The rules of converfion cannot be applied to all propofitions, but only to those that are categorical; and we are left to the direction of common fense in the converfion of other propofitions. To give an example: Alexander was the fon 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 transpose the subject and predicate. Both must undergo fome change, in order to fit them for their new ftation: for in every propofition the subject 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 instance, fhall we convert this propofition, God is omniscient? 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 subject. SECT. 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 fyllogifms, he is more full, more minute and particular, than any of them: fo that they seem 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 Ariftotle. 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 Ariftotle 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 that useful. 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 D 2 therefore he might think, that there was no occafion to multiply the modes of fyllogifm upon their . account. These attempts, therefore, fhow rather inclination than power, to difcover any material defect in Ariftotle's theory. The most valuable addition made to the theory of categorical fyllogifms, feems to be the invention of those technical names given to the legitimate modes, by which they may be easily remembered, and which have been comprised in these barbarous verfes. Barbara, Celarent, Darii, Ferio, dato primæ ; In these verses, every legitimate mode belonging to the three figures has a name given to it, by which it may be distinguished and remembered. And this name is so 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 univerfal affirmative; and being in the third figure, the middle term must be the fubject of both premifes. This is the mystery contained in the vowels of thofe barbarous words. But there are other myf teries 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 firft. So that the four modes of the firft 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 species of it, called oftenfive and per impoffible, 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 Ariftotle had fome contrivance of this kind, which was kept as one of the fecret doctrines of his fchool, and handed down by tradition, until fome perfon brought it to light. This is offered only as a conjecture, leaving it to those who are better acquainted with the moft ancient commentators on the Analytics, either to refute or to confirm it. SECT. 3. On Examples ufed to illuftrate this Theory. We may observe, that Ariftotle hardly ever gives examples of real fyllogifms to illuftrate his rules. In demonftrating the legitimate modes, he takes A, B, C, for the terms of the fyllogifm. Thus, D 3 figure is demon For," fays he, Thus, the first mode of the firft ftrated by him in this manner. "if A is attributed to every B, and B to every C, "it follows neceffarily, that A may be attributed "to every C." For difproving the illegitimate modes, he uses the fame manner; with this difference, that he commonly for an example gives three real terms, fuch as, bonum, habitus, prudentia; of which three terms you are to make up a fyllogifm of the figure and mode in question, which will appear to be inconclufive. The commentators and fyftematical writers in logic, have fupplied this defect; and given us real examples of every legitimate mode in all the figures. We acknowledge this to be charitably done, in order to affift the conception in matters fo very abftract; but whether it was prudently done for the honour of the art, may be doubted. I am afraid this was to uncover the nakedness of the theory; it has undoubtedly contributed to bring it into contempt; for when one confiders the filly and uninftructive reasonings that have been brought forth by this grand organ of fcience, he can hardly forbear crying out, Parturiunt montes, et nafcitur ridiculus mus. Many of the writers of logic are acute and ingenious, and much practised in the fyllogiftical art; and there must be fome reason why the examples they have given of fyllogifms are fo lean, We |