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removed by his followers. For, 1. There are propofitions in which it is difficult to find a fubject and a predicate; as in these, It rains, It fnows. 2. In fome propofitions either term may be made the subject or the predicate as you like beft; as in this, Virtue is the road to happiness. 3. The fame example may ferve to fhew, that it is fometimes difficult to fay, whether a propofition be universal or particular. 4. The quality of fome propofitions is fo dubious, that logicians have never been able to agree whether they be affirmative or negative; as in this propofition, Whatever is infentient is not an 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; so 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 conversion of propofitions, and concerning the figures and modes of fyllogifins, are accommodated. The subsequent 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 endlefs, they have left us to manage the reft by the rules of common fenfe.

CHAP.

С НА Р. III.

Account of the First Analytics.

Ν

SECT. I. Of the Converfion of Propofitions.

IN attempting to give fome account of the Analytics and of the Topics of Ariftotle, ingenuity requires me to confefs, that tho' 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 those ages when the knowledge of Aristotle's Organon intitled a man to the highest rank in philosophy, ambition might have induced me to employ upon it fome years painful study; and lefs, I conceive, would not be fufficient. Such reflections as these, always got the better of my refolution, when the first ardor began to cool. All I can fay is, that I have read some parts of the different 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 most dry and, the most painful, employing an infinite labour of demonstration, about things of the most abstract nature, delivered in a laconic ftyle, and often, I think, with affected obfcurity; and all to prove general propofitions, which when applied to particular inftances appear felf-evident.

VOL. II.

B b

There

There is probably but little in the Categories, or in the book of Interpretation, which 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 fabrick, a monument of a great genius, which we could wish to have been more usefully employed. There must be something however adapted to please the human understanding, or to flatter human pride, in a work which occupied men of speculation 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 second, of the structure 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 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 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 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 conversion, omitted in this place by Ariftotle, but fupplied by his followers, called converfion by contra

pofition,

pofition, in which the term which 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 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 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 premise 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 thefe 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 다 also either the subject 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 stands in both premifes, either in the position of fubject or of predicate.

According to the various pofitions which the middle term may

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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, 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 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 subject 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 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 observed, 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 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 combation 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

just

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