Plato suggests the following problem in the Theaetetus:
In judging one judges something; in judging something, one judges something real; so in judging something unreal, one judges nothing; but judging nothing, one is not judging at all.According to Anscombe* Wittgenstein returned to this problem again and again throughout his life. It presents a formidable challenge to his picture theory of language. He thought, in his early work, that in a proposition we supposedly put together a picture of the world just as in the law-courts of Paris of the early twentieth century, a car accident is represented by means of dolls. So how do we get a picture of negation?
What any picture, of whatever form, must have in common with reality, in order to be able to depict it - correctly or incorrectly - in any way at all, is logical form, i.e. the form of reality. So what reality does a negative proposition represent? What is the reality represented by 'snow is not black'? According to Wittgenstein, the negation operator 'not' does not make a picture at all, but simply performs a truth functional operation on the picture given by the corresponding affirmation. The picture he drew in his early Notebooks (above) shows this clearly**. And in the Tractatus he writes (my emphasis)
4.0621 But it is important that the signs 'p' and '-p' can say the same thing. For it shows that nothing in reality corresponds to the sign '-'.Determinatio negatio est. Determination is negation. By drawing a circle in the sand we delimit all the sand on the beach outside the circle as well as all which is inside.
Does this help us to understand how the concept of negation is learned? Is negation a concept at all?
*G.E.M. Anscombe, An Introduction to Wittgenstein's Tractatus (London 1971) p.13
**Taken from a nice paper by Robert Pippin here about this subject.