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true conclufions may be drawn from falfe premises in fome, by affuming the conclufion and one premife, you may prove the other; you may turn a direct fyllogifm into one leading to an abfurdity.

We have likewife precepts given in this book, both to the affailant in a fyllogiftical difpute, how to carry on his attack with art, fo as to obtain the victory; and to the defendant, how to keep the enemy at fuch a distance as that he fhall never be obliged to yield. From which we learn, that Aristotle introduced in his own school, the practice of fyllogiftical difputation, instead of the rhetorical difputations which the fophifts were wont to use in more ancient times.



SECT. I. Of the Converfion of Propofitions.

WE have given a fummary view of the theory of pure fyllogifms as delivered by Aristotle, a theory of which he

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claims the fole invention. And I believe it will be difficult, in any fcience, to find fo large a fyftem of truths of fo very abftract and fo 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 fhall now make fome remarks upon it.

As to the converfion of propofitions, the writers on logic commonly fatisfy themselves with illuftrating each of the rules by an example, conceiving them to be felf-evident when applied to particular cafes. But Ariftotle has given demonftrations of the rules he mentions. As a fpecimen, I fhall give his demonstration of the firit rule. "Let A B be an univerfal "negative propofition; I fay, that if A is "in no B, it will follow that B is in no A. 66 If you deny this confequence, let B be "in fome A, for example, in C; then the "first fuppofition will not be true; for "C is of the B's." In this demonstration, if I understand it, the third rule of converfion is affumed, that if B is in fome A, then A muft be in fome B, which indeed is contrary to the firft fuppofition. If


the third rule be affumed for proof of the firft, the proof of all the three goes round in a circle; for the fecond and third rules are proved by the firft. This is a fault in reafoning which Ariftotle condemns, and which I would be very unwilling to charge him with, if I could find any better meaning in his demonftration. But it is indeed a fault very difficult to be avoided, when men attempt to prove things that are felfevident.

The rules of converfion cannot be applied to all propofitions, but only to thofe that are categorical; and we are left to the direction of common fenfe in the converfion of other propofitions. To give an ex< ample: Alexander was the son of Philip; therefore Philip was the father of Alexander: A is greater than B; therefore B is lefs than A. These are converfions which, as far as I know, do not fall within any rule in logic; nor do we find any lofs for want of a rule in fuch cafes.

Even in the converfion of categorical propofitions, it is not enough to tranfpose the fubject and predicate. Both muft undergo fome change, in order to fit them for their new ftation: for in every propofition

pofition the fubject must be a substantive, or have the force of a fubftantive; and the predicate must be an adjective, or have the force of an adjective. Hence it follows, that when the fubject is an individual, the propofition admits not of converfion. How, for inftance, fhall we convert this propofition, God is omnifcient?

These obfervations fhow, that the doctrine of the converfion of propofitions is not fo complete as it appears. The rules are laid down without any limitation; yet they are fitted only to one clafs of propofitions, to wit, the categorical; and of these only to fuch as have a general term for their fubject.

SECT. 2.

On Additions made to Ariftotle's

Although the logicians have enlarged the first and second parts of logic, by explaining fome technical words and diftinctions which Ariftotle has omitted, and by giving names to fome kinds of propofitions 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: fo 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 expreffed, fall into the first figure.

It is true alfo, that Peter Ramus, a professed enemy of Aristotle, introduced fome new modes that are adapted to fingular propofitions; and that Aristotle takes no notice of fingular propofitions, either in his rules of converfion, or in the modes of fyllogifm. But the friends of Aristotle have fhewn, that this improvement of Ramus is more fpecious than useful. Singular propofitions have the force of univerfal propofitions, and are fubject to the fame rules. The definition given by Ariftotle of an univerfal proposition ap¬ plies to them; and therefore he might think, that there was no occafion to mul

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