We learn some words only after we learn other words. Take ‘plus’, for instance. You cannot understand the concept of addition without knowing anything about numbers. First you have to learn ‘one’, ‘two’, ‘three’ a.s.o. and only afterwards you can learn to use ‘plus’.
The same with ‘subject’, ‘predicate’, or even ‘word’.
I want to say that ‘no’ is not in the same situation. Logicians understand it as a truth-function, on a pair with ‘plus’. However, you don’t have to know anything about sentences or their truth values to learn to say ‘no’.
Let’s compare, for instance, ‘plus’ with ‘addition’. While ‘plus’ is more like a technical term, used for a mathematical function, ‘addition’, in spite of being the name of that particular function, is also a word of our everyday language. ‘In addition, you have to clean your room.’ – there is nothing mathematical in that.
‘No’ is learned as a illocutionary negation. For instance: ‘No, I don’t want to eat now!’. Or: ‘No, leave me alone!’. The locutionary content of such a negation can be extremely vague. A child could say ‘no’ just to stop the adults from doing whatever they are doing. He doesn’t have to comprehend what are they doing. He could just want them to stop.
‘No’ is also quite versatile. As an illocutionary negation (see, for instance, ‘Nein!’, in German), it can be used to perform different illocutionary acts:
– refusing an invitation;
– refusing to execute an order or a request;
– dissaproving of some behaviour;
– expressing an interdiction;
– expressing disbelief, discontent, sorrow, disagreement, despair etc.
– asking, requesting or commanding somebody to stop an action;
– preventing somebody to act;
– discourageing a behaviour by negative feedback (when training a pet, for instance);
– answering a question in the negative;
– making a promise or some other commitment in the negative;
– denying (as opposed to confessing);
Not all the acts in the above list are on a par. They could be analysed in different ways, put into different kinds of categories, in different classifications. However, they show the multitude of uses the word ‘no’ can be put to. Some of them might be closer to the sentential negation of the logician, but some are rather far from it.
If I deny that I did not take care of my child, I might be taken to say that I did take care of my child, but if I refuse your invitation to take part in a protest, for instance, by not turning on my lights for an hour tomorrow, I do not say (and I do not even suggest) that I will turn on my lights tomorrow, during that time.
Back to the main point I am trying to make. At some stage in our life we learn to use ‘no’ as a truth function. When we do this, we expand on the illocutionary negations we have already performed. The new use of ‘no’ is somehow related to the older uses, which are necessary for our new understanding. Our learned concept of negation is not a completely new concept.
Parent: ‘You will go to sleep in half an hour.’
Child: ‘What a lie!’
The illocutionary uses of ‘no’ can be learned by interacting with other people (and even by interacting with animals). Such uses are, in fact, related to non-verbal actions by which we can achieve similar purposes.
If we don’t see the link between all these actions (preventing the occurence of a particular event – preventing an action – reacting negatively to what somebody did or said – reacting with disbelief to something said – stating a negated locutionary content), I do not think that we can explain how did we aquire our concept of negation.