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div id="section26" class="section" title="26">
26
Refutations that depend on the definition of a refutation must, according to the plan sketched above, be met by comparing together the conclusion with its contradictory, and seeing that it shall involve the same attribute in the same respect and relation and manner and time. If this additional question be put at the start, you should not admit that it is impossible for the same thing to be both double and not double, but grant that it is possible, only not in such a way as was agreed to constitute a refutation of your case. All the following arguments depend upon a point of that kind. ‘Does a man who knows A to be A, know the thing called A?’ and in the same way, ‘is one who is ignorant that A is A ignorant of the thing called A?’ ‘Yes.’ ‘But one who knows that Coriscus is Coriscus might be ignorant of the fact that he is musical, so that he both knows and is ignorant of the same thing.’ Is a thing four cubits long greater than a thing three cubits long?’ ‘Yes.’ ‘But a thing might grow from three to four cubits in length; ‘now what is ‘greater’ is greater than a ‘less’: accordingly the thing in question will be both greater and less than itself in the same respect.
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div id="section27" class="section" title="27">
27
As to refutations that depend on begging and assuming the original point to be proved, suppose the nature of the question to be obvious, one should not grant it, even though it be a view generally held, but should tell him the truth. Suppose, however, that it escapes one, then, thanks to the badness of arguments of that kind, one should make one’s error recoil upon the questioner, and say that he has brought no argument: for a refutation must be proved independently of the original point. Secondly, one should say that the point was granted under the impression that he intended not to use it as a premiss, but to reason against it, in the opposite way from that adopted in refutations on side issues.
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div id="section28" class="section" title="28">
28
Also, those refutations that bring one to their conclusion through the consequent you should show up in the course of the argument itself. The mode in which consequences follow is twofold. For the argument either is that as the universal follows on its particular-as (e.g.) ‘animal’ follows from ‘man’-so does the particular on its universal: for the claim is made that if A is always found with B, then B also is always found with A. Or else it proceeds by way of the opposites of the terms involved: for if A follows B, it is claimed that A’s opposite will follow B’s opposite. On this latter claim the argument of Melissus also depends: for he claims that because that which has come to be has a beginning, that which has not come to be has none, so that if the heaven has not come to be, it is also eternal. But that is not so; for the sequence is vice versa.
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div id="section29" class="section" title="29">
29
In the case of any refutations whose reasoning depends on some addition, look and see if upon its subtraction the absurdity follows none the less: and then if so, the answerer should point this out, and say that he granted the addition not because he really thought it, but for the sake of the argument, whereas the questioner has not used it for the purpose of his argument at all.
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div id="section30" class="section" title="30">
30
To meet those refutations which make several questions into one, one should draw a distinction between them straight away at the start. For a question must be single to which there is a single answer, so that one must not affirm or deny several things of one thing, nor one thing of many, but one of one. But just as in the case of ambiguous terms, an attribute belongs to a term sometimes in both its senses, and sometimes in neither, so that a simple answer does one, as it happens, no harm despite the fact that the question is not simple, so it is in these cases of double questions too. Whenever, then, the several attributes belong to the one subject, or the one to the many, the man who gives a simple answer encounters no obstacle even though he has committed this mistake: but whenever an attribute belongs to one subject but not to the other, or there is a question of a number of attributes belonging to a number of subjects and in one sense both belong to both, while in another sense, again, they do not, then there is trouble, so that one must beware of this. Thus (e.g.) in the following arguments: Supposing to be good and B evil, you will, if you give a single answer about both, be compelled to say that it is true to call these good, and that it is true to call them evil and likewise to call them neither good nor evil (for each of them has not each character), so that the same thing will be both good and evil and neither good nor evil. Also, since everything is the same as itself and different from anything else, inasmuch as the man who answers double questions simply can be made to say that several things are ‘the same’ not as other things but ‘as themselves’, and also that they are different from themselves, it follows that the same things must be both the same as and different from themselves. Moreover, if what is good becomes evil while what is evil is good, then they must both become two. So of two unequal things each being equal to itself, it will follow that they are both equal and unequal to themselves.
Now these refutations fall into the province of other solutions as well: for ‘both’ and ‘all’ have more than one meaning, so that the resulting affirmation and denial of the same thing does not occur, except verbally: and this is not what we meant by a refutation. But it is clear that if there be not put a single question on a number of points, but the answerer has affirmed or denied one attribute only of one subject only, the absurdity will not come to pass.
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div id="section31" class="section" title="31">
31
With regard to those who draw one into repeating the same thing a number of times, it is clear that one must not grant that predications of relative terms have any meaning in abstraction by themselves, e.g. that ‘double’ is a significant term apart from the whole phrase ‘double of half’ merely on the ground that it figures in it. For ten figures in ‘ten minus one’ and in ‘not do’, and generally the affirmation in the negation; but for all that, suppose any one were to say, ‘This is not white’, he does not say that it is white. The bare word ‘double’, one may perhaps say, has not even any meaning at all, any more than has ‘the’ in ‘the half’: and even if it has a meaning, yet it has not the same meaning as in the combination. Nor is ‘knowledge’ the same thing in a specific branch of it (suppose it, e.g. to be ‘medical knowledge’) as it is in general: for in general it was the ‘knowledge of the knowable’. In the case of terms that