collects fome rules which may aid the memory in diftinguishing the falfe from the true, and point out the properties of each figure.

The firft figure has only four legitimate modes. The major propofition in this figure must be univerfal, and the minor affirmative; and it has this property, that it yields conclufions of all kinds, affirma tive and negative, univerfal and particular.

The fecond figure has alfo four legiti mate modes. Its major propofition must be univerfal, and one of the premises muft be negative. It yields conclufions both univerfal and particular, but all negative.

The third figure has fix legitimate modes. Its minor must always be affirmative; and it yields conclufions both affirmative and negative, but all particular.

Befides the rules that are proper to each figure, Aristotle has given fome that are common to all, by which the legitimacy of fyllogifms may be tried. These may, I think, be reduced to five. 1. There must be only three terms in a fyllogifin. As each term occurs in two of the propofitions, it must be precisely the fame in both if it be not, the fyllogifin is said to

have four terms, which makes a vitious fyllogifm. 2. The middle term must be taken univerfally in one of the premises. 3. Both premises 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 premises 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 affirma¬ tive 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 fubject and predicate of the proposition 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 likewife, 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; firft, That the predicate of the propofition to be proved can be univerfally affirmed of it; and secondly, That it can be univerfally affirmed of the fubject 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 illustrated, or rather, in my opinion, purposely darkened, by putting letters of the alphabet for the several 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 reafoning to fyllogifms, by supplying one of the premises when it is understood, by rectifying inversions, 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 Firfi Analytics.

powers of

The fecond book treats of the 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