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logism, 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 collect's 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 negatįve.

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

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vicious syllogism. 2. The middle term must be taken universally in one of the premises. 3. Both premises must not be particular propositious, nor both negative. 4. The conclusion must be parti, cular, 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 conclu, sion, 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.

Sect. 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 syllo gisms, 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 dark

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Sect. 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.

Sect. 5. Of the Second Book of the First Analytics.

The second book treats of the powers of syllogisms, and shews, 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.

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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 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. MADE

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** Sect. 1. Of the Conversion of Propositions.

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of pure syllogisms as delivered by Aristotle, à theory of which he claims the sole invention. "And I believe it will be difficult, in any science, to find so large å system of truths of sa very Abstract and so general a'nature, "all fortified by demonstration, and all invented and perfected by one man.” It shews'a force of génius and la

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