or negative; as in this propofition, Whatever is infentient is not animal. 5. As there is one class of propofitions which have only two terms, to wit, one fubject and one predicate, which are called categorical propofitions; fo there are many claffes that have more than two terms. What Aristotle delivers in this book is applicable only to categorical propofitions; and to them only the rules concerning the converfion of propofitions, and concerning the figures and modes of fyllogifms, are accommodated. The fubfequent writers of logic have taken notice of some of the many claffes of complex propofitions, and have given rules adapted to them; but finding this work endless, they have left us to manage the reft by the rules of common fenfe.

CHAP.

III.

ACCOUNT OF THE FIRST ANALYTICS.

SECT. I. Of the Converfion of Propofitions.

IN attempting to give some account of the Ana

lytics and of the Topics of Ariftotle, ingenuity requires me to confefs, that though I have

often

Al

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 should 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 entitled 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. I can fay is, that I have read fome parts of the dif ferent books with care, fome flightly, and fome perhaps not at all. I 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 the most abftract nature, delivered in a laconic ftyle, and often, I think, with affected obfcurity; and all to prove general propofitions, which when applied to particular instances appear felf-evident.

1

There is probably but little in the Categories or in the book of Interpretation, that Ariftotle could claim as his own invention but the whole theory of fyllogifms 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 fomething however adapted to please the human understanding, or to flatter human pride, in a work which occupied men of fpeculation for more than a thousand 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 fecond, of the ftructure of fyllogifms, 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, whofe fubject is the predicate of the first, and whofe predicate is the fubject of the firft. 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 man. 2. An universal affirmative can be converted only into a particular affirmative: thus, All men are mortal; stherefore, Some mortal beings are men. 3. A particular affirmative may be converted into a particular affirmative as, Some men are juft; therefore, Some juft perfons are men, When a propofition

may

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 fubject, and the quality of the propofition is changed; as, All animals are sentient ; 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 fyllogifin is an argument, or reasoning, 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 fub. ject 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

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 fyllogum conuits of three propofitions, diftinguifhed, by the names of the major, the minor, and the conclufion: and although each of thefe has two terms, a fubject and a predicate, yet three are only three different terms in all. The major term is always the predicate of the conclufion, and is also either the subject 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 term never enters into the conclufion, but ftands in both premises, 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 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 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