term occurs in two of the propofitions, it must be precifely the fame in both: if it be not, the fyllogifm is faid to have four terms, which makes. a vitious fyllogifin. 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 premifes 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 fubject 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 special for the invention of a middle term; and this the author 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: thefe things collected together, are the materials from which your middle term is to be taken.

The fpecial rules require you to confider the quantity and quality of the propofition to be proved, that you may difcover in what mode and figure of fyllogifm the proof is to proceed. Then

from the materials before collected, you must seek 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 universal affirmative, I know by the rules of syllogifms, 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 must be the fubject of the major, and the predicate of the minor. Therefore of the terms collected according to the general 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 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 anfwering that end. And the rules are illuftrated, or rather, in my opinion, purpofely 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 those before laid down for constructing them. However it is treated of largely, and rules laid down for reducing reafon to fyllogifms, by supplying one of the premises when it is un

derstood,

derstood, 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 observed; and which he promifes to handle afterwards. But this promife is not fulfilled, as far as I know, in any of his works that are extant,

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 premises: in fome, 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 difputation, inftead of the rhetorical difputations which the fophifts were wont to ufe in more ancient times.

CHAP.

CHA P. IV.

REMARK S.

SECT. I. Of the Converfion of Propofitions.

WE have given a fummary view of the the

ory 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 fcience, to find fo 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 fhows a force of genius and labour of investigation, equal to the moft 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 demonftrations of the rules he mentions. As a fpecimen, I fhall give his demonftration of the first rule. Let A B be an universal negative propo"fition; I fay, that if A is in no B, it will fol"low that B is in no A. If you deny this con

fequence, 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 demonstration, if I understand 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.

fuppofition. If the third rule be affumed for proof of the first, the proof of all the three goes round in a circle; for the second and third rules are proved by the firft. This is a fault in reafoning which Ariftotle condemns, and which I fhould be very unwilling to charge him with, if I could find any better meaning in his demonstration. But it is indeed a fault very difficult to be avoided, when men attempt to prove things that are felf-evident.

The rules of converfion cannot be applied to all propofitions, but only to thofe that are categorical; and we are left to the direction of common fenfe in the converfion of other propofiti

ons.

To give an example: Alexander was the fon of Philip; therefore Philip was the father of Alexander: A is greater than B; therefore B is lefs than A. Thefe are converfions which, as far as I know, do not fall within any rule in logic; nor do we find any lofs for want of a rule in fuch cafes.

Even in the converfion of categorical propofitions, it is not enough to tranfpofe the fubject and predicate. Both must undergo fome change, in order to fit them for their new ftation, for in every propofition the fubject must be a fubftantive; and the predicate must be an adjective.Hence it follows, that when the subject is an individual, the propofition admits not of converfion. How, for inftance, fhall we convert this propofition, God is omnifcient?

Thefe obfervations fhow, that the doctrine of the converfion of propofitions is not fo complete as it appears. The rules are laid down without limitation; yet they are fitted only to one clafs of propofitions, to wit, the categorical; and of thefe only to fuch as have a general term for their fubject.

SECT.