fubject or predicate of the major propofition.

The

minor term is always the fubject of the conclufion, and is also either the fubject or predicate of the minor propofition. The middle terin never enters into the conclufion, but ftands in both premiffes, either in the pofition of fubject or of predicate.

According to the various pofitions which the middle term may have in the premiffes, fyllogifms are faid to be of various figures. Now all the poffible pofitions of the middle term are only four: for, first, it may be the fubject of the major propofition, and the predicate of the minor, and then the fyllogifm is of the first figure: or it may be the predicate of both premiffes, and then the fyllogifm is of the fecond figure; or it may be the fubject of both, which makes a fyllogifm of the third figure; or it may be the predicate of the major propofition, and the fubje&t of the minor, which makes the fourth figure. Ariftotle takes no notice of the fourth figure. It was added by the famous Galen, and is often called the Galenical figure.

There is another divifion of fyllogifins according to their modes. The mode of a fyllogifm is determined by the quality and quantity of the propofitions of which it confifts. Each of the three propofitions must be either an univerfal affirmative, or an univerfal negative, or a particular affirmative, or a particnlar negative. Thefe four kinds of propofitions, as was before obferved, have been named by the four vowels, A, E, I, O, by which means the mode of a fyllogifm is marked by any three of those four vowels. Thus, A, A, A, denotes that mode in.. which the major, minor, and conclufion, are all univerfal affirmatives; E, A, E, denotes that mode in which the major and conclufion are univerfal negatives, and the minor is an univerfal affirmative.

To know all the poffible modes of fyllogifin, we must find how many different combinations may be made of three out of the four vowels, and from the art of combination the number is found to be fixty-four. So many poflible modes there are in every figure, confequently in the three figures of Ariftotle there are one hundred and ninety-two, and in all the four figures two hundred and fifty-fix.

Book III. Now the theory of fyllogifm requires, that we fhew what are the particular modes in each figure, which do, or do not, form a juft and conclufive fyllogifm, that fo the legitimate may be adopted, and the fpurious rejected. This Ariftotle has fhewn in the first three figures, examining all the modes one by one, and paffing fentence upon each; and from this examination he collects fome rules which may aid the memory in diftinguishing the false from the true, and point out the properties of each figure.

The first figure has only four legitimate modes. The major propofition in this figure muft be universal, and the minor affirmative; and it has this property, that it yields conclufions of all kinds, affirinative and negative, univerfal and particular.

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

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

Befides the rules that are proper to each figure, Ariftotle 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 fyllogifm. As each 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 premifes. 3. Both premiffes muft 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 thefe 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 fpecial 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: those 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 discover in what mode and figure of fyllogifin 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 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 firft mode of the firft figure. I know likewife, that in this mode both the premiffes must be univerfal affirmatives; and that the middle term inuft 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 thefe 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 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 modés in which they may be proved, and the properties which the middle term must have to make it fit for answering

H 5

that

Book III. 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 Firft Book.

The refolution of fyllogifms requires no other principles but thofe before laid down for conftructing them. However it is treated of largely, and rules laid down for reducing reafoning 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 fyllogifins; which he acknowledges, cannot be refolved into any of the figures, although there be many kinds of them which 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 extant.

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

The second book treats of the powers of fyllogifms, and thows, 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 feveral diftinct conclufions may be drawn from the fame premifes in fome, true conclufions inay be drawn from falfe premifes: 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 dif tance as that he fhall never be obliged to yield. From which we learn, that Aristotle introduced in his own school, the practice of difputing fyllogiftically, inftead of the rhetorical difputations which the fophifts were wont to use in more ancient times.

CHAP.

WE

WE have given a fummary view of the theory of pure fyllogifms as delivered by Ariftotle, a theory of which he claims the fole invention. And I believe it will be difficult, in any science, to find fo large a fyftem of truths of fo very abftract and so 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.

46

As to the converfion of propofitions, the writers on łogic commonly fatisfy themselves with illuftrating each of the rules by an example, conceiving them to be felfevident when applied to particular cafes.. But Ariftotle has given demonftrations of the rules he mentions. As a fpecimen, I fhall give his demonstration of the first 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 fuppofi"tion 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. If the third rule be affùmed for proof of the first, the proof of all the three goes round in a circle; for the fecond 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 demonftration. 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 con

verfion