Jason suggested in a comment on the last post that my problem about how we learn to apply negation is related to the ‘Meno question’.
A couple of comments. First, there are two Meno questions or Meno problems. The first is to explain how knowledge is more valuable than mere true belief, and that is the Meno problem as commonly understood. The second problem, which is clearly related to the first, is to explain how we learn anything at all. If knowledge is different from true belief, how can we possibly acquire knowledge by teaching? If teaching is the mere repetition of true propositions (‘The battle of Hastings was in 1066’), and if learning is the acceptance of those propositions as true, on account of the authority of the teacher, or for whatever reason, and if knowledge is more than simple acceptance of the truth, it logically follows that we can’t acquire knowledge from teaching, as so defined. So how do we acquire knowledge? Is it already there, and does teaching in the proper sense require uncovering what lay hidden? – the Latin root of ‘educate’ means ‘drawing out’. Or does it come from without?
The second problem clearly underlies the difficulty about negation, but there is a further difficulty. The medieval philosophers, following Boethius*, divided discourse into three types, namely written, spoken and conceptual. Written discourse signifies spoken discourse, by convention. It is a convention, e.g., that the written word ‘dog’ signifies the noise that comes out of my mouth when I utter ‘dog’. In turn, spoken discourse signifies mental discourse, also by convention. It is by convention that the spoken word ‘dog’ signifies the idea of a dog. French people use the word ‘chien’ to signify that same idea, Germans use the word ‘Hund’ (I think). Ockham, though he was English, would have used the Latin word canis. However, mental discourse signifies not by convention, but ‘naturally’. The English and French and German and Latin words for dog all signify exactly the same thing, namely the idea of a dog. For otherwise we could not communicate, unless we could signify the same idea in another person’s mind as the one we want to convey. But we cannot teach the signification of the idea itself – we don’t have it available to match up with the thing signified, for ideas are private. So ideas or ‘mental terms’ signify naturally. Ockham explains this right at the beginning of his Summa Logicae.
Now the word ‘not’ is what Ockham would have called a syncategorematic term. He explains the distinction in chapter 4, although it does not originate with him. A syncategorematic term is one that does not signify on its own (in the way that the term ‘dog’ on its own signifies or ‘supposits for’ all dogs), but signifies by making other words signify. For example, ‘every’, ‘some’, ‘only’ and of course ‘not’.
If Ockham is right, there is a sense in which we cannot learn the meaning of the word ‘not’. Of course we learn that the English word ‘not’, the spoken word, corresponds to the mental ‘not’, and in that sense we learn the meaning. But in another sense we cannot learn or acquire the mental term itself. It must be already there.
Thus, if he is right, we don’t learn the meaning of negation. It is already there. But is he right?
*See his commentary on Aristotle’s Perihermenias ed. 2a, I, Patrologia Latina 64, col. 407B.