Aristotle

“ It is clear then that not everything which is capable of demonstration also admits of being defined; but then the further question arises:—When a thing is definable is it invariably capable of demonstration or not? ”

“ One argument against the possibility of this latter suggestion has already been mentioned, namely, that a single subject is, as such, treated of by a single science. Hence if demonstrative knowledge of a thing consists in having a demonstration of it we are placed in a dilemma, as one who possesses a definition without demonstration will have real knowledge. ”

“ Hence, generally speaking, one cannot have both for any one subject. It is therefore clear that definition and demonstration cannot be identical, nor can one be part of another, for then their objects would have borne a like relation to one another. ”