have four terms, which makes a vitious fyllogifm. 2. The middle term must be taken univerfally in one of the premises. 3. Both premifes must not be particular propofitions, nor both negative. 4. The conclufion must be particular, if either of the premises be particular; and negative, if either of the premifes be negative. 5. No term can be taken univerfally in the conclufion, if it be not taken univerfally in the premises.

For understanding the fecond and fifth of these rules, it is neceffary to obferve, that a term is faid to be taken univerfally, not only when it is the fubject of an univerfal propofition, but when it is the predicate of a negative propofition; on the other hand, a term is faid to be taken particularly, when it is either the subject of a particular, or the predicate of an affirmative propofition.

SECT. 3. Of the Invention of a Middle Term.

The third part of this book contains rules general and fpecial for the invention. of a middle term; and this the author conceives

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 those 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 subject and predicate of the proposition to be proved, which the nature of the fyllogifm requires. Thus, suppose 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 univerfal affirmatives; and that the middle

term

term must be the fubject 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; first, 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 fubject of the propofition to be proved. Every term you can find which has thofe 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 fyllogifins requires no other principles but thefe before laid down. Z z

VOL. III.

for

for conftructing them.

However it is

treated of largely, and rules laid down for reducing reasoning to fyllogifms, by fupplying 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 promise 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 fyllogifins feveral diftinct conclufions may be drawn from the fame premifes: in fome,

true

true conclufions may be drawn from falfe premises in fome, by affuming the conclufion and one premife, 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 fyllogiftical 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 Ariftotle introduced in his own fchool, the practice of fyllogiftical disputation, inftead 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 have given a fummary view of the theory of pure fyllogifms as delivered by Aristotle, a theory of which he