Notes on Moore’s Proof of an External World

Despite what I said in my last post about being enticed into the world of sense, reference, descriptions, rigid designators and necessary a posteriori truths, I’m beginning with scepticism after all. This post is my initial response to G.E. Moore’s essay, Proof of an External World, from 1939. I like his common-sense approach, but no doubt my thoughts will develop after I read his Defence of Common Sense and Wittgenstein’s responses in On Certainty. I should also add that I am looking at how Moore’s argument works as a response to the sceptical position, though he was actually responding partly to the idealism of Bradley and McTaggart.

Before giving the proof we’re all waiting for, he spends a long time establishing exactly what he means by an external thing, and I don’t quite see the importance of this. He is taking his cue from Kant, and it seems that he is trying to clear up some of Kant’s ambiguities. In the end, I understand his “external thing” to be just something existing independently of any mind.

Now for the proof. He says (I’m paraphrasing) “here is a hand,” holding up a hand, and then “here is another hand,” holding up the other hand, and “therefore two external objects exist.” This, he claims, proves the existence of an external world.

Furthermore, it is a rigorous proof. The standards of rigour are that the premise is different from the conclusion; that he knows the premise rather than simply believing it; and that the conclusion follows from the premise. Moore claims that these standards are satisfied.

At once we notice that he is assuming the falsity of the sceptical position, which is that we cannot know that there really are two hands in front of us. On the other hand, the sceptical position might be restated as saying that we cannot prove that we can know that external objects exist, and Moore is not denying this.

[UPDATE: this is actually just the mild sceptical position. See my later post on this topic.]

How Do I Know I Have Two Hands? I Just Do!

His proof that the external world exists rests partly on the assumption that he does know that “here is a hand”. Perhaps he can make this assumption because there is no reason for thinking otherwise, or because there is no philosophical argument that could be more certain to him than that.

Thus the premise “here is a hand, and here is another hand”, though itself unproven, yet leads conclusively to: “therefore there exists an external world”.

That the premise itself is not rigorously proved is conceded to the sceptics, but this is neither here nor there: such a proof will not be forthcoming and we have no more reason for believing in the sceptical hypothesis – that we are being deceived by a trickster demon or that we are dreaming – than we are in taking our knowledge for what it appears to be.

So he is not directly addressing scepticism on its own terms. Instead, he is trying to show that scepticism is unwarranted. We cannot prove that we can know the world exists, but we can in fact prove that it exists. But doesn’t this mean that when Moore says that his proof is rigorous he is saying, not exactly that the proof is watertight, but that it is as rigorous as one can expect?

I’m sure everyone feels that Moore is right, but from a sceptical standpoint he is hardly convincing. His argument doesn’t seem to bear upon the sceptical position except as an appeal to common sense. And isn’t there some kind of contradiciton hiding in there somewhere? Early on in his explanation of the proof, in demonstrating its rigour, he says:

“I certainly did at the moment know that which I expressed…”

But later he admits that, although he has evidence that he is not dreaming, “that is a very different thing from being able to prove it.”

Is there a contradiction here? No: Moore says that we can know without being able to prove that this knowledge is possible. I think this is the gist.

Begging the Question

No contradiction, but surely a fallacy. In assuming that he knows that “here is a hand,” he is thereby assuming the existence of an external world, because to know something is to believe it (for appropriate reasons) and for it to be true. This means that the conclusion is assumed in the premise, so the argument begs the question.

It is his ability to know in the first place that is questioned by the sceptic, so Moore cannot prove anything beginning with “I know”. He may well be certain, but certainty does not always entail knowledge.

But I still want to side with Moore, because the deeper point he is making is that we do know things, and we know that we know them, but we do not know exactly how we know them, so we can never prove that we do. But then, nearly everyone feels this way. How are we any further forward in resisting scepticism after giving this proof of an external world? Isn’t he just stating the obvious, and at the same time side-stepping the real problem?

The Moore Shift

In a way he is. Moore may be saying that in the absence of proof for or against the sceptical hypothesis, it is better to rely on our common sense intuition that our knowledge is as it appears. This is the best explanation of our experiences.

This way of presenting things has been called the “Moore shift”, which is the replacement of scepticism’s modus ponens argument with a new modus tollens argument:

From the sceptical modus ponens…

(P1) If I cannot tell the difference between waking and dreaming, then I cannot be sure that there are two hands in front of me

(P2) I cannot tell the difference between waking and dreaming

∴ I cannot be sure that I have two hands in front of me

...to Moore’s modus tollens…

(P1) If I cannot tell the difference between waking and dreaming, then I cannot be sure that there are two hands in front of me

(P2) I am sure that I have two hands in front of me

∴ I can tell the difference between waking and dreaming

And for the hell of it, and for my own clarification, here they are in symbols. First the sceptic’s modus ponens:

(P1) ¬P → ¬Q

(P2) ¬P

∴ ¬Q

Now Moore’s modus tollens:

(P1) ¬P → ¬Q

(P2) Q

∴ P

where:

P = I can tell the difference between waking and dreaming

Q = I am sure that I have two hands in front of me

In Moore’s reformulation, (P1) is retained, but (P2) is now denying the consequent of the implication (P1). Both arguments are valid, but they cannot both be sound. Which one is it? It looks like it’s back to square one: we cannot prove which (P2) is true.

But, Moore is saying that, although he cannot prove the belief expressed in Q, it is more compelling than ¬P. It is what has come to be known as a “Moorean fact”: I can be sure that I have two hands in front of me, or just I have two hands in front of me. This might be seen as appealing to a kind of inference to the best explanation, and the reasoning of the second argument is offered up as the practical one, and the one that we in fact use; and to genuinely doubt it is not a trivial or easy move to make.

Don’t Think – Look!

All things considered, we should remember that he presented his proof in a lecture full of students. In holding up his hand and saying “here is a hand”, he demonstrated the extremism of the claim that maybe he did not know it after all. Who among the audience would have dared to put up their hand and honestly question his knowledge?

Thus, maybe we ought to think of Moore’s proof as a performance rather than as a deductive argument.

See my later post on the dream argument for a more about this.

Moore, G.E., “Proof of an External World”, Proceedings of the British Academy, 25 (1939) 273-300