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THus much for the simple syllogisme. The com∣pound syllogisme is that wherein the whole que∣stion maketh the one part of the proposition affir∣med and compounded: And the argument inuen∣ted,
maketh the other part of the proposition, or is conteyned in it.
To deny or remooue any part in a compound syllogisme is to set downe the speciall contradiction thereof.
The compound syllogisme is eyther connexiue, or dis∣iunctiue.
The connexiue is that whose proposition is connexiue, and is made after two sortes.
First when the former part of the proposition maketh the assumption, the later part the conclusion. As in this,
Héere oftentimes the former parte of the proposition ma∣keth not the assumption, but that which is greater, and of more force to conclude then it is, as,
Piers vseth this in May, in the gates spéech to her little one.
Maister Plowden: Fol. 11. a.
The same kinde of syllogisme or reasoning is framed by a coniunction of time, with the same force, which this con∣nexiue hath, As
But see, the Welkin thicks apace, And stouping Phebus steepes his face, It's time to haste vs homeward.
Mayster Plowden: Fol. 263. a.
THe speciall contradiction:] when that which was affir∣med in generall, is denyed in speciall: or contrarily, affir∣med, when it was denyed: and when the same thing in spe∣ciall, is both affirmed before and denyed after.
[Connexiue or disiunctiue:] So then of an axiome co∣pulatiue or discretiue, wée vnderstand, that no seuerall and peculier disposition ariseth.
Vide 10. E. 4. Lyttleton contra Danby: si le proper∣tie des biyus le mort soit en ascun, tunc serra in le testator,
vel in les executors: mes est en ascun, ergò in l'un ou l'au∣ter: •…•…est connexiue: Then agayne:
In composito syllogismo, assumptio, praeter argumentum, nihil assumit quaestionis; quod tamen fit semper in simplici syllogismo.
If not the whole question, but onely the latter part of it bée conteyned together with the argument inuented, in the proposition, then the syllogisme is simple, although the pro∣position bée compound. For as I sayd elswhere, whenso∣euer the disposition is simple, there the syllogisme is simple, though the partes bée compound. So that in Catullus is a simple syllogisme. 1. Gen.
Nay, which is more, the syllogisme may bée simple, though all the partes bée conditionall and compound, thus:
Elenchs. There bée two other connexiue syllogismes different from these already rehearsed: but because they are not certayne, constant, and alwayes infallible: therefore they be not put downe in the text, as precepts of Art: yet are they diligently to •…•…e obserued, for they are often in autors: especially the first, which is very vsuall: but the second is not so common.
The first kinde is that which taketh away the former part, that it may also take away the later. Terence in A∣dolphis.
Dem: Caeterum. Placet tibi factum Mitio? Mr: Non, si queam mutare: •…•…nc cum non queo, aequo animo fero.
Cicero for Muraena.
Etenim si largitionem factam esse confiterer, idque recte esse factum defenderem, facerem improbe, etiamsi alius legem tulisset. Cum verò nihil commissum esse contra legem defendam, quid est quod meam defensionem latio legis impediat?
Ouid in his second booke of sorrowfull songs.
Caesar in Salust. Si digna poena pro factis corum reperitur, no∣uum consilium approbo: sin magnitudo sceleris omnium in∣genia exuperat, his vtendum censeo, quae legibus comparata sunt.
Colyn in Iune hath the like.
For, although all the examples of this kinde bée not false and deceiptfull, but good and sufficient, as in these now re∣hearsed; yet, false may bée concluded by the selfe same dispo∣sition, as
In which example, the proposition and assumption are both true, yet the conclusion is false: but it is the office of a syllogisme, as hath béene sayde, to lay downe, a necessary, perpetuall, and immutable rule, by the which, vppon the premisses once graunted, the consequence must bée ne∣cessary.
The second, which is not so vsuall, is that which taketh the latter parte, that it may also haue the former concluded, as in that of Ouide in the fourth booke of his transforma∣tions.
Quem si cura deûm tam certa vindicat ira, Ipse precor serpens in longam porrigar aluum: Dixit; et, vt serpens, in longam tenditur aluum.
The argumentation is thus:
Take an other example, and you shall sée, that by the same rule you may conclude that which is starke false, As
For heere the forerunning axiomes being both true, the conclusion for all that, is manifestly false. This is called of Aristotle an Elench of the consequent: yet in trueth it is no Elench of argument, but of argumentation: when wée are perswaded foolishly that the consequution is reciprocall, and that the putting downe of the one bringeth in of necessitie the other, and contrarily, As,
So, that of Melissus.
The consequution, sayth Aristotle, is not reciprocall.
Ramus in the 20. of his Logicall animaduersions, the sixt Chapter sayth thus.
Theophrastus autem & Eudemus docuerunt in connexo, Antecedentis negati, & consequentis affirmati tolli posse an∣tecedens, vt tollatur consequens; & consequens retineri, vt re∣tineatur antecedens. In quo genere, etsi rarus error est, est ta∣men aliquando: Vt,
Cum maius aliquid concluditur, videntur esse tres termini, sed reuera, res illa maior contine •…•…rem ante propositam in se, & quiddam amplius: Ita{que} tres tantum termini sunt.