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 premifes, compared with a third term, called the middle term. By this means one of the premifes 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 premise must have for its two terms the minor term and the middle term, and it is called the minor propofition. Thus the fyllogifm confifts of three propofitions, distinguished by the names of the major, the minor, and the conclufion and altho' each of these has two terms, a fubject 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 ftands in both premifes, either in the pofition of fubject or of predicate.

According

According to the various pofitions which the middle term may 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 fyllogism is of the first figure; or it may be the predicate of both premises, and then the fyllogifm is of the fecond figure; or it may be the subject of both, which makes a fyllogifm of the third figure; or it may be the predicate of the major propofition, and the subject 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 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 propofitions must be either an univerfal 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 fyllogifm is marked by any three of thofe 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 fyl- . logifm, 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 fixtyfour. 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 juft and conclufive fyllogifm, that so the legitimate may be adopted, and the fpuri ous rejected. This Ariftotle has fhewn in figures, examining all the

the first three

modes one by one, and paffing fentence upon each; and from this examination he

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

The first figure has only four legitimate modes. The major propofition in this fi figure must be univerfal, 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 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 fyllogifins may be tried. Thefe may, I think, be reduced to five. 1. There muft be, only three terms in a fyllogifin. 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
fyllogifm. 2. The middle term must be
taken univerfally in one of the premiles.
3. Both premises 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 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 thefe rules, it is neceffary to obferve,
that a term is faid to be taken univerfally,
not only when it is the subject of an uni-
verfal propofition, but when it is the pre-
dicate of a negative propofition; on the o-
ther hand, a term is faid to be taken. par-
ticularly, when it is either the subject of a
particular, or the predicate of an affirma-
tive propofition.

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

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

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