years. These books are called Analytics, because the intention of them is to refolve all reasoning into its fimple ingredients.

The first book of the First Analytics, confifting of forty-fix chapters, may be divided into four parts; the first treating of the converfion of propofitions; the second, of the structure of fyllogisms in all the different figures and modes; the third, of the invention of a middle term; and the laft, of the refolution of fyllogifms. We fhall give a brief account of each.

To convert a propofition, is to infer from it another propofition, whose subject is the predicate of the firft, and whofe predicate is the subject of the first. This is reduced by Aristotle to three rules. 1. An univerfal negative may be converted into an univerfal negative: thus, No man is a quadruped; therefore, No quadruped is a man. 2. An univerfal affirmative can be converted only into a particular affirmative: thus, All men are mortal; therefore, Some mortal beings are men. 3. A particular affirmative may be converted into a particular affirmative: as, Some men are juft; therefore, Some just perfons are men. When a propofition may be conVOL. III. verted

Y y

verted without changing its quantity, this is called fimple converfion; but when the quantity is diminished, as in the univerfal affirmative, it is called converfion per accidens.

There is another kind of converfion, omitted in this place by Ariftotle, but fupplied by his followers, called converfion by contrapofition, in which the term that 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 laft 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

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 premises will have for its two terms the major term and the middle term; and this premite is called the major premise, 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 propositions, distinguished 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 ftands in both premifes; either in the pofition of fubject or of predicate.

According to the various pofitions which the middle term may have in the premifes, fyllogifms are faid to be of various figures. Now all the poffible positions 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 premises, and then the fyllogifm is of the second 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 fubject 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 muft be either an univerfal affirmative, or an universal 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,

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 universal affirmatives; E, A, E, denotes that mode in which the major and conclusion 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 fixtyfour. So many poffible modes there are in every figure, confequently in the three figures of Aristotle 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 fyllogifin, 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