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pofition, in which the term which is contradictory to the predicate is put for the fubject, and the quality of the propofition is changed; as, All animals are fentient; therefore, What is infentient is not an animal. A fourth rule of converfion therefore is, That an univerfal affirmative, and a particular negative, may be converted by contrapofition.

SECT. 2. Of the Figures and Modes of pure Syllogifms.

A fyllogifm is an argument, or reafoning, confifting of three propofitions, the last of which, called the conclufion, is inferred from the two preceding, which are called the premises. The conclufion having two terms, a fubject and a predicate, its predicate is called the major term, and its fubject the minor term. In order to prove the conclufion, each of its terms is in the premises compared with a third term, called the middle term. By this means one of the premises will have for its two terms the major term and the middle term; and this premife is called the major premife, or the major propofition of the fyllogifm. The other premife muft have for its two terms the minor term and the middle term, and it is called the minor propofition. Thus the fyllogifin confifts of three propofitions, diftinguished by the names of the major, the minor, and the conclufion and altho' each of these has two terms, a subject and a predicate, yet there are only three different terms in all. The major term is always the predicate of the conclufion, and is alfo either the fubject or predicate of the major propofition. The minor term is always the fubject of the conclufion, and is alfo either the fubject or predicate of the minor propofition. The middle term never enters into the conclufion, but flands in both premifes, either in the pofition of fubject or of predicate.

According to the various pofitions which the middle term may

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have in the premises, 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 firft figure; or it may be the predicate of both premifes, and then the fyllogifm is of the fecond figure; or it may be the fubject of both, be the which makes a fyllogifm of the third figure; or it may predicate of the major propofition, and the fubject of the minor, which makes the fourth figure. Aristotle 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 fyllogifms 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 propositions must be either an universal affirmative, or an univerfal negative, or a particular affirmative, or a particular negative. These 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 fyllogifin 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 fyllogifm, we must find how different combinations many be made of three out of the four may vowels, and from the art of combination the number is found to be fixty-four. So many poffible 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.

Now the theory of fyllogifm requires, that we fhew what are the particular modes in each figure, which do, or do not, form a

just

just 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 distinguishing 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 must be universal, and the minor affirmative; and it has this property, that it yields conclufions of all kinds, affirmative and negative, univerfal and particular.

The fecond figure has alfo four legitimate modes. Its major propofition must be univerfal, and one of the premises must 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.

Besides the rules that are proper to each figure, Aristotle has given fome that are common to all, by which the legitimacy of fyllogifins may be tried. Thefe 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 precisely 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 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 premises be negative. 5. No term can be taken universally in the conclufion, if it be not taken univerfally in the premises.

For understanding the fecond and fifth of these rules, it is necessary to obferve, that a term is faid to be taken univerfally, not

only

only when it is the fubject of an universal 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: thofe 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 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; first, That the predicate of the propofition to be proved can be univerfally affirmed of it; and, fecondly,

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 several

terms.

SECT. 4. Of the remaining part of the First 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 fyllogifins, by fupplying one of the premifes when it is understood, by rectifying inverfions, and putting the propositions 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 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 fyllogifins, and fhows, in twenty-feven chapters, how we may perform many feats by

them,

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