the third rule be affumed for proof of the first, 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 felf-evident.

D

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 con29167 verfion of other propofitions. To give an example: Alexander was the fon of Phi

lip; therefore Philip was the father of Alexander: A is greater than B; therefore B is less 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 transpose the fubject and predicate. Both muft undergo fome change, in order to fit them for their new station: for in every proVOL. III. pofition

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pofition the fubject must be a fubftantive, 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?

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Thefe 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 class of propofitions, to wit, the categorical; and of thefe only to fuch as have a general term for their fubject.

SECT. 2. On Additions made to Ariftotle's
Theory.

Although the logicians have enlarged the first and fecond 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.

F

It is true, that Galen added a fourth figure to the three mentioned by Aristotle. But there is reafon to think that Ariftotle. omitted the fourth figure, not through ignorance or inattention, but of defign, as containing only fome indirect modes, which, when properly expreffed, fall into the first figure.

It is true alfo, that Peter Ramus, a profeffed enemy of Ariftotle, 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 Ariftotle have fhewn, that this improvement of Ramus is more fpecious than ufeful. Singular propofitions have the force of univerfal propofitions, and are fubject to the fame rules. The definition given by Ariftotle of an univerfal propofition applies to them; and therefore he might think, that

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that there was no occafion to multiply the modes of fyllogifm upon their account.

Thefe attempts, therefore, fhow, rather inclination than, power, to discover any material defect in Ariftotle's theory.

The most valuable addition made to the theory of categorical fyllogifms, feems to be the invention of thofe technical names given to the legitimate modes, by which they may be eafily remembered, and which have been comprised in these barbarous verfes, rail to

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Barbara, Celarent, Darii, Ferio, dato primæ ;
Cefare, Cameftris, Feftino, Baroco, fecundæ ;
Tertia grande fonans recitat Darapti, Felapton
Adjungens Difamis, Datifi, Bocardo, Ferifon.

In these verses, every legitimate mode belonging to the three figures has a name given to it, by which it may be diftinguished and remembered. And this name is fo contrived as to denote its nature: for the name has three vowels, which denote the kind of each of its propofitions.

Thus, a fyllogifm in Bocardo must be made up of the propofitions denoted by the three vowels, O, A, O; that is, its major and conclufion must be particular negative propofitions, and its minor an u

niverfal

niverfal affirmative; and being in the third figure, the middle term must be the fubject of both premises.

This is the mystery contained in the vowels of those barbarous words. But there are other myfteries contained in their confonants: for, by their means, a child may be taught to reduce any fyllogifm of the second or third figure to one of the first. So that the four modes of the first figure being directly proved to be conclufive, all the modes of the other two are proved at the fame time, by means of this operation of reduction. For the rules and manner of this reduction, and the different fpecies of it, called oftenfive and per impoffibile, I refer to the logicians, that I may not disclose all their mysteries.

The invention contained in thefe verfes is fo ingenious, and fo great an adminicle to the dextrous management of fyllogifms, that I think it very probable that Aristotle had fome contrivance of this kind, which was kept as one of the secret doctrines of his school, and handed down by tradition, until fome perfon brought it to light. This is offered only as a conjecture, leaving it to thofe who are better ac-. quainted

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