which we may add, a question, a command, a promife, a contract, and many others. Thefe Aristotle pronounces to have nothing to do with his fübject, and remits them to oratory, or poetry; and fo they have remained banished from the regions of philosophy to this day: yet I apprehend, that an analysis of such fpeeches, and of the operations of mind which they exprefs, would be of real ufe, and perhaps would difcover how imperfect an enumeration the logicians have given of the powers of human understanding, when they reduce them to fimple apprehenfion, judgement, and reasoning.

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SECT. 6. On Propofitions.

Mathematicians ufe the word propofition in a larger sense than logicians. A problem is called a propofition in mathematics, but in logic it is not a propofition: it is one of those speeches which are not enunciative, and which Aristotle remits to oratory or poetry.

A propofition, according to Ariftotle, is a fpeech wherein one thing is affirmed or denied of another. Hence it is easy to diftinguish the thing affirmed or denied, which is called the predicate, from the thing of which it is affirmed or denied, which is called the fubject; and these two are called the terms of the propofition. Hence likewife it appears, that propofitions are either affirmative or negative; and this is called their quality. All affirmative propofitions have the fame quality, so likewise have all the negative; but an affirmative and a negative are contrary in their quality.

When the subject of a propofition is a general term, the predi cate is affirmed or denied, either of the whole, or of a part. Hence propofitions are diftinguished into univerfal and particular. All men are mortal, is an universal propofition; Some men are learn

ed,

ed, is a particular, and this is called the quantity of the propofition. All univerfal propofitions agree in quantity, as alfo all particular: while an univerfal and a particular are faid to differ in quantity. A propofition is called indefinite, when there is no mark either of univerfality or particularity annexed to the fubject: thus, Man is of few days, is an indefinite propofition; but it must be understood either as universal or as particular, and therefore is not a third fpecies, but by interpretation is brought under one of the other two.

There are alfo fingular propofitions, which have not a general term but an individual for their fubject; as, Alexander was a great conqueror. These are confidered by logicians as univerfal, because, the fubject being indivifible, the predicate is affirmed or denied of the whole, and not of a part only. Thus all propofitions, with regard to quality, are either affirmative or negative; and with regard to quantity, are univerfal or particular; and taking in both quantity and quality, they are univerfal affirmatives, or univerfal negatives, or particular affirmatives, or particular negatives. These four kinds, after the days of Ariftotle, came to be named by the names of the four firft vowels, A, E, I, O, according to the following distich:

Afferit A, negat E, fed univerfaliter ambe ;

Afferit I, negat 0, fed particulariter ambo.

When the young logician is thus far instructed in the nature of propofitions, he is apt to think there is no difficulty in analysing any proposition, and fhewing its subject and predicate, its quantity and quality; and indeed, unless he can do this, he will be unable to apply the rules of logic to use. Yet he will find, there are fome difficulties in this analysis, which are overlooked by Aristotle altogether; and altho' they are fometimes touched, they are not

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removed

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 best; 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 clafs 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 Ariftotle 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 fyllogifms, are accommodated. The fubfequent writers of logic have taken notice of some of the many classes 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.

CHA P.

Ν

SECT. I. Of the Converfion of Propofitions.

IN attempting to give some account of the Analytics and of the Topics of Aristotle, 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 Ariftotle'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 thefe, always got the better of my refolution, when the first 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. 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 demonftration, 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 inflances appear felf-evident.

VOL. II.

B b

There

There is probably but little in the Categories, or in the book of Interpretation, which Aristotle could claim as his own invention: but the whole theory of fyllogifins he claims as his own, and as the fruit of much time and labour. And indeed it is a stately 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 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 fyllogifms in all the different figures and modes; the third, of the invention of a middle term; and the last, of the resolution of fyllogifins. 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 first, and whose predicate is the subject of the first. This is reduced by Aristotle to three rules. 1. An universal 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 juft 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 contra

pofition,