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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 fyllogifm 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 propofition I would prove is an universal affirmative, I know by the rules of fyllogisms, that there is only one legitimate mode in which an universal affirmative propofition 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 geneneral rule, I feek 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 fecondly, 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 aš a middle term, but no other. In this way, the author gives fpecial rules for all the various kinds of propofitions 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.
Sect. 4. Of the remaining part of the First
The resolution of fyllogisms requires no
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 fyllogisms; 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 Firf
The second book treats of the powers of fyllogisms, 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 fyllogifms several distinct conclusions may be drawn from the same premises : in fome,
true conclusions may be drawn from falfe
We have likewise precepts given in this
сн А Р.
SECT, 1. Of the Conversion of Propositions.
E have given a summary view of the
theory of pure fyllogisms as delivered by Aristotle, a theory of which he Z. z 2
claims the fole invention. And I believe it will be difficult, in any science, to find so large a system of truths of fo
abstract and so general a nature, all fortified by demonstration, and all invented and perfected by one man. It fhows a force of genius and labour of investigation, equal to the most arduous attempts. I shall now make some remarks upon it.
As to the conversion of propositions, the writers on logic commonly satisfy themselves with illustrating each of the rules by an example, conceiving them to be felf-evident when applied to particular cafes. But Aristotle has given demonstrations of the rules he mentions. As a specimen, I shall give his demonstration of the firit rule. Let A B be an universal " negative proposition ; I say, that if A is
in no B, it will follow that B is in no A. “ If you deny this consequence, let B be " in some A, for example, in C; then the
first supposition will not be true; for “ C is of the B's." In this demonstration, if I undersland it, the third rule of conversion is assumed, that if B is in some A, then A must be in some B, which indeed is contrary to the first fuppofition. If