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Top. IV. The argument from greater to less—from that which is more to be expected to that which is less (Brandis)—and the converse; Top. B 10, 114 b 37 seq. To which is subjoined, § 5, εἰ μήτε μᾶλλον μήτε ἧττον, where two things are compared which are equally likely or probable, and accordingly the one may be inferred from the other: of this there are three cases, ἐκ τοῦ ὁμοίως ὑπάρχειν δοκεῖν ὑπάρχειν τριχῶς. Top. Ib. 115 a 15. Of the first there are four varieties: according as (1) the more or less is predicated of the same object—if pleasure is good, then the greater the pleasure the greater the good; and if wrong-doing is bad, the greater the wrong the worse; the fact is to be ascertained by induction—or (2) when one of two things is predicated (in the way of comparison), if that of which it is more likely to be predicated is without it (any property or quality), the same may be inferred of the less likely; or conversely, if the less likely has it, a fortiori the more likely: or (3) (the reverse of the preceding) when two things are predicated of one, if the more likely is not there, we may infer that the less likely will not, or if the less likely be found there, that the more likely will also: (4) when two things are predicated of two others, if that which is more likely is wanting to the one, the less likely will surely be wanting to the other; or, conversely, if that which is less likely to be present to the one is there, the other will be sure to have that which is more likely [Grote's Ar. I. p. 425]. These nice distinctions, though appropriate to Dialectics, are unnecessary in Rhetoric, and are therefore here omitted; but the examples will suggest the proper use of the topic. The inference in all these cases is plain and will be acknowledged by the audience, and that is all that is required.

The inference from greater to less, or from more to less likely or probable, is commonly called the argumentum a fortiori; the rule omne maius continet in se minus may also be referred to the same principle, though the two are not absolutely coextensive.

Cic.Topic. III 11, Alia (ducuntur argumenta) ex comparatione maiorum aut parium aut minorum. This is well exemplified in IV 23. XVIII 68, Reliquus est comparationis locus cuius...nunc explicanda tractatio est. Comparantur igitur ea quae aut maiora aut minora aut paria dicuntur: in quibus spectantur haec, numerus, species, vis, quaedam etiam ad res aliquas affectio. These four modes of application are clearly explained and illustrated in the following sections, 69—71.

De Orat. II 40. 172, Maiora autem et minora et paria comparabimus sic: ex maiore; si bona existimatio divitiis praestat et pecunia tanto opere expetitur, quanto gloria magis est expetenda: ex minore; Hic parvae consuetudinis causa huius mortem fert tam familiariter; Quid si ipse amasset? quid hic mihi faciet patri? (Terent. Andr. I 1. 83): ex pari sic; est eiusdem et eripere et contra rempublicam largiri pecunias.

De Inv. I 28. 41, II 17. 55, de Orat. Part. II 7, ult. Quint. V 10. 86—93, Apposita vel comparativa dicuntur quae maiora ex minoribus, minora ex maioribus, paria ex paribus probant. These are applied, subdivided, and illustrated through the remaining sections.

‘Another from the more or less, as for instance, “if not even the gods are omniscient, surely men can hardly be supposed to be so:” for that is as much as to say, if that to which something is more likely to belong wants it, plainly that which is less likely must want it too. Again (the argument) that a man who was capable of striking his father would also strike his neighbours, follows (is derived from) the (general rule or principle), that the less involves or implies the (possible existence, or capacity, δύναμις, of the) greater; in whichever way we are required to argue (the inference is required to be drawn), whether the affirmative or the negative’. This last example, as an exemplification of the inference from less to greater, has been looked upon as an error, and various corrections have been proposed, as by Vater, and Spengel in Specim. Comm. ad Ar. Rhet. II c. 23, p. 12, 1844. The latter has subsequently altered his opinion, and in 1851 (Trans. of Bav. Acad. p. 58) he admits that the explanation suggested by Victorius, and adopted by Muretus, Majoragius, and others, is sufficient to support the text; which, as usual, is retained by Bekker. No doubt, according to the ordinary interpretation of μᾶλλον and ἧττον in one of these comparisons, where the greater and less are referred to the magnitude and importance of the crime, the argument is ἐκ τοῦ μᾶλλον, ex maiore ad minus: the man who would strike his father (the greater) would a fortiori strike an ordinary acquaintance. But Ar. has here departed from this usual application of the topic, and makes the comparison in respect of the frequency of the crime: as it is less usual to strike one's father than one's neighbour, a man that could be guilty of the former, is much more likely to commit the latter and lesser offence: and the inference is from the less to the greater in this sense. “Aristoteles, cum boni viri officium sit nemini vim afferre, cumque iniuria ab omni abesse debeat, si tamen ibi manet ubi minus esse debebat, illic etiam existet ubi frequentius esse consuevit: et haec causa est cur εἰ τὸ ἧττον ὑπάρχει appellarit, a minore que eam significari voluerit.” Victorius.

On the double reading of MS A^{c}, see Spengel, Trans. of Bav. Acad. 1851 p. 57 [and to the same effect in Spengel's ed., 1867; “in A post δέῃ δεῖξαι haec sententia alia ratione verbis τύπτει ὅτι...δεῖ δεῖξαι explicatur...duplicem sententiae formam iuxta positam melius perspiciemus: On these Aristotelian διττογραφίαι, see Torstrik, Praef. ad de Anima, p. xxi, seq.

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