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.

## 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.