Abstract of Logic, Book 2 · Chapter 6
CHAP. VI. Of the Definition of Syllogiſm, and its Parts.
Ax. 1. A Syllogiſm is a Speech in which ſomething being ſuppos'd, ſomething different from that ſuppos'd, by Reaſon of the Suppos'd, does of Neceſſity follow.
COMMENTARY.
1. §. So that to Syllogiſe is to collect, that is, conclude, or from ſome certain Propoſitions to draw up the Summ of an Argument or Proof.
2. §. The Genus of Syllogiſm is Speech, viz. principally Internal; becauſe, without External, a Syllogiſm may conſiſt, viz. in the Mind.
3. §. By ſomething diverſe from the Suppoſed, is to be underſtood, the Concluſion. Yet,
4. §. When the Concluſion is ſaid neceſſarily to follow, we are not to underſtand it of the Neceſſity of the Concluſion it ſelf, viz. that of the Conſequent but Conſequence: For that of the Conſequent or Concluſion it ſelf, has Place only in Demonſtration of the Conſequence in every well-form'd Syllogiſm: For this being taken away, a Syllogiſm, will be no Syllogiſm but a Paralogiſm.
5. §. Laſtly, By reaſon of the Premiſſes, that is, the Premiſſes, muſt be ſo very clear, that to the Neceſſity of ſuch a Sequel, nothing out of the Syllogiſm need to be ſought for. For Example: If it be true that every thing be good, that is, according to Nature, and that all Pleaſure is according to Nature, it muſt neceſſarily follow, that all Pleaſure is good, and that by Force of the Terms that are contain'd in the two Premiſſes without the Help of any other, &c. Now,
Ax. 2. A Syllogiſm is either abſolutely conſidered, that is, in it ſelf, or with reſpect to thoſe diverſe Effects which it produces, by reaſon of the Diverſity of the Conditions of its Matter.
Ax. 3. And the firſt Tract will conſiſt of three Members, viz. firſt of Geneſis, or the manner of making a Syllogiſm; ſecondly, finding out a Medium; and thirdly, of the Diviſion of Syllogiſm, and of the various Species's of ſuch Argumentations.
Ax. 4. And the firſt of theſe will be underſtood by the Explication of the Matter, as well remote as proximate, and the Form. Now,
Ax. 5. The remote Matter of Syllogiſm are three Terms, to wit, two Extremes, major and minor, that is, Subject and Predicate, and one Middle, which is the Argument fetch'd from without to prove the Queſtion.
1. §. The Parts of the Queſtion and the Middle, by which we mean the Medium, are thus called, not becauſe of their Site, but Office.
2. §. Secondly, now the Argument muſt be but One; becauſe that which unites, ought it ſelf to be but One. And if two in one Syllogiſm, a third would be wanted, by which to find out the Convenience or Inconvenience of thoſe two: As, when the Equality or Inequality of two Magnitudes are explorated or tryed by two diverſe Meaſures, there will be Occaſion for a Third, by which to find out the Equality or Inequality, even of thoſe two.
Ax. 6. The Proximate Matter are only three Propoſitions, which are made out of theſe Terms Combin'd together, of which the two firſt,
Ax. 7. Antecede and infer, and the third follows and is inferr'd.
Ax. 8. The firſt is term'd Propoſition or Major Propoſition; the ſecond, Aſſumption, or Minor; and the third, Collection, Concluſion or Commplexion.
1. §. The firſt Propoſition is call'd Propoſition; becauſe firſt propos'd, or prepos'd to the reſt of the Propoſitions: The ſame Major, becauſe compos'd of the Major Term, and Medium; as the ſecond Minor, becauſe of the Minor and Medium. The third Concluſion, becauſe it collects together the Parts of the Queſtion which were ſeparated in the Premiſſes, and joyns them.
2. §. Of this two-fold Matter, a Syllogiſm may be made or compos'd in this manner. In the firſt Place ſome Queſtion is to be ſought for: As for Inſtance; Is Logick an Art? This Queſtion contains two Parts, the Subject Logick, and Predicate Art. To the Proof of Logick's being an Art, let us take ſome Argument, or Medium, and let that be Habit Effective. Let this Argument in the firſt Place be joyn'd to the Predicate of the Queſtion, which is Art, and then the Major is made, which is, every Habit effective is an Art: And then with the Subject, and then the Minor, viz. Logick is a Habit Effective: From whence unavoidably will follow this Concluſion, viz. that Logick is an Art, &c. And thus much of the Matter, as well remote as proximate.
Ax. 9. The Syllogiſtick Form is only an apt Diſpoſition of the three Propoſitions for the neceſſary Collection of a Concluſion from the Premiſſes.
Ax. 10. Which Aptitude or Diſpoſition conſiſteth in Figure and Mode.
Ax. 11. A Figure is a legitimate Diſpoſition of the Medium with the Parts of the Queſtion.
Ax. 12. A Mode is a legitimate Determination of the Propoſitions according to Quantity and Quality.
1. §. For the Concluſion follows not from any Premiſſes at leaſt, not neceſſarily, but only thoſe that are affected with a certain Quantity, and after a certain Law and Manner are affirmed and denyed.
Ax. 13. Of Modes in Syllogiſm, ſome are direct, others inverſe, and indirect.
Ax. 14. Direct, thoſe in which the Major Extreme is collected of the Minor: as in this,
Every Man is an Animal.
Socrates is a Man.
And therefore Socrates is an Animal, &c.
Ax. 15. Invers'd on the contrary thoſe in which the Minor from the Major: as here,
Every Man is an Animal.
No Stone is a Man.
Some Animal therefore is not a Stone.
But of theſe Sorts of Modes there is but little or no Uſe.
Ax. 16. The Direct are either Univerſal or Singular.
Ax. 17. Univerſal are thoſe in which either both, or One of the Premiſſes are Univerſal, as here.
Every Animal lives.
Every Man is an Animal.
And therefore every Man lives, &c.
Or, Every Man is a Rational Animal.
Socrates is a Man.
And therefore Socrates is a Rational Animal, &c.
Ax. 18. Thoſe Singular, in which both Singular: as here.
Judas was a Wicked Man.
Judas was an Apoſtle.
Some Apoſtle therefore was a Wicked Man, &c.
But ſuch Argumentations as theſe Ariſtotle has not vouchſafed to call Syllogiſms, but only Expoſitions or Exhibitions; becauſe they expound the Neceſſity of the Sequel in Syllogiſms of the third Figure, and exhibit it to the Senſes. By the Peripateticks, his Followers, they are call'd Expoſitories, and by Ramus, proper, others ſingular Syllogiſms: But now of the three Figures in Syllogiſm with the Modes Univerſal and Singular which belong to them.