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• Book III: Progress of Sciences
• Preface
• Sketch I: Principles and Progress of Reason
• Section I: Principles of Reason.
• Section II: Progress of Reason.
• Appendix: a Brief Account of Aristotle’s Logic. With Remarks.
• Chapter I.: Of the First Three Treatises.
• Chapter II.: Remarks.
• Chapter III.: Account of the First Analytics. 20
• Chapter IV.: Remarks.
• Chapter V.: Account of the Remaining Books of the Organon.
• Chapter VI.: Reflections On the Utility of Logic, and the Means of Its Improvement.
• Sketch II: Principles and Progress of Morality
• Part I: Principles of Morality
• Section I: Human Actions Analysed.
• Section II: Division of Human Actions Into Right, Wrong, and Indifferent.
• Section III: Laws of Nature Respecting Our Moral Conduct In Society.
• Section IV: Principles of Duty and of Benevolence.
• Section V: Laws Respecting Rewards and Punishments.
• Section VI: Laws Respecting Reparation.
• Section VII: Final Causes of the Foregoing Laws of Nature.
• Section VIII: Liberty and Necessity Considered With Respect to Morality.
• Appendix: Upon Chance and Contingency.
• Part II: Progress of Morality
• Sketch III: Principles and Progress of Theology
• Chapter I.: Existence of a Deity.
• Chapter II.: Progress of Opinions With Respect to Deity.
• Chapter III.: Religious Worship.
• Section I: Religious Worship Respecting the Deity Singly. 15
• Section II: Morality Considered As a Branch of Duty to Our Maker.
• Appendix: Sketches Concerning Scotland
• Sketch I: Scotch Entails Considered In Moral and Political Views 1
• Sketch II: Government of Royal Boroughs In Scotland
• Sketch III: Plan For Improving and Preserving In Order the Highways In Scotland
• Latin Tags and Phrases

CHAPTER III.

Account of the First Analytics.20

SECTION 1

Of the Conversion of Propositions.

In attempting to give some account of the Analytics and of the Topics of Aristotle, ingenuity requires me to confess, 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 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 intitled 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 quadruped; 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 con-verted 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.

SECTION 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 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 altho’ 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 affirmatives; 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, that so the legitimate may be adopted, and the spurious rejected. This Aristotle has shewn in the first three figures, examining all the modes one by one, and passing sentence upon each; and from this examination he collects some rules which may aid the memory in distinguishing the false from the true, and point out the properties of each figure.

The first figure has only four legitimate modes. The major proposition in this figure must be universal, and the minor affirmative; and it has this property, that it yields conclusions of all kinds, affirmative and negative, universal and particular.

The second figure has also four legitimate modes. Its major proposition must be universal, and one of the premises must be negative. It yields conclusions both universal and particular, but all negative.

The third figure has six legitimate modes. Its minor must always be affirmative; and it yields conclusions both affirmative and negative, but all particular.

Besides the rules that are proper to each figure, Aristotle has given some that are common to all, by which the legitimacy of syllogisms may be tried. These may, I think, be reduced to five. 1. There must be only three terms in a syllogism. As each term occurs in two of the propositions, it must be precisely the same in both: if it be not, the syllogism is said to have four terms, which makes a vitious syllogism. 2. The middle term must be taken universally in one of the premises. 3. Both premises must not be particular propositions, nor both negative. 4. The conclusion must be particular, if either of the premises be particular; and negative, if either of the premises be negative. 5. No term can be taken universally in the conclusion, if it be not taken universally in the premises.

For understanding the second and fifth of these rules, it is necessary to observe, that a term is said to be taken universally, not only when it is the subject of an universal proposition, but when it is the predicate of a negative proposition; on the other hand, a term is said to be taken particularly, when it is either the subject of a particular, or the predicate of an affirmative proposition.

SECTION 3

Of the Invention of a Middle Term.

The third part of this book contains rules general and special for the invention of a middle term; and this the author conceives to be of great utility. The general rules amount to this, That you are to consider well both terms of the proposition to be proved; their definition, their properties, the things which may be affirmed or denied of them, and those of which they may be affirmed or denied: these things collected together, are the materials from which your middle term is to be taken.

The special rules require you to consider the quantity and quality of the proposition to be proved, that you may discover in what mode and figure of syllogism the proof is to proceed. Then from the materials before collected, you must seek a middle term which has that relation to the subject and predicate of the proposition to be proved, which the nature of the syllogism requires. Thus, suppose the proposition I would prove is an universal affirmative, I know by the rules of syllogisms, that there is only one legitimate mode in which an universal affirmative proposition can be proved; and that is the first mode of the first figure. I know likewise, that in this mode both the premises must be universal affirmatives; and that the middle term must be the subject of the major, and the predicate of the minor. Therefore of the terms collected according to the general rule, I seek out one or more which have these two properties; first, That the predicate of the proposition to be proved can be universally affirmed of it; and secondly, That it can be universally affirmed of the subject of the proposition to be proved. Every term you can find which has those two properties, will serve you as a middle term, but no other. In this way, the author gives special rules for all the various kinds of propositions to be proved; points out the various modes in which they may be proved, and the properties which the middle term must have to make it fit for answering that end. And the rules are illustrated, or rather, in my opinion, purposely darkened, by putting letters of the alphabet for the several terms.

SECTION 4

Of the remaining part of the First Book.

The resolution of syllogisms requires no other principles but these before laid down for constructing them. However it is treated of largely, and rules laid down for reducing reasoning to syllogisms, by supplying one of the premises when it is understood, by rectifying inversions, and putting the propositions in the proper order.

Here he speaks also of hypothetical syllogisms; which he acknowledges cannot be resolved into any of the figures, although there be many kinds of them that ought diligently to be observed; and which he promises to handle afterwards. But this promise is not fulfilled, as far as I know, in any of his works that are extant.

SECTION 5

Of the Second Book of the First Analytics.

The second book treats of the powers of syllogisms, and shows, in twenty-seven chapters, how we may perform many feats by them, and what figures and modes are adapted to each. Thus, in some syllogisms several distinct conclusions may be drawn from the same premises: in some, true conclusions may be drawn from false premises: in some, by assuming the conclusion and one premise, you may prove the other; you may turn a direct syllogism into one leading to an absurdity.

We have likewise precepts given in this book, both to the assailant in a syllogistical dispute, how to carry on his attack with art, so as to obtain the victory; and to the defendant, how to keep the enemy at such a distance as that he shall never be obliged to yield. From which we learn, that Aristotle introduced in his own school, the practice of syllogistical disputation, instead of the rhetorical disputations which the sophists were wont to use in more ancient times.

[20. ]Now generally known as the Prior Analytics.