conceives to be of great utility. The general rules amount to this, That you are to confider well both terms of the propofition to be proved; their definition, their properties, the things which may be affirmed or denied of them, and thofe of which they may be affirmed or denied: these things collected together, are the materials from which your middle term is to be taken.

The special rules require you to confider the quantity and quality of the propofition to be proved, that you may discover in what mode and figure of fyllogifm the proof is to proceed. Then from the materials before collected, you must feek a middle term which has that relation to the fubject and predicate of the propofition to be proved, which the nature of the fyllogifm requires. Thus, fuppofe the propofition I would prove is an univerfal affirmative, I know by the rules of fyllogifms, that there is only one legitimate mode in which an univerfal affirmative propofition can be proved; and that is the first mode of the first figure. I know likewise, that in this mode both the premises must be universal affirmatives; and that the middle

term

term must be the subject of the major, and the predicate of the minor. Therefore of the terms collected according to the geneneral rule, I feek out one or more which have these two properties; firft, That the predicate of the propofition to be proved can be univerfally affirmed of it; and fecondly, That it can be univerfally affirmed of the subject of the propofition to be proved. Every term you can find which has those two properties, will ferve you as a middle term, but no other. In this way, the author gives fpecial rules for all the various kinds of propofitions to be proved; points out the various modes in which they may be proved, and the properties which the middle term must have to make it fit for answering that end. And the rules are illuftrated, or rather, in my opinion, purposely darkened, by putting letters of the alphabet for the feveral terms.

SECT. 4. Of the remaining part of the First Book:

The refolution of fyllogifms requires no other principles but thefe before laid down VOL. III. Z z

for

for constructing them. However it is treated of largely, and rules laid down for reducing reasoning to fyllogifms, by supplying one of the premises when it is understood, by rectifying inverfions, and putting the propofitions in the proper order.'

Here he speaks alfo of hypothetical fyllogifms; which he acknowledges cannot be refolved into any of the figures, although there be many kinds of them that ought diligently to be obferved; and which he promises to handle afterwards. But this promife is not fulfilled, as far as I know, in any of his works that are ex

tant.

SECT. 5. Of the Second Book of the First Analytics.

The fecond book treats of the powers of fyllogifms, and fhows, in twenty-feven chapters, how we may perform many feats by them, and what figures and modes are adapted to each. Thus, in fome fyllogifms several diftinct conclufions may be drawn from the fame premises in fome,

true

true conclufions may be drawn from false premises in fome, by affuming the conclufion and one premise, you may prove the other; you may turn a direct fyllogifm into one leading to an abfurdity.

We have likewife precepts given in this book, both to the affailant in a syllogistical difpute, how to carry on his attack with art, fo as to obtain the victory; and to the defendant, how to keep the enemy at fuch a distance as that he fhall never be obliged to yield. From which we learn, that Aristotle introduced in his own school, the practice of fyllogistical disputation, instead of the rhetorical difputations which the fophifts were wont to use in more ancient times.

CHA P. IV.

Remarks.

SECT. I. Of the Converfion of Propofitions.

WE

E have given a summary view of the theory of pure fyllogifms as delivered by Aristotle, a theory of which he

claims the fole invention. And I believe it will be difficult, in any science, to find so large a fyftem of truths of fo very abstract and fo general a nature, all fortified by demonstration, and all invented and perfected by one man. It shows a force of genius and labour of investigation, equal to the most arduous attempts. I fhall now make fome remarks upon it.

As to the converfion of propofitions, the writers on logic commonly fatisfy themselves with illuftrating each of the rules by an example, conceiving them to be felf-evident when applied to particular cafes. But Ariftotle has given demonstrations of the rules he mentions. As a fpecimen, I fhall give his demonftration of the firit rule.. "Let A B be an univerfal "negative propofition; I fay, that if A is "in no B, it will follow that B is in no A. "If you deny this confequence, let B be

in fome A, for example, in C; then the "firft fuppofition will not be true; for "C is of the B's." In this demonftration, if I underfland it, the third rule of converfion is affumed, that if B is in fome. A, then A must be in fome B, which indeed is contrary to the first fuppofition. If

the