It is, too, altogether absurd to discuss Refutation without first discussing Proof: for a refutation is a proof, so that one ought to discuss proof as well before describing false refutation: for a refutation of that kind is a merely apparent proof of the contradictory of a thesis.Accordingly, the reason of the falsity will be either in the proof or in the contradiction (for mention of the 'contradiction' must be added), while sometimes it is in both, if the refutation be merely apparent.In the argument that speaking of the silent is possible it lies in the contradiction, not in the proof;in the argument that one can give what one does not possess, it lies in both; in the proof that Homer's poem is a figure through its being a cycle it lies in the proof.An argument that does not fail in either respect is a true proof.
But, to return to the point whence our argument digressed, are mathematical reasonings directed against the thought, or not? And if any one thinks 'triangle' to be a word with many meanings, and granted it in some different sense from the figure which was proved to contain two right angles, has the questioner here directed his argument against the thought of the former or not?
Moreover, if the expression bears many senses, while the answerer does not understand or suppose it to have them, surely the questioner here has directed his argument against his thought! Or how else ought he to put his question except by suggesting a distinction-suppose one's question to be speaking of the silent possible or not?'-as follows, 'Is the answer "No" in one sense, but "Yes" in another?' If, then, any one were to answer that it was not possible in any sense and the other were to argue that it was, has not his argument been directed against the thought of the answerer? Yet his argument is supposed to be one of those that depend on the expression.There is not, then, any definite kind of arguments that is directed against the thought.Some arguments are, indeed, directed against the expression: but these are not all even apparent refutations, let alone all refutations.For there are also apparent refutations which do not depend upon language, e.g.those that depend upon accident, and others.
If, however, any one claims that one should actually draw the distinction, and say, 'By "speaking of the silent" I mean, in one sense this and in the other sense that', surely to claim this is in the first place absurd (for sometimes the questioner does not see the ambiguity of his question, and he cannot possibly draw a distinction which he does not think to be there): in the second place, what else but this will didactic argument be? For it will make manifest the state of the case to one who has never considered, and does not know or suppose that there is any other meaning but one.
For what is there to prevent the same thing also happening to us in cases where there is no double meaning? 'Are the units in four equal to the twos? Observe that the twos are contained in four in one sense in this way, in another sense in that'.Also, 'Is the knowledge of contraries one or not? Observe that some contraries are known, while others are unknown'.Thus the man who makes this claim seems to be unaware of the difference between didactic and dialectical argument, and of the fact that while he who argues didactically should not ask questions but make things clear himself, the other should merely ask questions.