Abstract of Logic, Book 1 · Chapter 33
CHAP. XXXIII. Of Oppoſition of Enunciations.
Ax. 1. OPpoſition of Enunciations, is either in- Truth or Appearance. And
Ax 2. A True Oppoſition is a Fight of Enunciations in Affirming and Denying. Now
Ax. 3. Enunciations are ſaid to fight, in which the ſame, of the ſame, according to the ſame, to the ſame, in the ſame manner and time, is Affirmed and Denyed.
Ax. 4. True Oppoſition afore-mentioned is either Contrariety or Contradiction.
Ax. 5. Contrariety that which is between Two Univerſals.
Ax. 6. Of which both may not be together true, altho' falſe they may.
1 §. For Example; both theſe Enunciations, Every Man is juſt; no Man is juſt, are falſe. But neither theſe nor any other Contraries can be together true; becauſe thoſe things which are both at the ſame time true, are not truly oppoſed.
Ax. 7. A Contradiction is an Oppoſition between one Univerſal and a Particular; or two Singulars.
Ax. 8. Of which the one is always true, and the other falſe.
1. §. As, Every Man is juſt, every Man not juſt; no Man is juſt, ſome Man is; Ariſtides is juſt, Ariſtides not juſt, &c. Of theſe the one is true, and the other falſe; and ſo in other Inſtances of the like Nature, the ſame. In Singulars of future Contingents, indeed, it appears not to Man, which of the two is true, which falſe: But yet this is evident, that both cannot be together true, nor both falſe. For Example: One of theſe is true, that a Player at Dice will win or loſe; but whether, cannot by Man be defined, tho' before God it be certain and determined.
Ax. 9. An Oppoſition appearing is either Subcontrariety or Indefinite Oppoſition.
Ax. 10. Subcontrariety is between two Particulars; Oppoſition Indefinite between two Infinites.
Ax. 11. Both of which may be together true, but not falſe.
1 §. Subcontraries are, Some Man is juſt, ſome Man is not juſt: Of theſe both are true: For Ariſtides was juſt, Verres not juſt; but not falſe: For if Subcontraties might be together falſe, then Contraries might be together true; becauſe Contraries, the Negation added, or taken away, contradict Subcontraries. Indefinite Oppoſitions are much the ſame with Contradictings, For the one is always true, the other falſe. But this proceeds not from the Form of the Oppoſition, but the particular Condition of the Matter.
2 §. Subcontraries are ſaid to be in Appearance oppos'd not Truth, both becauſe they may be together true; as alſo, becauſe they have not the ſame Subject: For when I ſay ſome Man is juſt, ſome Man not juſt, I underſtand not in both the ſame Perſon; or if I do, it will be a Contradiction of Singulars. After the ſame Manner, is the Ratio of Indefinitely oppoſed.
Ax. 12. Contradiction in Modals conſiſts in the Affirmation and Negation of the Mood in the ſame Dictum.
As it is neceſſary Man ſhould be an Animal; not neceſſary Man ſhould be an Animal. So are Impoſſible, not Impoſſible; Contingent not Contingent, oppoſed.
Ax. 13. Contrariety of them conſiſts Part in the Dictum, Part in the Mode.
Ax. 14. By reaſon of the Dictum, thoſe Enunciations are contrary; both which have the Mode Neceſſary or Impoſſible; if in one the Dictum be affirmed, the other denyed.
1 §. As it is neceſſary Man ſhould be an Animal, it is neceſſary Man ſhould not be an Animal; impoſſible Man ſhould be a Stone, impoſſible Man ſhould not be a Stone, &c.
Ax. 15. By reaſon of Mode, two, the one of which has the Mode neceſſary, the other impoſſible; if the Dictum of both be of the ſame Quality.
1. §. As, it is neceſſary Man ſhould be an Animal, impoſſible he ſhould be ſo.
Ax. 16. Subcontraries are two, having the Mode Poſſible or Contingent, if in one the Dictum be affirmed, the other denyed.
1 §. As, It is poſſible, or may happen that one Playing at Dice, may win; it is poſſible, or may happen, that one playing at Dice may not win, &c.
Ax. 17. Now Enunciations that are Excluſive and Reſtrictive, receive Contradiction from a Negation added to the Excluſive or Reſtrictive Particles.
1. §. As only Faith juſtifies, Faith only does not juſtifie; or, Man is Mortal as to his Soul; Man is Mortal, but not as to his Soul, &c.
Ax. 18. Contradiction of Compoſed is plac'd in that Negation, which appertains to the Connection of the Conſequent with the Antecedent.
1. §. And therefore this, viz. if he is not miſerable, he is yet vain, and of a lying Tongue, is thus everted by Virgil, Book 2. of Aenaeids. Nec ſi miſerum fortuna Sinonem, &c. That is, Nor yet, if hard Fortune has made him miſerable, has ſhe alſo made him a Lyer too. Which you may thus reſolve: Nor if Sinon be made miſerable, is he alſo vain, and of a lying Tongue, &c. And ſo of all other the like.
But that the Aequipollency, Subalternation, and Oppoſition of Enunciations may the better appear, behold a Diagram in which they may be ſeen at one View.
DIAGRAM.
Aequipollents
1.
A- It is impoſſible to be.
MA- It may happen to be.
BI- It is not impoſſible to be.
MUS.- It is not neceſſary not to be.
Subcontraries.
Aequipollents.
2.
E- It is poſſible not to be.
DEN- It may happen not to be.
TU- It's not impoſſible not to be.
LI.- It's not neceſſary it ſhou'd be.
Subalterns.
Contradictions
Contradictions
Subalterns.
Aequipollents.
4.
PUR- It is not impoſſible it ſhould not be.
PU- It cannot happen not to be.
RE- It is impoſſible not to be.
A.- It is neceſſary it ſhould be.
Contraries.
Aequipollents.
3.
I- It is not poſſible to be.
LI- It cannot happen to be.
A- It is impoſſible to be.
CE- It is neceſſary it ſhould not be.
In which are to be obſerved four Claſſes of Enunciations; and in each of them, four Enunciations, according to the four Modes. Firſt, The Enunciations of the ſame Claſs are Aequipollents. Secondly, The Enunciations of the Firſt, are ſubordinated to thoſe of the Fourth; and thoſe of the Second to thoſe of the Third. Thirdly, the Enunciations of the Firſt and Third, as alſo the Second and Fourth, are contradictory to each other. Fourthly, thoſe of the Third and Fourth are Contraries, by reaſon either of their Dictum or Mood. Fifthly, the Enunciations of the Firſt and Second, are Subcontraries. Sixthly, The Vowels of the Words which are prefix'd to each Claſs, denote the Quality of the Dictum and Mood; as,
AEIU
Denotes
The Dictum and Mood to be affirm'd.
The Dictum to be deny'd and Mood affirm'd.
The Dictum to be affirm'd, and Mood deny'd.
The Dictum and the Mood both to be deny'd.
And thus far of the Thematick Part, which was in the firſt Place to be handl'd: Now follow Definition, Diviſion, Syllogiſm, and Method; of which in the ſecond Part we are to entreat.
The End of the Firſt Book.