Abstract of Logic, Book 2 · Chapter 12
CHAP. XII. Of Syllogiſm Hypothetical, Disjunctive and Relative.
Ax. 1. IN the third Place a Syllogiſm may be divided into Simple and Compoſed. A Simple is that which neither conſiſts of Compoſed Propoſitions, nor yet can be reſolved into more Syllogiſms.
Ax. 2. A Compoſed is that in the which either one or both of the Premiſſes are compoſed, or elſe is made up of more Syllogiſms than one.
Ax. 3. That of the firſt Nature, viz. that in which either one or both of the Premiſſes are compoſed, is either Hypothetical, Disjunctive or Relative.
Ax. 4. Hypothetical is that in which either the Major, or Minor, or both, are Hypothetical.
Ax. 5. If only the Major, then the Concluſion is Categorical: But if the Minor, then the Concluſion, of Neceſſity muſt be Hypothetical too.
COMMENTARY.
1. §. As every Compoſed Enunciation is vulgarly called Hypothetical, ſo is alſo every Syllogiſm in which either one or both of its Propoſitions are ſo too. But add we now Examples of Hypothetical or Suppoſition-Syllogiſms, as follows, viz.
1. If God is, the World is rul'd by a Providence;
But God is:
And Therefore the World is rul'd by a Providence.
2. Whatſoever is nouriſhed, has Heterogeneous Parts;
But if a Stone lives, it is nouriſhed:
And therefore if a Stone lives, it has Heterogeneous Parts.
3. If a Man feels, he alſo lives;
But if a Man be an Animal, he feels:
And therefore if a Man be an Animal, be alſo lives, &c.
Ax. 6. Now of Hypothetical Syllogiſms, in which the Major is ſo, there are two Moods well concluding; the firſt from the Poſition of the Antecedent to the Poſition of the Conſequent; and the ſecond from the Remotion of the Conſequent to the Remotion of the Antecedent.
Ax. 7. And as many Fallacious, viz. the firſt from the Remotion of the Antecedent to the Remotion of the Conſequent; and the ſecond from the Poſition of the Conſequent, to the Poſition of the Antecedent, &c.
1. §. Now to Poſit, or put the Antecedent or Conſequent, is no more than to aſſume it; ſaving its Quality, that is, to affirm the Affirmed, or deny the Denyed. On the contrary to remove, only to aſſume the Contradiction of them, that is, to affirm the Denyed, or deny the Affirmed Contradictorily, &c. As for Example;
1. If a Man feels, he is an Animal;
But a Man feels:
And therefore he is an Animal.
2. If Stones live, they are nouriſhed;
But Stones are not nouriſhed:
And therefore they do not live.
Of theſe the firſt proceeds the firſt way, viz. from a Poſition of the Antecedent, to a Poſition of the Conſequent; that is, aſſumes the Antecedent of the Major Hypothetical and infers from thence its Conſequent; the latter, the other; that is, from the Remotion of the Conſequent to the Remotion of the Antecedent; that is, aſſumes the Contradiction of the Conſequent, and from thence infers the Contradiction of the Antecedent. But now in Diſputations in which we ſtudy Brevity, when we would infer the Conſequent from the Antecedent; propoſing only the Major, we ſay, But the Antecedent is true; and therefore the Conſequent: Or if out of the Conſequent the Antecedent, the Conſequent is falſe; and therefore the Antecedent, or the latter is ſo, and therefore the former, &c. But,
2. Add we Examples now of Vicious Syllogiſms.
1. If a Plant is an Animal, it lives;
But a Plant is not an Animal:
And therefore a Plant does not live.
2. If a Plant is an Animal, it lives;
But a Plant lives:
And therefore a Plant is an Animal, &c.
Now of theſe the firſt is Vicious; becauſe it proceeds from a Remotion of the Antecedent; and the other, becauſe from a Poſition of the Conſequent.
But this alſo is Vicious.
3. If every Animal is Rational, then every Beaſt is Rational.
But no Beaſt is Rational.
And therefore no Animal is Rational.
Now this is ſo, not for the Reaſons before, but, becauſe the Minor is contrary to the Conſequent, and Concluſion to the Antecedent, but not Contradictory. For it ought to have been this; and therefore ſome Animal is not Rational, &c. For this it is to remove the Antecedent, as we have ſaid before: The Way of making theſe Syllogiſms Categorical may be better fetch'd from the Original.
Ax. 8. The Disjunctive Syllogiſm is only that whoſe Major Propoſition is Disjunctive.
Ax. 9. Which if conſiſting of two Members immediately oppoſed, may proceed from a Poſition of one Member to an Everſion of the other, or from an Everſion of one to a Poſition of the other.
1. §. As for Example; from this Poſition, Or it is Day, or it is Night, may be inferred, that it is Day, and therefore not Night; or it is Night, and therefore not Day; or it is not Day, and therefore it is night; or it is not Night, and therefore it is Day, &c.
Ax. 10. Now if the Major Disjunctive have more than two, that is, more than two Members or Parts, the reſt taken away, what is left of them is concluded.
1. §. As, it is Winter, or Summer, or Spring, or Autumn.
But not Winter, or Autumn, or Summer:
And therefore Spring, &c.
But if the Members of ſuch a Propoſition are not oppoſed, or not fully numbered up, the Syllogiſm will then be Vicious; as this,
Either he is a Lawyer, or a Phyſician, or a Philoſopher;
But not a Lawyer or a Phyſician;
And therefore a Philoſopher, &c.
In which the Illation's falſe; becauſe to be a Lawyer or a Phyſician, or a Philoſopher, are not oppoſed; becauſe the ſame Perſon may be one as well as the other; and then the Members are not fully number'd up; becauſe a Man may be, neither as he who is either unlearned, or a Theologer, or a Philologer, &c.
Ax. 11. Now when it happens that the two, or all the Members being removed, the Whole alſo is removed; the Syllogiſm is then a Syllogiſm of Enumeration of Parts.
1. §. For Example; He that does Injury, does it either by Theft, Adultery, or Contumely, or ſome ſuch Way: But no body ſteals of his own, commits Adultery upon himſelf, or caſts Reproaches upon himſelf: And therefore no body does Injury to himſelf, &c.
Ax. 12. A Syllogiſm Disjunctive is then made an Hypothetical, when the Major Disjunctive is ſo.
1. §. For Example; this Propoſition, either it is Day, or it is Night, may be chang'd into an Hypothetical, thus, viz. If it is Day, it is not Night; or if it is Night, it is not Day, &c.
Ax. 13. A Relative is that whoſe Major is compoſed of a Relation of Parts; as this.
There …where Chriſt is, there will alſo the Faithful be;
But Chriſt is in Heaven:
And therefore there alſo will the Faithful be.
Hitherto appertain likewiſe the Proportional Syllogiſms. As for Example this:
As two are in Reſpect of four, ſo three are in reſpect of ſix.
But two are in reſpect of four, as the half is in reſpect of the whole:
And therefore three are in reſpect of ſix, as the half is in reſpect of the whole,
And thus far of Syllogiſms that conſiſt of Compoſed Propoſitions. Now of thoſe that are compoſed of many Syllogiſms.