G. E. Moore It seems to me that, so far from its being true, as Kant declares to be his opinion, that there is only one possible proof of the existence of things out- side of us, namely the one which he has given, I can now give a large number of different proofs, each of which is a perfectly rigorous proof, and that at many other times I have been in a position to give many others. I can prove now, for instance, that two human hands exist. How? By holding up my two hands, and saying, as I make a certain gesture with the right hand, ‘Here is one hand’, and adding, as I make a certain gesture with the left, ‘and here is another’. And if, by doing this, I have proved ipso facto the existence of external things, you will all see that I can also do it now in numbers of other ways: there is no need to multiply examples. But did I prove just now that two human hands were then in existence? I do want to insist that I did; that the proof which I gave was a perfectly rigorous one; and that it is perhaps impossible to give a better or more rigorous proof of anything whatever. Of course, it would not have been a proof unless three conditions were satisfied; namely (1) unless the premiss which I adduced as proof of the conclusion was different from the conclusion I adduced it to prove; (2) unless the premiss which I adduced was something which I knew to be the case, and not merely something which I believed but which was by no means certain, or something which, though in fact true, I did not know to be so; and (3) unless the conclu- sion did really follow from the premiss. But all From G. E. Moore, Philosophical Papers (New York: Collier Books, 1962), pp. 144-8. these three conditions were in fact satisfied by my proof. (1) The premiss which I adduced in proof was quite certainly different from the conclusion, for the conclusion was merely “Two human hands exist at this moment’; but the premiss was some- thing far more specific than this — something which I expressed by showing you my hands, making certain gestures, and saying the words ‘Here is one hand, and here is another’. It is quite obvious that the two were different, because it is quite obvious that the conclusion might have been true, even if the premiss had been false. In asserting the premiss I was asserting much more than I was asserting in asserting the conclusion. (2) I certainly did at the moment know that which I expressed by the combination of certain gestures with saying the words ‘Here is one hand and here is another’. I knew that there was one hand in the place indicated by combining a certain gesture with my first utterance of ‘here’ and that there was another in the different place indicated by combining a certain gesture with my second utter- ance of ‘here’. How absurd it would be to suggest that I did not know it, but only believed it, and that perhaps it was not the case! You might as well suggest that I do not know that I am now standing up and talking — that perhaps after all ’'m not, and that it’s not quite certain that I am! And finally (3) it is quite certain that the conclusion did follow from the premiss. This is as certain as it is that if there is one hand here and another here now, then it follows that there are two hands in existence now. My proof, then, of the existence of things out- side of us did satisfy three of the conditions neces- sary for a rigorous proof. Are there any otherconditions necessary for a rigorous proof, such that perhaps it did not satisfy one of them? Perhaps there may be; I do not know; but I do want to emphasise that, so far as I can see, we all of us do constantly take proofs of this sort as absolutely conclusive proofs of certain conclusions — as finally settling certain questions, as to which we were previously in doubt. Suppose, for instance, it were a question whether there were as many as three misprints on a certain page in a certain book. ‘A says there are, B is inclined to doubt it. How could A prove that he is right? Surely he could prove it by taking the book, turning to the page, and pointing to three separate places on it, saying ‘There’s one misprint here, another here, and another here’: surely that is a method by which it might be proved! Of course, A would not have proved, by doing this, that there were at least three misprints on the page in question, unless it was certain that there was a misprint in each of the places to which he pointed. But to say that he might prove it in this way, is to say that it might be certain that there was. And if such a thing as that could ever be certain, then assuredly it was certain just now that there was one hand in one of the two places I indicated and another in the other. I did, then, just now, give a proof that there were then external objects; and obviously, if I did, I could then have given many other proofs of the same sort that there were external objects then, and could now give many proofs of the same sort that there are external objects now. But, if what I am asked to do is to prove that external objects have existed in the past, then I can give many different proofs of this also, but proofs which are in important respects of a different sort from those just given. And I want to emphasise that, when Kant says it is a scandal not to be able to give a proof of the existence of external objects, a proof of their existence in the past would cer- tainly help to remove the scandal of which he is speaking. He says that, if it occurs to anyone to question their existence, we ought to be able to confront him with a satisfactory proof. But by a person who questions their existence, he certainly means not merely a person who questions whether any exist at the moment of speaking, but a person who questions whether any have ever existed; and a proof that some have existed in the past would certainly therefore be relevant to part of what such a person is questioning. How then can I prove that there have been external objects in the past? Here is one proof. I can say: ‘I held up two hands above this desk not very long ago; therefore two hands existed not very long ago; therefore at least two external objects have existed at some time in the past, QED’. This is a perfectly good proof, provided I know what is asserted in the premiss. But I do know that I held up two hands above this desk not very long ago. As a matter of fact, in this case you all know it too. There’s no doubt what- ever that I did. Therefore I have given a perfectly conclusive proof that external objects have existed in the past; and you will all see at once that, if this is a conclusive proof, I could have given many others of the same sort, and could now give many others. But it is also quite obvious that this sort of proof differs in important respects from the sort of proof I gave just now that there were two hands existing then. Thaye, then, given two conclusive proofs of the existence of external objects. The first was a proof that two human hands existed at the time when I gave the proof; the second was a proof that two human hands had existed at a time previous to that at which I gave the proof. These proofs were of a different sort in important respects. And I pointed out that I could have given, then, many other conclusive proofs of both sorts. It is also obvious that I could give many others of both sorts now. So that, if these are the sort of proof that is wanted, nothing is easier than to prove the existence of external objects. But now I am perfectly well aware that, in spite of all that I have said, many philosophers will still feel that I have not given any satisfactory proof of the point in question. And I want briefly, in con- clusion, to say something as to why this dissatis- faction with my proofs should be felt. One reason why, is, I think, this. Some people understand ‘proof of an external world’ as includ- ing a proof of things which I haven’t attempted to prove and haven’t proved. It is not quite easy to say what it is that they want proved — what it is that is such that unless they got a proof of it, they would not say that they had a proof of the exist- ence of external things; but I can make an approach to explaining what they want by saying that if I had proved the propositions which I used as premisses in my two proofs, then they would perhaps admit that I had proved the existence of external things, but, in the absence of such a proof (which, of course, I have neither given nor attempted to give), they will say that I have not given what they mean by a proof of the existence of (BEYG. E. Moore external things. In other words, they want a proof of what I assert now when I hold up my hands and say ‘Here’s one hand and here’s another’; and, in the other case, they want a proof of what I assert now when I say ‘I did hold up two hands above this desk just now’. Of course, what they really want is, not merely a proof of these two propositions, but something like a general statement as to how any propositions of this sort may be proved. This, of course, I haven’t given; and I do not believe it can be given: if this is what is meant by proof of the existence of external things, I do not believe that any proof of the existence of external things is possible. Of course, in some cases what might be called a proof of propositions which seem like these can be got. If one of you suspected that one of my hands was artificial he might be said to get a proof of my proposition ‘Here’s one hand, and here’s another’, by coming up and examining the suspected hand close up, perhaps touching and pressing it, and so establishing that it really was a human hand. But I do not believe that any proof is possible in nearly all cases. How am I to prove now that ‘Here’s one hand, and here’s another’? I do not believe I can do it. In order to do it, I should need to prove for one thing, as Descartes pointed out, that I am not now dreaming. But how can I prove that I am not? I have, no doubt, conclusive reasons for asserting that I am not now dreaming; I have conclusive evidence that I am awake: but that isa very different thing from being able to prove it. I could not tell you what all my evidence is; and I should require to do this at least, in order to give you a proof. But another reason why some people would feel dissatisfied with my proofs is, I think, not merely that they want a proof of something which I haven’t proved, but that they think that, if I cannot give such extra proofs, then the proofs that I have given are not conclusive proofs at all. And this, T think, is a definite mistake. They would say: ‘If you cannot prove your premiss that here is one hand and here is another, then you do not know it. But you yourself have admitted that, if you did not know it, then your proof was not conclusive. Therefore your proof was not, as you say it was, a conclusive proof.’ This view that, if I cannot prove such things as these, I do not know them, is, I think, the view that Kant was expressing in the sentence which I quoted at the beginning of this lecture, when he implies that so long as we have no proof of the existence of external things, their existence must be accepted merely on faith. He means to say, I think, that if I cannot prove that, there is a hand here, I must accept it merely as a matter of faith — I cannot know it. Such a view, though it has been very common among philoso- phers, can, I think, be shown to be wrong ~ though shown only by the use of premisses which are not known to be true, unless we do know of the exist- ence of external things. I can know things, which I cannot prove; and among things which I certainly did know, even if (as I think) I could not prove them, were the premisses of my two proofs. I should say, therefore, that those, if any, who are dissatisfied with these proofs merely on the ground that I did not know their premisses, have no good reason for their dissatisfaction.