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Ax. 1. OPposition of Enunciations, is either in- Truth or Appearance. And
Ax 2. A True Opposition is a Fight of Enunciati∣ons 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, al∣tho' false they may.
1 §. For Example; both these Enunciations, Eve∣ry Man is just; no Man is just, are false. But nei∣ther 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, in∣deed, 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 de∣fined, tho' before God it be certain and determi∣ned.
Ax. 9. An Opposition appearing is either Subcon∣trariety or Indefinite Opposition.
Ax. 10. Subcontrariety is between two Particu∣lars; Opposition Indefinite between two Infi∣nites.
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 Subcontra∣ties 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 Con∣tradictings, 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 Mat∣ter.
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 Sub∣ject: 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. Af∣ter 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 ne∣cessary Man should be an Animal. So are Impossible, not Impossible; Contingent not Contingent, op∣posed.
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 Neces∣sary 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; im∣possible 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 hap∣pen, that one playing at Dice may not win, &c.
Ax. 17. Now Enunciations that are Exclusive and Restrictive, receive Contradiction from a Negation ad∣ded 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 Con∣sequent with the Antecedent.
1. §. And therefore this, viz. if he is not misera∣ble, 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 mi∣serable, 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.
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.
Contra∣dictions
Contra∣dictions
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 Enun∣ciations; and in each of them, four Enunciations, according to the four Modes. First, The Enunciati∣ons 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 con∣tradictory 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
And thus far of the Thematick Part, which was in the first Place to be handl'd: Now follow Defi∣nition, Division, Syllogism, and Method; of which in the second Part we are to entreat.