*Does the external world exist? Most people don’t really question this. But how could you prove it? Since Descartes’ arguments in his *Meditations, *philosophers have discussed whether the existence of the external world can be proven. In this post, I want to summarize G. E. Moore’s famous talk, “Proof of an External World.”*

G. E. Moore begins the paper by saying that, even though Kant claimed that there could be only one possible proof of the external world (the one Kant gave), to Moore it seems that many perfectly rigorous arguments can be given. Suppose he holds up his right hand and says, “Here is one hand”; and then he holds up his other hand and says, “Here is another hand.” To Moore, this is a perfectly rigorous proof of the proposition “There now exists two hands.”

Here is Moore’s argument:

- Here is a hand.
- Here is another hand.
*Therefore*, there now exists two hands.

(3) implies that an external world exists, so the argument proves the existence of the external world.

Three things are necessary for a proof to be considered rigorous:

- The premises must be known.
- The conclusion must be different than the premise(s).
- If the premises are true, then the conclusion must be true.

Moore says that these arguments are met in the “Here is a hand argument,” because:

**(The First Requirement)**When he is holding up one hand and then another, he certainly he*knows*that “here is one hand” and “here is another.” He knows this as well as he knows that he is standing there. Surely there is nothing more certain than that he is holding up his hands.**(The Second Requirement)**Although he recognizes that there might be some people who would think the conclusion “There exists a hand” to be no different than the premise “Here is a hand,” Moore argues that the conclusion is different from the premise because the conclusion could be true even if the premise is false. (If he had his hands amputated, “Here is a hand” would be false, but “There exists a hand” would be true in our world. In fact, many hands exist.) So, the premise and the conclusion are not identical, since one can be true and the other false.**(Third Requirement)**If the premise “Here is a hand” is true, then surely the conclusion “A hand exists” is true.

Moore says that, if this argument is perfectly rigorous, as he thinks it is, then it should be obvious that many more can be given.

He says that his argument would be accepted as a good argument in normal, everyday circumstances. If someone were to question whether there were three typos on a certain page in a book, it would be a perfectly acceptable proof to open the book and say “Here’s one typo, here’s another, and here’s the third.” That’s be acceptable proof.

Besides the question of whether the external world exists *now*, philosophers are interested in whether it existed in the past as well. But, Moore claims, proofs similar to the one above would show the past existence of an external world. The proofs will resemble the proofs of things existing now, but they will also have important differences. One such proof could be: You remember *that a few minutes ago* I held up one hand, and then the other, therefore, two hands existed in the past.

Moore knows that his proofs won’t convince many philosophers. They want something more than this, but it can be difficult to know exactly what else they want. One thing they probably desire is a proof of the premises of Moore’s argument. But, Moore says, he won’t give one, nor does he think one can be given. To prove that Moore really held up his hands would require, as Descartes pointed out, that Moore prove he isn’t dreaming. Moore doesn’t think he can do that. But he can know that he is holding up his hands, without being able to prove it. That’s all he needs. (So, Moore claims that *I know x* doesn’t imply *I can give a proof of x*.)

They also would object to Moore’s proof since some philosophers think that his proof isn’t conclusive if he can’t prove his premises (so either they think that a rigorous proof requires that the premises be proven or, at least, provable; or they think that to know something means that you can prove it). Moore, however, rejects this idea, even though it is common among philosophers. People claim that if you can’t prove something, you can only accept it on faith. But Moore says this isn’t so. You can know something you can’t prove. So, their objection is misguided.