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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 so much time and painful attention upon a thing of so little real use? If I had lived in those ages when the knowledge of Aristotle's Organon entitled a man to the highest rank in philosophy, ambition might have induced me to employ upon it some years of painful study; and less, I conceive, would not be sufficient. Such reflections as these, always got the better of my resolution, when the first ardor began to cool. All I can say is, that I have read some parts of the different books with care, some slightly, and some 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 satisfied. 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 style, and often, I think, with affected obscurity; and all to prove general propositions, which when applied to particular instances appear self-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 syllogisms he claims as his own, and as the fruit of much time and labour. And indeed
it is a stately fabric, 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 resolve all reasoning into its simple ingredients.
The first book of the First Analytics, consisting of forty-six chapters, may be divided into four parts; the first treating of the conversion of propositions; the second, of the structure of syllogisms, in all the different figures and modes; the third, of the invention of a middle term; and the last, of the resolution of syllogisms. We shall give a brief account of each.
To convert a proposition, is to infer from it another proposition, 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 universal negative; thus, No man is a quadrųped; therefore, No quadruped is a man. 2. An universal 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 persons are men. When a proposition
may be converted without changing its quantity, this is called simple conversion; but when the quantity is diminished, as in the universal affirmative, it is called conversion per accidens.
There is another kind of conversion, omitted in this place by Aristotle, but supplied by his followers, called conversion by contraposition, in which the term that is contradictory to the predicate is put for the subject, and the quality of the proposition is changed; as, All animals are sentient ; therefore, What is insentient is not an animal. A fourth rule of conversion therefore is, That an universal affirmative, and a particular negative, may be converted by contraposition.
SECT. 2. Of the Figures and Modes of pure Syllogisms.
A syllogism is an argument, or reasoning, consisting of three propositions, the last of which, called the conclusion, is inferred from the two preceding, which are called the premises. The conclusion having two terms, a subject and a predicate, its predicate is called the major term, and its subject the minor term. In order to prove the conclusion, 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 premise is called the major premise, or the major proposition of the syllogism. The other premise must have for its two terms the minor term and the middle term, and it is called the minor proposition. Thus the syllogism consists of three propositions, distinguished by the names of the major, the minor, and the conclusion; and although 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 conclusion, and is also either the subject or predicate of the major proposition. The minor term is always the subject of the conclusion, and is also either the subject or predicate of the minor proposition. The middle term never enters into the conclusion, but stands in both premises, either in the position of subject or of predicate.
According to the various positions which the middle term may have in the premises, syllogisms are said to be of various figures. Now all the possible positions of the middle term are only four: for, first, it may be the subject of the major proposition, and the predicate of the minor, and then the syllogism is of the first figure; or it may be the predicate of both premises, and then the syllogism is of the second figure; or it may be the subject of both, which makes a syllogism of the third figure; or it may be the predicate of the major proposition, 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 division of syllogisms according to their modes. The mode of a syllogism is determined by the quality and quantity of the propositions of which it consists. Each of the three propositions must be either an universal affirmative, or an universal negative, or a particular affirmative, or a particular negative. These four kinds of propositions, as was before observed, have been named by the four vowels, A, E, I, O; by which means the mode of a syllogism is marked by any three of those four vowels, Thus A, A, A, denotes that mode in which the major, minor, and conclusion, are all universal affimatives; E, A, E, denotes that mode in which the major and conclusion are universal negatives, and the minor is an universal affirmative.
To know all the possible modes of syllogism, 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 sixty-four. So many possible modes there are in every figure; consequently in the three figures of Aristotle there are one hundred and ninety-two, and in all the four figures two hundred and fifty-six.
Now, the theory of syllogism requires, that we shew what are the particular modes in each figure, which do, or do not, form a just and conclusive syllogism,