Thinking, wishing, hoping, believing, and negation all have something in common. The same sort of puzzling questions can be asked about each: How can one wish for a thing that does not happen or hope that something will happen that does not? How can not-p negate p, when p may not be the case, i.e., when nothing corresponds to p?
To the latter question I have pointed out one possible answer: that what corresponds to the negation of p, although not the fact, are the constituents of the fact. For example, corresponding to "There is no chair here" there is the place here, and there are chairs in the world. A similar thing can be said of wishing for something which does not happen...
The problem as to the constituents of the wish is the problem concerning part of a complex sign, taken separately. Just as a box consists of a bottom and lid, we suppose that a proposition such as "I wish Smith would come" must consist of constituents put together in some way. We wrongly compare this proposition with a box consisting of parts, "I wish that" and "Smith comes"' being the different parts.
If "~p" is understood, then "p'" must also be understood. But if p is false, then nothing corresponds to it. We know what it means even though it is not true; but what is it to understand it, or know what it means?
For example, what does it mean to understand the order "Leave the room", when you do not leave the room? Your understanding may be a picture of your leaving the room, but of course that is not the same as leaving the room.
...it won't do to say that understanding the order consists of nothing more than translating the words into a visual image or picture. If that were all, one might say you did not understand the order; you were not ordered to have an image or make a picture but to leave the room. You have not carried out the order, and are no nearer to carrying out the order by making a picture. It is as if understanding ought to have taken you up to the point of carrying out the order. Yet one does not mean that you should have carried it out, for it may be understood without being carried out. The difficulty would disappear if a class of cases of understanding orders was correlated with a class of acts of carrying them out.
Wittgenstein's Lectures, Cambridge, 1932-1935, edited by Alice Ambrose