though it is. We had hoped to be shown how to defend the claim that I know that I have hands against sceptical attack. And that hope seems to embed the further hope that we would be shown precisely where the sceptical argument goes wrong. On the face of it, Moore's strategy doesn't satisfy those hopes. Put another way, in the face of the sceptical argument, it seems reasonable to expect to be given reasons for nonetheless accepting that I know that I have hands. But Moore's strategy seems to involve simply reasserting that I do know that I have hands without presenting any reasons for favouring that claim over the sceptic's counter-claim. The question at issue concerns whether, as I claim, I know that I have hands or whether, as the sceptic claims, I don't know that I have hands. If the most that Moore's strategy can deliver is a simple reassertion of my claim, and thus a simple denial of the sceptic's claim, then it seems to beg the question against the sceptic. As Moore puts the worry:

In the face of that worry, it is apt to seem that the only reasonable response would be either to argue directly in support of the claim that I know that I have hands or to argue directly against one or more of the premises and principles on which the sceptic's conclusion depends. And yet, as we have seen, Moore thinks that no better argument is available than the one we've characterized: ‘I think that this argument really is as strong and good a one as any that could be used.’ Why does Moore think that no superior argument is available here?

Central to Moore's reasons for thinking that no superior argument is available is the thought that proofs, and arguments more generally, must come to an end somewhere. In order to have an argument at all, one needs at least principles of logic and, typically, also one or more premises. Insofar as an argument supports one in coming to know its conclusion, it plausibly does so only because one knows any principles and premises on which that conclusion depends. Thus, since any argument or proof will depend on principles and premises, there must be principles and premises that one knows without having derived that knowledge from argument or proof.

Here is Moore expressing one version of that thought:

Moore's key move here is his last one. The exploitation of arguments or proofs in order to come to decide the truth or falsity of some claim depends on the truth of the general claim that arguments or proofs are means of deciding the truth or falsity of claims. It follows that we cannot use arguments or proofs to enhance our certainty that arguments or proofs are a means of deciding the truth or falsity of claims. For our exploitation of any such argument or proof would depend on that certainty. If someone really doubted that arguments or proofs can be used to establish truths, then it would not be possible to overcome their doubt by presenting them with arguments or proofs. That key move is at the service of his central thought: not everything that we know can be supported by argument or proof.

To return to Moore's discussion of his pencil, he seeks to make use of the idea that if proof is to be possible, then not everything that we know can be proved, in the following passage:

Moore's first thought here derives from the fact that if anything is known mediately – that is, on the basis of deduction from other things that one knows – then we must know the things from which it is deduced. Those things, in turn, must be either known mediately or known immediately – that is, known without having been deduced from other knowledge. Moore's first thought is that any such chain of mediated knowledge must eventually terminate in knowledge that is not mediated, and so in immediate knowledge. Thus, Moore thinks that there must be things that are not known mediately but only immediately.

Moore's second thought is that because there must be things that are known only immediately, it cannot be an objection to someone's claim to know something to point simply to the fact that they cannot provide an argument for that which they claim to know. Thus, it cannot be an objection to the claim that I know that I have hands (or that I know that here is a hand) simply to point out that I haven't provided an argument for that claim. For perhaps that claim is something that I know only immediately. Since there must be such claims – that is, claims that are known only immediately – it can't be ruled out without further discussion that the claim that I know that I have hands is among them. (We noted earlier that I might have presented an argument for the claim that I have hands based on the premises that here is one hand and that here is another. If that was the only way for me to know that I have hands, then the present issue would best be seen as focused on my knowledge of the premises about individual hands rather than the conclusion that I have hands. The proposal would be that the claim that here is one hand might be among the claims that are known immediately.)

If Moore is right so far, then we have a first response to the basic concern about the claim that I know that I have hands. The basic concern was that we would be entitled to make that claim only if we did so on the basis of an argument. The response is that there must be some claims that we are entitled to make because we know them only immediately. The mere fact that we make a claim without offering supporting argument is no objection, since our lacking an argument for the claim is consistent with our nonetheless knowing it to be true.

That first response to the basic concern is fine as far as it goes. However, we might think that it does not go very far. The first response appeals to the fact that there must be things that we know immediately. On that basis, it proposes that the claim that I know that I have hands might be among the things that we know immediately. However, someone might consistently accept that there must be things that we know immediately while rejecting the proposal that the claim that I know that I have hands is among them. It is therefore open to the sceptical philosopher to attempt just that. In doing so, they would claim, first, that the claim that I know that I have hands can be known only mediately – that is, on the basis of an argument from other things we know. And they would claim, second, that because the claim can be known only mediately, its advocates must support it with an argument.

At that stage of discussion, Moore has a natural response. Just as the sceptical philosopher challenged Moore to defend the claim that I know that I have hands, Moore can challenge the sceptical philosopher to defend the claim that such argument is required. For in requiring Moore to defend the claim that I know that I have hands, the sceptical philosopher has committed themselves to the claim that Moore's claim can be known only mediately. The sceptical philosopher must hold, then, that they know that Moore's claim can be known only mediately. And they must therefore hold that they know that about Moore's claim either mediately or immediately. And now, if they claim to know it immediately, then they will have no grounds on which to complain if Moore makes the counter-claim that he has immediate knowledge that it is false. Alternatively, if they claim to know it only mediately, and present an argument in its support, then Moore will be liable to exploit his main strategy again. In doing so he would argue that since the premises of the sceptical philosopher's argument are incompatible with something Moore knows – namely, that the claim that I know that I have hands is known immediately – at least one of the sceptical philosopher's premises must be rejected. There is more to say about the way the dispute is liable to develop from that stage, but it is likely that that development will lead, at worst, to a stand-off between Moore and the sceptical philosopher. If that is right, then it is far from clear that Moore can fairly be accused of begging the question in a way in which the sceptical philosopher cannot.

5. The outcome to this point is that both Moore and the sceptical philosopher are dependent, ultimately, on a range of principles and premises with respect to which they must claim immediate knowledge. If that were the end of the matter, then, as was noted at the end of the last section, we would face a stand-off. Can Moore, or the sceptical philosopher, advance the issue beyond that outcome?

A way forward for Moore is provided by a comparison between the claims that he takes to be items of immediate knowledge and the claims that the sceptical philosopher must take to be items of immediate knowledge.

Examples of claims that Moore takes to be items of immediate knowledge include the claims that I have hands, that I know that I have hands, and that Moore knows that the pencil he is holding exists. By contrast, examples of claims that the sceptical philosopher must take to be items of immediate knowledge include the various elements of the sceptical argument, including whatever claims ultimately underlie their arguments for premises I and IV. If that is right, then Moore can reasonably claim that we find it perfectly intelligible how the examples on his list can be known immediately. Before we consider the sceptical philosopher's arguments, we find it entirely unmysterious that I can know immediately that I have hands. And we are perfectly willing to accept that I can know that I have hands without supporting argument. We might be willing to consider the possibility that further explanation could be offered of these feats of immediate knowing. But we would not ordinarily suspend judgement on such claims to know until a satisfactory explanation had been provided. Put simply, we ordinarily take ourselves to have the abilities required to know that we have hands, and that we are often in a position to exercise those abilities successfully.

By contrast, the items of immediate knowledge claimed by the sceptical philosopher are apt to seem esoteric, and it is not immediately intelligible to us how they could have come into the sceptical philosopher's possession. It is not obvious, for example, how the sceptical philosopher is supposed to know that I cannot know that I am not a handless Brain-in-a-Vat. Or, if the sceptical philosopher allows that that claim is known only mediately, how they are supposed to know the various premises from which that claim can be deduced. Put simply, it is not obvious to us what sorts of abilities are involved in coming to know the things that the sceptical philosopher claims to know, or whether anyone has abilities of the required sort. If that is right, then since there is reason to favour what we find intelligible over what we don't, there is reason to favour Moore's claims over those made by the sceptical philosopher.

Minimally, the difference in immediate intelligibility between Moore's claims to knowledge and the sceptical philosopher's claims imposes an obligation on the sceptical philosopher to render their claims intelligible. To discharge that obligation, the sceptical philosopher must explain how their claims can be items of knowledge. And if they cannot discharge that obligation, then a natural reaction will be that it is because their claims, unlike Moore's, are not items of knowledge at all.

If that is right, then it places the sceptical philosopher in the following bind. The claims to knowledge that they seek to defend are not immediately intelligible to us. If they are intelligible at all, then, it seems that they must be mediately intelligible. That means that they must be derivable, ultimately, from claims that are themselves immediately intelligible. However, it seems plausible that there are only two ways for such claims to derive support from other more immediately intelligible pieces of knowledge.

The first way is by the sceptical philosopher's claims being deduced from the other pieces of knowledge. But seeking support for the sceptical philosopher's claims via that route is liable to push one towards ever more general, and more recherché, claims to knowledge. Consider, for example, a deductive argument that Moore offers to the sceptical philosopher and that might be used to provide deductive support for premise IV, the claim that I cannot know that I am not a handless Brain-in-a-Vat. (Moore is discussing a different premise, that I cannot know that I am not dreaming, but the difference won't matter for present purposes. See Moore Reference Moore1959: 244–5.)

1. i. It is logically possible for my Brain-in-a-Vat counterpart to have some sensory experiences that are exactly like the sensory experiences I am in fact having.

2. ii. If it is logically possible for my Brain-in-a-Vat counterpart to have some sensory experiences that are exactly like the experiences I am in fact having, then it is logically possible for all of my Brain-in-a-Vat counterpart's sensory experiences to be exactly like some of my sensory experiences.

3. iii. If it is logically possible for all of my Brain-in-a-Vat counterpart's experiences to be exactly like some of my sensory experiences, then it is possible for all of my sensory experiences to be like some of my Brain-in-a-Vat counterpart's experiences.

4. iv. If it is logically possible for all of my sensory experiences to be exactly like some of my Brain-in-a-Vat counterpart's sensory experiences, and if my sensory experiences were my only experiences, then I could not know that I was not a Brain-in-a-Vat.

5. v. My sensory experiences are my only experiences.

6. vi. Therefore, I cannot know that I am not a Brain-in-a-Vat.

The argument presents a set of premises from which the conclusion vi can be deduced. Although the argument is deductively secure, each of its premises might reasonably be challenged. However, Moore's strategy is not to argue that any particular premise of this argument is false. Rather, as we have seen, it is to argue that, given our earlier argument I–IV, the conclusion of the argument conflicts with something that we know – namely, that I know that I have hands. At this stage of the dispute, however, the challenge facing the sceptical philosopher is not just to defend the truth of premises i–v. Rather, it is to defend the further claim that they know each of premises i–v. For the claim that the sceptical philosopher knows any one of the premises isn't apt to strike us as immediately intelligible.

For one example, it is not obvious to us how the sceptical philosopher is supposed to know that my sensory experiences could be replicated perfectly by a Brain-in-a-Vat. (How do they know that my experiences aren't dependent on my relations to my body or my wider environment in a way that would preclude their replication by a Brain-in-a-Vat? What sorts of abilities would be involved in knowing that?) For another example, it is not obvious how the sceptical philosopher is supposed to know that my sensory experiences are my only experiences. (How do they know that my memory isn't an additional source of experiences? What sorts of abilities would be involved in knowing that?) And similar worries might reasonably be raised about each of the other premises.

If it isn't immediately intelligible that the sceptical philosopher knows any one of the premises, then the sceptical philosopher's claim to know the conclusion cannot acquire mediate intelligibility by inheriting it from their knowledge of those premises. In that case, the sceptical philosopher's claims to know the required bases for deduction would be no more intelligible than their initial claim to know. That way of deriving support for the sceptical philosopher's claims would not, therefore, serve to render those claims to know as intelligible as Moore's.

The second way of deriving support for the sceptical philosopher's claims would be via abduction. Here, the idea would be that the sceptical philosopher's claims would be supported by their capacity to explain other facts. It was that sort of route that we took in seeking to make intelligible our knowledge of Closure. We sought to derive support for that principle from its capacity to explain our possession of ordinary pieces of knowledge. More generally, this appears to be Moore's favoured route to knowledge of the sorts of recherché claims made by philosophers when they attempt to go beyond what he takes to be obvious to common sense. If taking that sort of route is to render the sceptical philosopher's claims to knowledge more intelligible, then the facts that they seek to explain must themselves be intelligible. But the only clearly intelligible facts in the vicinity seem to be of broadly the same sorts as those to which Moore appeals: for example, the fact that I know that I have hands. And the sceptical philosopher cannot explain those facts on pain of accepting that they are facts, and so accepting that I can know that I have hands.

If the only ways to render the sceptical philosopher's claims to knowledge intelligible are the deductive way and the abductive way, then it is far from clear that those claims can be made intelligible. And even if they can be made intelligible, it is not obvious that this can be achieved without relying on the intelligible truth of the ordinary claims to knowledge that the sceptical philosopher had hoped to throw into doubt. It is therefore unclear, in light of the difficulties that Moore raises, that the sceptical philosopher has raised a significant challenge to the claim that I know that I have hands.Footnote ¹