Abstract of Logic, Book 1 · Chapter 32
CHAP. XXXII. Of Converſion, Aequipollence, and Subalternation of Enunciations.
Ax. 1. THoſe Affections are ſaid to be Related, which agree to Enunciations amongſt themſelves Compared.
Ax. 2. And theſe are four, viz. Converſion, Aequipollence, Subalternation and Oppoſition. And,
Ax. 3. Converſion is the Tranſpoſition ſaving the Truth of the Predicate into the Place of the Subject; and the Subject into the Place of the Predicate.
COMMENTARY.
1. §. In which Action the Truth muſt be ſaved, becauſe the Converſion is to follow from the Converted. Now this Related Affection of
Ax. 4. Converſion may be divided into Simple, that which is by Accident, and that which is by Contrapoſition.
Ax. 5. Simple's that in which the Quantity and Quality of the Enunciation are preſerved.
Ax. 6. And has Place in the Univerſal Denying, and Particular Affirming: As,
1. §. No Man is a Beaſt; and therefore no Beaſt is a Man: Some Man is white; and therefore ſomething white is a Man, &c.
Ax. 7. By Accident, that in which the Quality being preſerv'd, the Quantity is diminiſhed.
Ax. 8. And takes Place in the Univerſal Affirming.
1 §. Quantity diminiſh'd, that is, the Univerſal is chang'd into a Particular; as, Every Plant lives; and therefore ſomething which lives is a Plant, &c.
Ax. 9. Contrapoſition, that in which in Place of the Subject and the Predicate is put the Contradiction of them both.
Ax. 10. And has, Place in the Univerſal Affirming.
1 §. As every Mortal is generated; and therefore that which is not Generated, is not Mortal, &c.
Ax. 11. The particular Denying is not ordinarily converted.
1. §. For it does not follow, that becauſe ſome Animal is not a Man, that therefore ſome Man ſhould not be an Animal, &c. And if a particular Denying be at any time converted; as, ſome Man is not white, and therefore ſomething white not Man: It is fortuitous, and to be imputed to the Matter: As alſo that, ſometimes a Univerſal Affirming may be converted, ſaving the Quantity, to wit, when conſiſting of Reciprocal Terms: As, every Man is a Rational Animal, and therefore every Rational Animal is a Man, &c.
Ax. 12. But it muſt be obſerved in Converſion of Enunciations, that the whole Predicate muſt be changed into Place of the Subject. And likewiſe whole Subject into the Predicates, or elſe the Place of the Converſion may be fallacious.
1. §. For Example: This Enunciation, Some Church is in the City, muſt not be converted into this; Some City is in the Church; but this, Something which is in the City is a Church; becauſe the Predicate of the Enunciation to be converted, is not City, but, to be in it. In like manner, the Predicate of this Enunciation, Every old Man was a Boy's, not only Boy, but was a Boy. And therefore not to be converted into this, viz. Some Boy was an old Man; but this, viz. ſome one who was a Boy, is an Old Man, &c.
2. §. Now the Converſion of Modals is by means of the Dictum, the Mode ſtill remaining Enunciations neceſſary are converted as pure: Univerſals denying, and Particulars affirming, ſimply. Univerſals affirming either by Accident, or Contrapoſition; as, It is neceſſary that every Man ſhould be an Animal; and therefore that ſome, that is, that ſome Animal ſhould be a Man; or it is neceſſary, that that which is not an Animal, ſhould not be a Man, &c.
3 §. One thing is here to be obſerv'd, that thoſe Enunciations which have the Mode Neceſſary, be neceſſary of themſelves: For if they have not this Neceſſity, the Converſion will be falſe: As, it is neceſſary, that every old Man ſhould have been a Boy, and therefore that ſome one that was a Boy ſhould be an old Man. Every learned Perſon ſhould have been taught, and therefore that ſome one who has been taught ſhould be learned, &c. Such Converſions as theſe do not cohere; Becauſe that an old Man ſhould have been a Boy, or a learned Man taught, is not neceſſary of its ſelf, or abſolutely, but only of every one, becauſe by the Supernatural Power of God it might have been otherwiſe, &c. Converſion of Modals in the other Moods can not be preſcrib'd by any certain Rules: For thoſe things that Ariſtotle ſays in the firſt Book of Prior. Cap. 3. have more in them of Difficulty than Uſe.
As to the Aequipollency or like Value of Enunciations in Senſe, which differ in Words, which the Author ſays ſomething of, I thought it of little Significancy to be mentioned here; and therefore I paſs'd it by as well that of thoſe differing in Site of the Negative-Particle only, as Mood. The Rules about one and the other being no great Matter; and for that Aequipollencies of this Nature, may eaſily be diſcern'd without Rule.
Ax. 13. By Subalternation we expreſs our Meaning when we would ſignifie that one Enunciation is ſubordinated to another, and does neceſſarily follow from it, but not on the contrary, as Particulars and Singulars from Univerſals, to which they are indiſpenſably and neceſſarily ſubordinate.
1. §. For if every Man is Mortal, then alſo this or that Man muſt be ſure to be Mortal: And if none, then this or that Man to be ſure, is not ſo, &c.
2. §. In Modals, Subalternation is conſidered, not only in reference to the Dictum, but to the Mood. Alſo Subalternation of Dictum is the ſame in Modals as it is in the Pure: And the Modes of Poſſible and Contingent, are Subalternated to thoſe of Neceſſary and Impoſſible. For Neceſſary includes the Adverb always; whilſt Impoſſible, never: Which denote a Univerſality of Time. Contingent and Poſſible, ſometimes, which is a Note of Particularity of Time. And hence come we to the 33 Chapter, viz. That