The first philosophical thought most people have goes something like this: ‘Maybe what I’m seeing right now isn’t real. Maybe this world of trees and buildings and cars doesn’t really exist. Maybe I’m dreaming it all. Maybe I’m in the Matrix.’

It’s a thought that’s concerned philosophers from the very beginning. Way back in the 4th century BCE, the Chinese philosopher Zhuangzhi was worried that he might really be a butterfly:

“Once, Zhuangzhi dreamed he was a butterfly, a butterfly flitting and fluttering about, happy with himself and doing as he pleased. He didn't know that he was Zhuangzhi. Suddenly he woke up and there he was, solid and unmistakable Zhuangzhi. But he didn't know if he was Zhuangzhi who had dreamt he was a butterfly, or a butterfly dreaming that he was Zhuangzhi.”
– Zhuangzhi, Zhuangzhi

Two thousand years later, the French philosopher René Descartes had similar worries. He was agonising over the possibility that he was being tricked by an evil demon:

“I shall then suppose that… some evil demon… has employed his whole energies in deceiving me; I shall consider that the heavens, the earth, colours, figures, sound, and all other external things are nothing but the illusions and dreams of which this demon has availed himself in order to lay traps for my credulity; I shall consider myself as having no hands, no eyes, no flesh, no blood, nor any senses, yet falsely believing myself to possess all these things.”
– Descartes, Meditations on First Philosophy

In 1981, the American philosopher Hilary Putnam described a similar concern. He thought we might all be brains-in-vats:

“Imagine that a human being (you can imagine this to be yourself) has been subjected to an operation by an evil scientist. The person’s brain (your brain) has been removed from the body and placed in a vat of nutrients which keeps the brain alive. The nerve endings have been connected to a super-scientific computer which causes the person whose brain it is to have the illusion that everything is perfectly normal. There seem to be people, objects, the sky, etc; but really all the person (you) is experiencing is the result of electronic impulses travelling from the computer to the nerve endings.”
– Putnam, 'Brains in a vat'

The idea behind all three of these worries is the same. They’re all expressions of external world scepticism. They cast doubt on whether the external world – everything outside of us – is real.

The disturbing part is that there seems to be no way of ruling these sceptical possibilities out. How, for instance, can you be sure that you’re not a brain-in-a-vat? Nothing you experience can be evidence against the possibility, since all of your experiences could be caused by the vat. It seems like you can’t know that you’re not a brain-in-a-vat, which means you can’t know that the external world is real. This means you can’t know all kinds of things which seem super obvious. You can’t know, for instance, that you have hands.

A lot of philosophers find this conclusion very embarrassing. What’s the point of seeking knowledge if we can’t even know the most obvious stuff? Immanuel Kant was so angry that he called it a scandal:

“It still remains a scandal to philosophy… that the existence of things outside of us must be accepted merely on faith, and that, if anyone thinks good to doubt their existence, we are unable to counter his doubts by any satisfactory proof.” 
– Kant, Critique of Pure Reason

Proof is what we need. The problem is, many philosophers think providing such proof is impossible. People had been trying for thousands of years without much success. Even Descartes couldn’t do it! The guy who is widely regarded as one of the greatest philosophers and mathematicians of all time couldn’t do it. So you can imagine the raised eyebrows when a Cambridge professor called G.E. Moore rocked up to the British Academy in 1939 to deliver a lecture called ‘Proof of an External World’.

Imagine him up at the podium now, lecturing to some of the most respected academics in Britain. It’s been all preliminaries up until now. We’re just about to reach the climax of the lecture, the long-awaited proof:

“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.”
– Moore, 'Proof of an External World'

Don’t let the sober language fool you. This is bonkers. Moore’s audience was doubtless expecting an intricate, technical proof. They were probably expecting an analysis of the terms that the sceptical hypothesis uses, a foray into the nature of belief itself, a subtle distinction that reveals a hidden inconsistency in the very act of doubting.

Instead Moore gave them two hands and eight words: ‘Here is one hand… and here is another.’

You can imagine the audience’s reaction. So far from providing proof of an external world, Moore seemed to have made an unbelievably basic mistake. His first premise – ‘here is one hand’ – is the very thing that the brain-in-a-vat hypothesis calls into question. For his argument to work, he needs to know that the thing he’s seeing is a real hand, but he can’t know that because he might be a brain-in-a-vat being stimulated to believe that he’s seeing a hand! It seems that Moore failed – and failed spectacularly – before he even began. His so-called ‘proof’ doesn’t even get off the ground.

If Moore were a lesser philosopher, our story might have ended here. His proof might have been chalked up as one more mistake on the long, long road to truth. But Moore was well-respected and it was inconceivable that he might make such an obvious error. This led philosophers to reinterpret Moore’s proof and look for new ways of understanding what he was doing. One of the most popular interpretations is this: Moore is pointing out just how weird the implications of the sceptical hypothesis are. The conclusion of the sceptical argument – ‘you don’t know that you have hands’ – is so absurd that it just can’t be right.

Let me elaborate a little more. The sceptical argument, beginning with the brain-in-a-vat hypothesis, goes like this:

(1)   You do not know that you are not a brain-in-a-vat.
(2)   If you do not know that you are not a brain-in-a-vat, you do not know that you have hands.
(C)   You do not know that you have hands.

The first premise is very plausible because there is no way of distinguishing between the situation in which you are a brain-in-a-vat and the situation in which you are a human being with hands. Your experience could be exactly the same in both situations. The second premise is very plausible because if you were a brain-in-a-vat, you wouldn’t have hands. The argument takes the form of a modus ponens (P. If P then Q. Therefore Q), so if the premises are true, the conclusion is too.

On the above interpretation of Moore’s argument, the implausibility of the sceptic’s conclusion outweighs the plausibility of his premises. Although both the sceptic’s premises are very plausible, they lead to an overwhelmingly implausible conclusion and so, Moore seems to be saying, we should run the argument in reverse. We should take the contrary of the sceptic’s conclusion as a premise and argue to the contrary of the sceptic’s premise, as so:

(1)   You know that you have hands.
(2)   If you know that you have hands, you know that you are not a brain-in-a-vat.
(C)   You know that you are not a brain-in-a-vat.

This interpretation is supported by some of Moore’s remarks in a later lecture. In ‘Certainty’ he claimed that the sceptic’s argument “cuts both ways” and that “the one argument is just as good as the other.” David Lewis calls ‘You know that you have hands’ a “Moorean fact.” He says it is one of those things that we know better than we know the premises of any philosophical argument to the contrary.” Moore is basically saying that, no matter what, he knows a hand when he sees one.

Now this argument is not so obviously fallacious, but that doesn’t mean there aren’t problems.  Crispin Wright points out that Moore seems to mischaracterise the sceptical argument. Moore fails to recognise that the reasonableness of his inference from ‘Here is one hand and here is another’ to ‘You know that you have hands’ depends on the prior reasonableness of his conclusion, ‘You know that you are not a brain-in-a-vat.’ Knowledge of the first doesn’t provide support for the second unless we already have a reason to accept the third. So Moore can’t flip the sceptical argument on his head.

To get a bit clearer on this objection, consider the following example from Barry Stroud. Imagine a murder has been committed in a country mansion. The detective’s apprentice has been given a short list of suspects. He manages to rule out everyone on the list except for the butler, so he says to the detective that the butler is the murderer. The detective points out, however, that it’s not guaranteed that the list is complete. He says to the apprentice, ‘Since you don’t know that the list is complete, it follows that you don’t know that the butler did it. The murderer could be someone who is not on the list.’ In this case, the apprentice can’t flip the detective’s argument and run it in reverse. He can’t say, ‘I can just as well argue: since I do know that the butler did it, it follows that I do know that the list is complete.’ What the apprentice has to do is give other reasons for his belief that the list is complete. In a similar way, Wright and Stroud argue, Moore must give other reasons for his belief that he’s not a brain-in-a-vat.

The problem is, this is something Moore can’t do. Later in the British Academy lecture, he says that he has conclusive evidence and conclusive reasons for believing that he is not a brain-in-a-vat, but concedes that he could not tell you what all [his] evidence is. This, I imagine, was maddening for his audience. If Moore’s got evidence, why can’t he reveal it? At this point you might have a sneaking suspicion that Moore’s ‘evidence’ for his belief that he’s not a brain-in-a-vat is… his belief that he’s not a brain-in-a-vat.

Not content with that, Moore ends his lecture on an even more contentious note. He says I can know things which I cannot prove. Unsurprisingly, Moore does not offer proof for this assertion. Presumably the statement itself is one of those things that he can know but cannot prove.

Of course, any sceptics in the audience would be inclined to disagree. The entire sceptical argument depends on the (widely-accepted) premise that knowledge requires proof, so to deny that is to dodge the whole issue. I suspect that this is exactly what Moore does in this lecture but others disagree. In any case, he did call it ‘Proof of an External World.’ Maybe we can at least accuse him of false advertising.

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