statements alluded to above do not correspond to thoughts which, by a sort of psychological experiment, we find ourselves unable to think; they do not correspond to any thoughts at all. When we hear the words, ‘A tower which is both 100 feet and 150 feet high’, the image of two towers of different heights may be in our mind, and we may find it psychologically (empirically) impossible to combine the two pictures into one image, but it is not this fact which is denoted by the words ‘logical impossibility’. The height of a tower cannot be 100 feet and 150 feet at the same time; a child cannot be naked and dressed at the same time — not because we are unable to imagine it, but because our definitions of ‘height’, of the numerals, of the terms ‘naked’ and ‘dressed’, are not compatible with the particular combinations of those words in our examples. 'They are not compatible with such combinations' means that the rules of our language have not provided any use for such combinations; they do not describe any fact. We could change these rules, of course, and thereby arrange a meaning for the terms ‘both red and green’, ‘both naked and dressed’; but if we decide to stick to the ordinary definitions (which reveal themselves in the way we actually use our words) we have decided to regard those combined terms as meaningless, i.e., not to use them as the description of any fact. Whatever fact we may or may not imagine, if the word ‘naked’ (or ‘red’) occurs in its description we have decided that the word ‘dressed’ (or ‘green’) cannot be put in its place in the same description. If we do not follow this rule it means that we want to introduce a new definition of the words, or that we don't mind using words without meaning and like to indulge in nonsense. (I am far from condemning this attitude under all circumstances; on certain occasions — as in Alice in Wonderland — it may be the only sensible attitude and far more delightful than any treatise on Logic. But in such a treatise we have a right to expect a different attitude.)
The result of our considerations is this: Verifiability, which is the sufficient and necessary condition of meaning, is a possibility of the logical order; it is created by constructing the sentence in accordance with the rules by which its terms are defined. The only case in which verification is (logically) impossible is the case where you have made it impossible by not setting any rules for its verification. Grammatical rules are not found anywhere in nature, but are made by man and are, in principle, arbitrary; so
