Abstract of Logic, Book 2 · Chapter 14
CHAP. XIV. Of Syllogiſm Modal and Indirect.
Ax. 1. IN the fourth Place may Syllogiſm be divided into Pure and Modal. A Pure is that which conſiſts of Propoſitions pure.
2. Modal either of one or both Modal.
COMMENTARY.
1. §. Of Modals, there are five Orders; and the firſt of them is that which conſiſts of both Propoſitions of the Mode neceſſary. As,
It is neceſſary that every Animal ſhould feel;
But it is neceſſary that every Man ſhould be an Animal:
And therefore it is neceſſary that every Man ſhould feel, &c.
The ſecond of the one Pure, and the other the Mode neceſſary, as it is neceſſary every Animal ſhould feel; But every Man is an Animal: And therefore 'tis neceſſary that every Man ſhould feel, &c.
The Third both of the Mode Contingit; as it may happen, that every Man may walk; but it may happen that ſome Man may be white: And therefore it may happen that ſomething white may walk, &c.
The Fourth of the One Pure, and the other of the Mode Contingit, as did the ſecond of the one Pure, and the other of the Mode Neceſſary.
The 5th and laſt, of the One Neceſſary and the Other of the Mode Contingit; as, It may happen, that every Animal may ſleep: It is neceſſary that every Man be an Animal: And therefore it may happen that every Man may ſleep, &c.
But becauſe the Uſe of theſe Sorts of Syllogiſms is very little, and Rules for them very hard, it was thought little worth our while to recite them.
Ax. 3. In the fifth Place may Syllogiſm be divided into that which is direct, and that which is indirect. Now the Direct is that which from the Pronunciated or foregoing collects the Queſtion it ſelf.
Ax. 4. Whilſt the Indirect, not, but only ſomewhat elſe, from which yet the Probation of the Queſtion, does by virtue of a certain ſort of an Agreement ariſe.
Ax. 5. An Indirect, either is that of foreign, that is, bringing one into an Inconvenience; or elſe foreign, that is, Concluding from a Conceſſion.
Ax. 6. That of bringing one into an Inconvenience, is this: When from the Contradiction of the Queſtion to be prov'd, and another manifeſt Propoſition we conclude ſomewhat which is manifeſtly falſe.
1. §. To declare this by Example, let our Queſtion be, Do Stones live? You deny that they do. The Adverſary, with Cardan, affirms it. Take Cardan's Opinion, and add too, that this Maxim, even in the Adverſary's Opinion true: viz. That whatever lives, is nouriſhed, and has Organical Parts; and then from thence you may thus argue, viz.
Whatever lives, is nouriſhed, and has Organical Parts;
But Stones live:
And therefore Stones are nouriſhed and have Organical Parts.
Now the Concluſion is falſe moſt certainly, and even by the Teſtimony of common Experience: And therefore when from true Premiſſes nothing can follow but what is true; Of Neceſſity one of the Propoſitions muſt be falſe. Now the Major cannot be ſo, nor does the Adverſary fail to grant it; and if the Minor, which certainly muſt, then it follows, that the Contradiction of it muſt be true; which was the Queſtion to be proved. Now
Ax. 7. This Syllogiſm foreign, or concluding from a Conceſſion, is then, when the Queſtion propoſed is transferred on ſome other, upon this Condition, that that being proved, this alſo ſhould be eſteemed to be ſo too.
1. §. So Ariſtotle Cap. 11. of his ſecond Book of the Heavens, proves that all the Stars are round. But becauſe it would be too hard a Task for him to prove that of all in one Ratiocination, he transferrs this Queſtion upon the Moon, and proves her to be ſo; and thence inferrs, that they all are ſo, pre-ſuppoſing the ſame Ratio to be in one, as the other. And that the Moon is ſo, he collects from her Lights being encreas'd and diminiſh'd by Sphaerical Degrees, &c.
And thus much in Reſpect to Abſolute Syllogiſm, and that to be conſider'd with Reſpect to Form. Now follows that which is to be conſider'd in Reſpect to its Matter: And firſt the Dialectical, of which we ſhall entreat in the next Chapter.