CHA P. III.

Account of the First Analytics.

SECT. I. Of the Converfion of Propofitions.

IN attempting to give fome account of the Ana

lytics and of the Topics of Ariftotle, ingenuity requires me to confefs, that though I have often purposed to read the whole with care, and to understand what is intelligible, yet my courage and patience always failed before I had done. Why fhould I throw away fo much time and painful attention upon a thing of fo little real ufe? If I had lived in thofe ages when the knowledge of Ariftotle's Organon intitled a man to the highest rank in philofophy, ambition might have induced me to employ upon it fome years of painful ftudy; and lefs, I conceive, would not be fufficient. Such reflections as thefe, always got the better of my refolution, when the firft ardor began to cool. All I can fay is, that I have read fome parts of the different books with care, fome flightly, and fome perhaps not at all. have glanced over the whole often, and when any thing attracted my attention, have dipped into it till my appetite was fatisfied. Of all reading it is the moft dry and the most painful, employing an infinite labour of demonftration, about things of

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the most abstract nature, delivered in a laconic style, and often, I think, with affected obfcurity; and all to prove general propofitions, which when applied to particular inftances appear felf-evident.

There is probably but little in the Categories or in the book of Interpretation, that Aristotle could claim as his own invention: but the whole theory of fyllogifm he claims as his own, and as the fruit of much time and labour. And indeed it is a ftately fabric, a monument of a great genius, which we could wish to have been more ufefully employed. There must be something however adapted to please the human understanding, or to flatter human pride, in a work which occupied men of fpeculation for more than a thoufand years. These books are called Analytics, because the intention of them is to refolve all reafoning 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 fyllogifms in all the different figures and modes; the third, of the invention of a middle term; and the last of the refolution of fyllogifms. We fhall give a brief account of each.

man.

To convert a propofition, is to infer from it another propofition, whofe fubject is the predicate of the firft, and whofe predicate is the fubject of the first. This is reduced by Ariftotle 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 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 just; therefore, Some just perfons are men. When a propofition may be converted 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 subject, 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 réafoning, 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 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 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 the three propofitions, diftinguished by the names of the major, the minor, and the conclufion: and although 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,

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 subject 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 premises, fyllogifins are faid to be of various figures. Now all the poffible pofitions of the middle term are only four: for, firft, it may be the subject 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, 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 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 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

To know all the poffible modes of fyllogifm, 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 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 shew 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 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 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.

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. Thefe may, I think, be reduced to five. I. There must be only three terms in a fyllogifin. As each

term