–Arts and letters for the modern age–

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–Arts and Letters for the Modern Age–

Moore’s Proof

by | Dec 20, 2023

If you were to pinch the nearest analytically trained philosopher and ask him for the worst, most obviously fallacious argument in his tradition, he might very well tell you that it is the so-called “proof” for the existence of the external world that G.E. Moore gives in his 1939 paper, “Proof of an External World,” originally delivered to the British Academy. And if you tried to push back – and if your interlocutor was sharp – he might refer you to two papers by Crispin Wright – his 1985 “Facts and Certainty” (also delivered to the British Academy, interestingly enough) and 2002 “Anti-Sceptics Simple and Subtle” – which really put the boot in, as far as Moore is concerned. 

This is not to say, of course, that there are no people in the business who think Moore was on to something. I’m one of those who do, and if I find myself alone at a wine-and-cheese, surrounded by Moore-haters and feeling a bit vulnerable, I can always point out that Wittgenstein has my back, having thought Moore’s thesis so interesting that he was motivated to write an entire book – On Certainty – on the arguments and theses presented in “Proof of an External World” and “In Defence of Common Sense,” which, according to Elizabeth Anscombe, Wittgenstein thought was Moore’s finest work.


Of course, Moore doesn’t always help himself. He begins “Proof of an External World” by referencing Kant’s remarks in the Prolegomena to any Future Metaphysics (1783) that it is a “scandal” that no proof of the external world has been given. What Kant is referring to, of course, is the skepticism of the Enlightenment and especially the kind articulated in Descartes’ (in)famous “Dreaming Argument.” The trouble is that by evoking Kant in this way, Moore gives the impression that his proof will be relatively straightforward – that it will take on the skeptical challenge head-on, as it were. And it is precisely this impression – and it is a misimpression – that has led so many people to think that Moore’s essay is little more than an embarrassment.

So, what does the proof consist of? This is what Moore gives us, verbatim:

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.”

Now you might immediately think, “Wait a minute. The statement ‘the external world exists’ is entirely absent from this proof, when it should be featured, prominently, as the conclusion,” but if you’ve read the entire article, you know that Moore addresses this point. By showing that the individual member of a class exists, one has thereby demonstrated the existence of the class itself. It does not require a separate proof of its own. In this case, the class in question is the class of things that belong to what we are calling “the external world”; which have, as Hume called it, “continued and distinct existence”; and to which Moore refers as “things to be met with in space.”

If you have proved that two plants exist, or that a plant and a dog exist, or that a dog and a shadow exist, etc. etc., you will ipso facto have proved that there are things to be met with in space: you will not require also to give a separate proof that from the proposition that there are plants it does follow that there are things to be met with in space.

But this on its own is unlikely to make critics any happier. “Wait another minute,” they will likely say. “How does Moore know that he has two hands? Wasn’t the entire point of Descartes’ Dreaming argument to show that we cannot justify beliefs like these? Doesn’t  Moore owe us a refutation of Descartes, before he carries on with his proof?”

The criticism doesn’t stop there. As already mentioned, Crispin Wright, in a number of essays, has absolutely skewered not just Moore’s proof, but any effort like it to demonstrate that the external world exists.  

Consider the following apparently valid argument –

1. Jones has just kicked the ball between the white posts. 

2. Jones has just scored a goal.


3. A game of soccer is taking place.

– as well as this one

1’. Jones has just placed an X on a ballot paper.

2’. Jones has just voted. 


3’. An election is taking place.

A careful examination of both cases reveals a common flaw. The first premise only counts as a reason for thinking the second premise is true, if one already has independent reason to believe that the conclusion is true. After all, it’s only if a game of soccer is taking place that kicking a ball between two posts counts as scoring a goal. And it is only if an election is taking place that putting an ‘x’ on a piece of paper counts as voting. So, one cannot justify the claim that soccer is being played or that an election is taking place, on the grounds of premises like 1 and 2.

Once we realize this, it’s a short step to seeing that Moore’s proof takes exactly the same form – 

1’’. My experience is in all respects as of a hand held up in front of my face 

2’’. Here is a hand 


3’’. There is a material world (since any hand is a material object existing in space)

– and that consequently, the same result follows. One cannot determine that the external world exists on the basis of sensory evidence, because sensory evidence only counts as a reason for thinking there are things “outside us,” if we already assume that there are.


While these sorts of critiques are valuable in their own right – and Wright’s, I think, really does uncover the underlying structure and logic that makes arguments like the Dreaming argument so powerful – they are ultimately misapplied to Moore’s proof. Now, of course, this is easy to say – “I was misunderstood” is the common excuse of many a scoundrel or fool – but in this case, I think it is sustainable. For Moore himself, immediately after delivering his proof, admits that he has not refuted the Dreaming argument and moreover, that he cannot refute it. And it is precisely this that must make us stop and wonder whether what Moore is doing is as straightforward – as head-on – as it seems at first glance. The unfortunate appeal to Kant notwithstanding, I think that the only conclusion one can reach is that Moore does not intend straightforwardly to prove that the external world exists; that in fact, his strategy for dealing with this most global of skepticisms is something much more subtle and indirect. And it is this that Wittgenstein picked up on and explored in far greater detail in On Certainty. In a way, On Certainty can be read as a way of developing the epistemological ideas that one finds in embryonic and often implicit form in “Proof of an External World” and “In Defence of Common Sense.”

The skeptic who doubts whether our belief in the external world is justified does so on the grounds that we might be making a mistake; indeed, that we often do make such mistakes.  Descartes’ appeal to dreaming in making this point is so strong, precisely because dreaming is such a common phenomenon. But it is here that Wittgenstein makes an important observation.  What does the skeptic mean, exactly, when he calls something a “mistake” or says that we are “mistaken”? For example, astronomers might have been wrong about the number of moons orbiting Saturn. Instruments may have failed or images delivered from telescopes and probes may have been misinterpreted. So, when an astronomer says “Saturn has 53 moons,” he might be making a mistake. The number might really be 52 or 55.

But what about a slightly different statement – “There are moons”? The skeptic wants to say that this also is something we can be wrong about; about which we can be mistaken. He may even appeal to the Dreaming argument in order to make that very point. But would we be wrong here in the same way that we might have been with respect to the previous case? Would this be the sort of thing we would even call a “mistake”? Consider the following bits and pieces from On Certainty.

74. Can we say: a mistake doesn’t only have a cause, it also has a ground? I.e., roughly: when someone makes a mistake, this can be fitted into what he knows aright.

257. If someone said to me that he doubted whether he had a body I should take him to be a half-wit. But I shouldn’t know what it would mean to try to convince him that he had one.  And if I had said something, and that had removed his doubt, I should not know how or why.

We only can understand something as a mistake, against a background of things that are not taken as mistaken. It is because I know that Saturn has moons – and that there are such things as moons – that I can make sense of the notion of being mistaken about the number of moons it has. Moreover, if I get the number of Saturn’s moons wrong, I have some idea of how I might go about correcting my mistake, with the hope of getting it right the next time. But none of this is the case with respect to the proposition that there are moons. If the skeptic tries to claim that this is mistaken, there is no backdrop of not-mistaken things concerning moons, against which the idea of its being a mistake makes any sense, and if it was a mistake I wouldn’t have the faintest idea of how to go about correcting it.

Wittgenstein makes the same point with respect to the common practice of calculation.  Certainly, I can make sense of the notion of making a mistake in adding, subtracting, multiplying, dividing, and the like. I can make an error in multiplication that leads me to believe that 6×7 is 48, rather than 42. The notion of a mistake here makes sense, again, because it occurs against a backdrop of correct calculation, and because it’s quite clear how one would go about correcting it – i.e. one would “check one’s work” and do the calculation again. When the skeptic suggests, however, that we might be mistaken about calculation generally – that we might never calculate correctly – the notion of a mistake makes little sense, because it is completely untethered, and what it would mean to correct it has become utterly obscure. How would one check the checking and how many times, in order to be persuaded that checking works? This is why, at one point, Wittgenstein says:

77. Perhaps I shall do a multiplication twice to make sure, or perhaps get someone else to work it over. But shall I work it over again twenty times, or get twenty people to go over it?  And is that some sort of negligence? Would the certainty really be greater for being checked twenty times?

To say that something is mistaken or could be mistaken, then, only makes sense against the backdrop of a whole number of other things that not only are not mistakes but which are fixed – or which, as Wittgenstein puts it, “stand fast.” And without those things, the notion of a mistake or being mistaken or of justification and being justified or unjustified, becomes obscure to the point of incoherence, because it is completely unmoored in any fixed point of reference. Which is why Wittgenstein says:

115. If you tried to doubt everything you would not get as far as doubting anything. The game of doubting itself presupposes certainty.


105. All testing, all confirmation and disconfirmation of a hypothesis takes place already within a system. And this system is not a more or less arbitrary and doubtful point of departure for all our arguments: no, it belongs to the essence of what we call an argument.  [It is] the element in which arguments have their life.

What the skeptic demands is not just proof for a proposition, but proof for all proofs, and it is here that he goes off the rails; that he ceases to play the game that the rest of us are playing, which is why, rather than being wrong, his critique is beside the point. I can use a proof to justify an arithmetic proposition, and if I get it wrong, I can check my proof and try again. But all of this only works, because it is done against a backdrop of beliefs that stand fast; that are beyond doubt; that are taken as certain; most important among them, the belief that arithmetic proofs, in general, work. And that this is precisely what Moore is getting at is revealed at the end of the essay, where he says:

[A] 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, I think, is a definite mistake.

I wholeheartedly agree, which is why I have little use – or time – for skeptics. Or at least, those who really mean it.