Enthymeuia then is a syllogism from probablea or signs. Analyt. Pr.,' ii. 27.) (33.) And an example is, when the first is shown to belong (inrcfpxov) to the middle through one like the third. But it must be known that both the middle belongs to the third and the first to the like. For example, let A be bad, and B be to take up war against neighbours; and C, the Athenians, taking up war against the Thebans; and n,'the Thelxins, taking up war against the I'hocians. If then we wish to show that to make war on the Thebans is a bad thing, we must assume that to make war on neighbours is bad. And the evidence of this is from the like things, for example., that the war of the Thebans against the l'hocians is bad. Since then to make war on neighbours is bad, and since the war against the Thebans is against neighbours, it is manifest that to war against the Thebana is bad. Accordingly it is clear that B belongs to o and to n (for both c and n are to take up war against neighbours), and that A belongs to n (for the war of the Thebans against the Phociana was not good); but that A belongs to will be shown through D.
And in the same manner also if through more like things, the evidence should exist of the middle belonging to the first. Accordingly it is manifest that the example is neither as a part to the whole, nor as a whole to a part, but as a part to a part, when both are included in the same notion, and the one is known. And it differs from induction, inasmuch as induction by means of all the particulars shows that the first belongs to the middle, and does not connect the syllogism with the first, hut the example both connects it and does not derive its evidence from all the particulars. (` Analyt. 24.) (39. Both modes of proof, that by syllogisms and that by induction, teach by means of things known before; tho one taking its assumptions from the general notions of mankind, and the other showing the uni versal through the evidence of the particular. And in the same manner rhetorical arguments persuade ; for they (the arguments) are either by means of example, which is or by means of cnthymemata, which is syllogism. Analyt. Post.,' (10.) Refutation (tas-sxos) is a syllogism of contradiction. ('Analyt. Pr.; ii. 20.) (41.) And objection ((vcrrams) is a proposition contrary to a propo sition. And it differs from the proposition, in as much as it is possible • for the objection to be particular, but the proposition either cannot be so at all, or at least not in the universal syllogisms. (Analyt. Pr.,' 26.) (42.) Since it is the nature of some things through themselves to be known, and of some through other things (for principles (iipxaf) are known through themselves, but other things subordinate to principles are known through other things), when any one attempts to show through itself a thing not known through itself, then the thing to be proved (sb g( apxiis) is assumed. ( Analyt. Pr.,' ii. 16.)
And people appear to assume what is to be proved in five ways. Most manifestly and first, if a person should assume that which requires to be proved. And this in itself does not easily escape notice; but in common names (cruvaivviza),* and in all those things in which the name and the notion (Ahos) have the same meaning, it is more easy to escape detection. And the second way is when a person assumes the universal when it is necessary to prove the particular ; for example, if a person attempting to show that of contrary things (?vdrria) there is one science, should universally assume that of opposed things (Itesissadva) there is one science; for he appears to assume with many other things that which it was requisite to prove by itself. The third way is, if any one, when the thing proposed is to show the universal should assume the particular ; for example, if he had to prove that of all con trary things there is one science, be should assume that there is one science of some particular contrary things ; for such a one also appears to assume separately by itself that which it was requisite to prove together with others. Again, if any one should assume the problem (rb irpol3)fnO‘v) by dividing it ; for example, if, when it was required to show that the art of medicine concerned both health and sickness, he should assume each separately. Or if any one should assume one of two things which follow one another of necessity; for example, that the side (of a square) has no common measure with the diagonal, when it was required to show that the diagonal has no common measure with the aide. Top.; viii. 13.) (43.) The affirmative (demonstration) is prior to the negative, and more easily known, for through the affirmation the negation is known, and the affirmation is prior, as being also is prior to not being. Further, it is nearer to a first principle ; for without the positive proof there is no negative proof. Analyt. Post.,' i. 25.) (44.) All persona who form a conclusion through that which is impossible, form indeed a false conclusion, but they show what has to be demonstrated by virtue of an hypothesis, when anything impossible results by the assumption of the contradiction (&uerfcpwris) (10).