people think they were synthetic and expressed real "knowledge"? I think it was the same error which made them believe that they had to do with a "material" a priori: they felt sure that their assertions expressed the very nature or essence of the Content of the colours or sounds they were speaking about. The proposition "a surface cannot be red and green at the same time and place" does not say anything about the content of "red" or "green", for all the reasons which were given in the first lecture and need not be repeated here, because they were entirely general — the proposition is nothing but a tautology which reveals the way (or form) in which the terms "red" and "green" are used. The incompatibility of the two is due not to some mysterious antagonism between two real essences, two kinds of content but to the internal structure of the two concepts "red" and "green". A surface cannot be red and green for exactly the same reason which makes it impossible for a tall man to be a short man at the same time. No one can seriously think that he has uttered anything but the merest tautology, when he tells us that a man who is 6 feet is not also 4½ feet. We know this a priori i.e. without consulting experience and we do not consider it to be a statement conveying knowledge about the essence of "man" or even about "length"!
We know its truth to be purely formal. It follows from the definition of measurement that if the result of it is indicated by one number all other numbers are excluded (provided we use the same unit), in the same way it follows from the way we use our colour names that if we attribute a certain colour to anything, we, at the same time exclude other colours. It is, as in all cases of internal structure, a matter of grammatical rules. In this case it is revealed by the use of the definite article: we have to say: The height of the Empire State Building is 1270 feet, we cannot say that this number indicates a height of the building. In the same way we can speak only of the colour of a definite place of a coloured patch. (If a patch has several colours they must be in different places, just as a building may have several towers, but not in the same place.)
The word "six" denotes a certain place in the structure of internal relations, called the system of numbers; in the same way the word "red" wherever it occurs in a sentence, stands for a place within a structure called the system of colours.
