Abstract of Logic, Book 2 · Chapter 13
CHAP. XIII. Of Dilemma, Proſyllogiſm and Sorites.
Ax. 1. A Syllogiſm compoſed of many Syllogiſms is either Dilemma, Proſyllogiſm, or Sorites.
Ax. 2. A Dilemma is an Argumentation of two Members, both which have ſome Inconvenience belonging to them.
COMMENTARY.
1. §. A Dilemma in Greek foreign, is ſo called becauſe it is as it were, foreign, that is, a Syllogiſm with two Handles, and catching one both ways, that is, binding one up. For Example; be that of Bias in Gellius's Book 5. Cap. 11, If a Wife be to be married, ſhe will be either a fair one or a deformed; if fair, ſhe will be common, if deformed a Loathing, &c.
Ax. 3. Which Argument conſiſts of a Disjunctive Syllogiſm, in which from the Remotion of the Parts is concluded the Remotion of the Whole; and two Categorical, by which the Remotion of thoſe Parts is confirmed: As for Example:
1. §. The Dilemma inſtanced, is thus to be reſolved:
Viz. if a Wife be to be marry'd, either ſhe will be a fair one, or a deformed;
But neither a fair, nor a deformed.
And therefore, a Wife is not to be marry'd.
1. Cat. A Wife that will be common is not to be marry'd;
But a fair one will be ſo:
And therefore a fair one is not to be marry'd.
2. Cat. One again, that will be a Vexation or Loathing, is not to be married:
But the deformed will be ſo:
And therefore a deformed is not to be married, &c.
Ax. 4. But a Dilemma will be Inefficacious three manner of Ways: And firſt, when the Members are not immediately oppoſed. Secondly, when it's not attended with ſufficient Inconvenience: And thirdly, when with the ſame Efficacy it may be retorted upon its Author.
1. §. Twofold therefore is the Infirmity of that Dilemma which is brought by Bias againſt Matrimony: For firſt, the Members of it are not immediately oppoſed; for there is a middle Term betwixt that of too much Fairneſs, which is expos'd to Peril and its contrary Deformity, by Ennius, termed Stata, or not deformed, and Favorinus, that of a Wife; and then it does not follow, that a Fair One muſt be Common, or a Deformed Hateful or Vexatious, &c. An Example alſo of Retortion is extant in the ſame Gellius, Book the ſame, Cap. 10. An Author that we have cited but too much already, and that is this, Eualthus deſirous of Eloquence, and the Art of Pleading becomes a Scholar to Protagoras, and pays him down one half of his Reward, promiſing him the reſt when he ſhould firſt plead a Cauſe before the J…dges and overcome. After a long time Protagoras commences a Suit with Eualthus, and thus argues with him. Whether declared for me or thee, ſays he, thou oughteſt to give me my Reward: For if for me the Reward will be due, becauſe of the Sentence, becauſe then I ſhall overcome; and if for thee by Agreement, becauſe then thou. To which Eualthus thus, viz. In the firſt Place, that he might eaſily obviate that Caption, if he ſhould ſay nothing himſelf, but make uſe of his Council or Attorney But afterwards retorts it in this Manner, viz. whether declared for me or thee, ſays he, I ought not to render thee the Reward; For if for me, then nothing will be due, becauſe of the Sentence; and if for thee, becauſe of the Agreement: Becauſe then thou wilt overcome, &c.
Ax. 5. A Proſyllogiſm is then when two Syllogiſms are ſo contained in five Propoſitions, as, that the Concluſion of the Firſt becomes the Major or Minor of the Following, as,
1. §. For Example, this; Every living thing is nouriſhed; But every Plant is a living thing: And therefore every Plant is nouriſhed. But no Stones are nouriſhed: And therefore no Stones are Plants. Or this, Every Antimal feels; Every Man is an Animal: And therefore every Man feels. But whatever feels is mortal: And therefore every Man is mortal, &c. Of which the laſt is the Principal, and the Firſt only called in as an Auxiliary for Proof either of the Major, as in the Firſt, or Minor, as in the ſecond Example, &c.
Ax. 6. A Sorites is an Argumentation conſiſting of many Propoſitions, and ſo placed as that the Predicate of the Preceding becomes the Subject of the Following, and the Laſt Predicate becomes Concluded of the Firſt Subject.
1. §. Now this Argumentation is ſo called from the Greek Word foreign, that is, an Heaping up or Gath ring together of Things: For a Sorites is a certain Heaping up or Coacervation of Propoſitions. For Example; that in the Eighth of the Romans, viz. Thoſe whom God has foreknown, he has alſo predeſtinated; whom he has predeſtinated, he has alſo called; whom he has called, he has alſo juſtified; whom he has juſtified, he has alſo glorified, &c. From whence collect that, whomhe has foreknown he has alſo glorify'd, &c.
Ax. 8. Now this ſort of Argumentation contains in it, as many Syllogiſms as there are Terms between the Subject of the firſt, and the Predicate of the laſt Propoſition.
1. §. And therefore this of St. Paul will contain three, which may be thus formed, viz. Thoſe whom God has predeſtinated, he has alſo called; but thoſe that he has foreknown, he has alſo predeſtinated; and therefore thoſe that he has foreknown, he has alſo called. Secondly, Thoſe whom he has called, he has alſo juſtified; But thoſe whom he has predeſtinated, he has alſo called; And therefore thoſe whom he has predeſtinated, he has alſo juſtified. Thirdly, thoſe that he has juſtified, he has alſo glorified; But thoſe that he has called, he has alſo juſtified, and therefore thoſe that he has called, he has alſo glorified, &c.
And ſo this brings us to the next Chapter, which is that of Syllogiſm Modal and Indirect, not hitherto entreated of.