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true conclufions 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 fyllogistical 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 fyllogistical disputation, instead of the rhetorical disputations which the sophists were wont to use in more ancient times.
C H A P.
Sect. 1. Of the Conversion of Propositions.
E have given a summary view of the
theory of pure syllogisms as delivered by Aristotle, a theory of which he
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claims the sole invention. And I believe it will be difficult, in any science, to find so large a system of truths of so
abstract and so general a nature, all fortified by demonstration, and all invented and perfected by one man. It shows a force of genius and labour of investigation, equal to the most arduous attempts. I shall now make fome 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 self-evident when applied to particular cases. But Aristotle has given demonstrations of the rules he mentions. As a fpecimen, I shall give his demonstration of the firit rule. “ Let AB be an universal
negative propofition; 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 understand it, the third rule of conversion is assumed, that if B is in some A, then A must be in fome B, which indced is contrary to the first fuppofition. If
the third rule be assumed for proof of the first, the proof of all the three in a circle; for the second and third rules are proved by the first. This is a fault in reasoning which Aristotle condemns, and which I would be very unwilling to charge him with, if I could find any better meaning in his demonstration. But it is indeed a fault very difficult to be avoided, when men attempt to prove things that are selfevident.
The rules of conversion cannot be applied to all propositions, but only to those that are categorical; and we are left to the direction of common sense in the converfion of other propositions. To give an exc ample: Alexander was the son of Philip; therefore Philip was the father of Alexander: A is greater than B; therefore B is less than A. These are conversions which, as far as I know, do not fall within
any rule in logic; nor do we find
loss for want of a rule in such cases.
Even in the conversion of categorical propositions, it is not enough to tranfpose the subject and predicate. Both must undergo fome change, in order to fit them for their new station : for in every pro
position position the subject must be a substantive, or have the force of a substantive; and the predicate must be an adjective, or have the force of an adjective. Hence it follows, that when the subject is an individual, the proposition admits not of conversion. How, for initance, shall we convert this proposition, God is omniscient?
These observations show, that the doctrine of the conversion of propositions is not so complete as it appears. The rules are laid down without
limitation; yet they are fitted only to one class of propofitions, to wit, the categorical; and of these only to such as have a general term for their subject.
SECT. 2. On Additions made to Aristotle's
Although the logicians have enlarged the first and second parts of logic, by exa plaining some technical words and distinctions which Aristotle has omitted, and by giving names to some kinds of propositions which he overlooks; yet in what concerns the theory of categorical fyllo
gifms, he is more full, more minute and particular, than any of them: so that they feem to have thought this capital part of the Organon rather redundant than deficient.
It is true, that Galen added a fourth figure to the three mentioned by Aristotle. But there is reason to think that Aristotle omitted the fourth figure, not through ignorance or inattention, but of design, as containing only fome indirect modes, which, when properly expressed, fall into the first figure.
It is true also, that Peter Ramus, a profefled enemy
of Aristotle, introduced some new modes that are adapted to singular propositions; and that Aristotle takes no notice of fingular propofitions, either in his rules of conversion, or in the modes of fyllogism. But the friends of Aristotle have shewn, that this improvement of Ramus is more specious than useful. Singular propositions have the force of universal propositions, and are subject to the fame rules. The definition given by Aristotle of an universal proposition apa plies to them; and therefore he might think, that there was no occasion to mul