Enthymemes, genuine and apparent, have now been described; the next subject is their Refutation.
An argument may be refuted either by a counter-syllogism or by bringing an objection. It is clear that counter-syllogisms can be built up from the same lines of arguments as the original syllogisms: for the materials of syllogisms are the ordinary opinions of men, and such opinions often contradict each other.
Objections, as appears in the Topics, may be raised in four ways-either by directly attacking your opponent's own statement, or by putting forward another statement like it, or by putting forward a statement contrary to it, or by quoting previous decisions.
1. By 'attacking your opponent's own statement' I mean, for instance, this: if his enthymeme should assert that love is always good, the objection can be brought in two ways, either by ****** the general statement that 'all want is an evil', or by ****** the particular one that there would be no talk of 'Caunian love' if there were not evil loves as well as good ones.
2. An objection 'from a contrary statement' is raised when, for instance, the opponent's enthymeme having concluded that a good man does good to all his friends, you object, 'That proves nothing, for a bad man does not do evil to all his friends'.
3. An example of an objection 'from a like statement' is, the enthymeme having shown that ill-used men always hate their ill-users, to reply, 'That proves nothing, for well-used men do not always love those who used them well'.
4. The 'decisions' mentioned are those proceeding from well-known men; for instance, if the enthymeme employed has concluded that 'that allowance ought to be made for drunken offenders, since they did not know what they were doing', the objection will be, 'Pittacus, then, deserves no approval, or he would not have prescribed specially severe penalties for offences due to drunkenness'.
Enthymemes are based upon one or other of four kinds of alleged fact: (1) Probabilities, (2) Examples, (3) Infallible Signs, (4)
Ordinary Signs. (1) Enthymemes based upon Probabilities are those which argue from what is, or is supposed to be, usually true. (2)
Enthymemes based upon Example are those which proceed by induction from one or more similar cases, arrive at a general proposition, and then argue deductively to a particular inference. (3) Enthymemes based upon Infallible Signs are those which argue from the inevitable and invariable. (4) Enthymemes based upon ordinary Signs are those which argue from some universal or particular proposition, true or false.
Now (1) as a Probability is that which happens usually but not always, Enthymemes founded upon Probabilities can, it is clear, always be refuted by raising some objection. The refutation is not always genuine: it may be spurious: for it consists in showing not that your opponent's premiss is not probable, but Only in showing that it is not inevitably true. Hence it is always in defence rather than in accusation that it is possible to gain an advantage by using this fallacy. For the accuser uses probabilities to prove his case: and to refute a conclusion as improbable is not the same thing as to refute it as not inevitable. Any argument based upon what usually happens is always open to objection: otherwise it would not be a probability but an invariable and necessary truth. But the judges think, if the refutation takes this form, either that the accuser's case is not probable or that they must not decide it; which, as we said, is a false piece of reasoning. For they ought to decide by considering not merely what must be true but also what is likely to be true: this is, indeed, the meaning of 'giving a verdict in accordance with one's honest opinion'. Therefore it is not enough for the defendant to refute the accusation by proving that the charge is not hound to be true: he must do so by showing that it is not likely to be true. For this purpose his objection must state what is more usually true than the statement attacked. It may do so in either of two ways: either in respect of frequency or in respect of exactness. It will be most convincing if it does so in both respects; for if the thing in question both happens oftener as we represent it and happens more as we represent it, the probability is particularly great.
(2) Fallible Signs, and Enthymemes based upon them, can be refuted even if the facts are correct, as was said at the outset. For we have shown in the Analytics that no Fallible Sign can form part of a valid logical proof.
(3) Enthymemes depending on examples may be refuted in the same way as probabilities. If we have a negative instance, the argument is refuted, in so far as it is proved not inevitable, even though the positive examples are more similar and more frequent. And if the positive examples are more numerous and more frequent, we must contend that the present case is dissimilar, or that its conditions are dissimilar, or that it is different in some way or other.
(4) It will be impossible to refute Infallible Signs, and Enthymemes resting on them, by showing in any way that they do not form a valid logical proof: this, too, we see from the Analytics. All we can do is to show that the fact alleged does not exist. If there is no doubt that it does, and that it is an Infallible Sign, refutation now becomes impossible: for this is equivalent to a demonstration which is clear in every respect.