minor Premiss of the original Syllogism, and a false conclusion will be proved; e. g. bAr.

"All true patriots are friends to religion;

bA, All great statesmen are true patriots; r▲, All great statesmen are friends to religion :" for as this Conclusion is the Contradictory of the original minor Premiss, it must be false, since the Premises are always supposed to be granted; therefore one of the Premises (by which it has been correctly proved) must be false also; but the major Premiss (being one of those originally granted) is true; therefore the falsity must be in the minor Premiss; which is the contradictory of the original conclusion; therefore the original Conclusion must be true. This is the indirect mode of Reasoning. (See Rhetoric, Part I. Ch. ii. §1.)

$ 7.

This kind of Reduction is seldom employed but for Baroko and Bokardo, which are thus reduced by those who confine themselves to simple Conversion, and Conversion by limitation, (per accidens ;) and they framed the names of their Moods, with a view to point out the manner in which each is to be reduced; viz. B, C, D, F, which are the initial letters of all the Moods, indicate to which Mood of the first figure (Barbara, Celarent, Darii, and Ferio) each of the others is to be reduced: m indicates that the Premises are to

be transposed; s and p, that the Proposition denoted by the vowel immediately preceding, is to be converted; s, simply, p, per accidens, (by limitation :) thus, in Camestres, (see example, p. 87,) the C indicates that it must be reduced to Celarent; the two ss, that the minor Premiss and Conclusion must be converted simply; the m, that the Premises must be transposed. The P, in the mood Bramantip, denotes that the premises warrant a universal conclusion in place of a particular. I, though of course it cannot be illatively converted per accidens, viz: so as to become A, yet is thus converted in the Conclusion, because as soon as the premises are transposed (as denoted by the m,) it appears that a universal conclusion follows from them.

The

K (which indicates the reduction ad impossibile) is a sign that the Proposition, denoted by the vowel immediately before it, must be left out, and the contradictory of the Conclusion substituted; viz. for the minor Premiss in Baroko and the major in Bokardo. But it has been already shown, that the Conversion by contraposition (by negation) will enable us to reduce these two Moods, ostensively.*

*If any one should choose that the names of these moods should indicate this, he might make K the index of conversion by negation; and then the names would be, by a slight change, Fakoro and Dokamo.

CHAP. IV.

SUPPLEMENT TO CHAP. III.

Of Modal Syllogisms, and of all Arguments besides regular and Pure-Categorical Syllogisms.

Of Modals.
§ 1.

Hitherto we have treated of pure categorical Propositions, and the Syllogisms composed of such. A pure categorical proposition is styled by some logicians a proposition "de inesse," from its asserting simply that the Predicate is or is not (in our conception) contained in the Subject; as "John killed Thomas." A modal proposition asserts that the Predicate is or is not contained in the Subject in a certain mode or manner; as, "accidentally," "wilfully," &c.

A Modal proposition may be stated as a pure one, by attaching the Mode to one of the Terms: and the Proposition will in all respects fall under the foregoing rules; e. g. "John killed Thomas wilfully and maliciously;" here the Mode is to be regarded as part of the

Predicate.

"It is probable that all knowledge

is useful;" "probably useful" is here the Predicate. But when the Mode is only used to express the necessary, contingent, or impossible connexion of the Terms, it may as well be attached to the Subject: e. g. 66 man is necessarily mortal;" is the same as "all men are mortal:" "injustice is in no case expedient," corresponds to "no injustice is expedient:" and "this man is occasionally intemperate," has the force of a particular: (vide Chap. ii. § 2. note.) It is thus, and thus only, that two singular Propositions may be contradictories; e. g. "this man is never intemperate," will be the contradictory of the foregoing. Indeed every sign (of universality or particularity) may be considered as a Mode.

Since, however, in all Modal Propositions, you assert that the dictum (i. e. the assertion itself) and the Mode, agree together, or disagree, so, in some cases, this may be the most convenient way of stating a Modal, purely:

e. g. "It is impossible that all all men should

subject.

be virtuous." Such is a proposition of the

Apostle Paul's: "This is a faithful saying, &c.

subject.

that Jesus Christ came into the world to save

subj. sinners."

In these cases one of your Terms (the subject) is itself an entire Proposition.

In English, the word In is often used in expressing one proposition combined with another, in such a manner as to make the two, one proposition: e. g. "You will have a formidable opponent to encounter in the Emperor:" this involves two propositions; 1st, "You will have to encounter the Emperor;" 2d, "He will prove a formidable opponent:" this last is implied by the word in, which denotes (agreeably to the expression of Logicians mentioned above, when they speak of a proposition "de inesse") that that Predicate is contained in that Subject.

It may be proper to remark in this place, that we may often meet with a Proposition whose drift and force will be very different, according as we regard this or that as its Predicate. Indeed, properly speaking, it may be considered as several different Propositions, each indeed implying the truth of all the rest, but each having a distinct Predicate; the division of the sentence being varied in each case; and the variations marked, either by the collocation of the words, the intonation of the voice, or by the designation of the emphatic words, viz.: the Predicate, as scored under, or printed in italics. E. G. "The

H