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bour 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 self-evident when applied to particular cases. But Aristotle has given demonstrations of the rules he mentions. As a specimen, I shall give his demonstration of the first 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 understand 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 supposition. If the third rule be assumed for proof of the first, the proof of all the three goes round 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 self-evident.
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 conversion of other propositions. To give an example: 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 any loss for want of a rule in such cases.
Even in the conversion of categorical propositions, it is not enough to transpose the subject and predicate. Both must undergo some change, in order to fit them for their new station: for in every proposition 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 instance, 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 any limitation; yet they are fitted only to one class of propositions, 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 Theory,
Although the logicians have enlarged the first and second parts of logic, by explaining some tech nical words and distinctions which Aristotle has omitted, and by giving names to some kinds of propositions which he overlooks; yet in what con→ cerns the theory of categorical syllogisms, he is more full, more minute and particular, than any of them so 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 Aristotle. But there is reason to think that Aristotle omitted the fourth figure, not through ignorance or inattention, but of design, as containing only some indirect modes, which, when properly expressed, fall into the first figure.
It is true also, that Peter Ramus, a professed enemy of Aristotle, introduced some new modes that are adapted to singular propositions; and that Aristotle takes no notice of singular propositions, either in his rules of conversion, or in the modes of syllogism. 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 same rules. The definition given by Aristotle of an universal proposition applies to them; and therefore
therefore he might think, that there was no occasion to multiply the modes of syllogism upon their
These attempts, therefore, show rather inclination than power, to discover any material defect in Aristotle's theory.
The most valuable addition made to the theory of categorical syllogisms, seems 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
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 propositions.
Thus, a syllogism in Bocardo must be made up of the propositions denoted by the three vowels, O, A, O; that is, its major and conclusion must be particular negative propositions, and its minor an universal affirmative; and being in the third figure, the middle term must be the subject of both premises.
This is the mystery contained in the vowels of those barbarous words. But there are other mys
teries contained in their consonants: for, by their means, a child may be taught to reduce any syllogism 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 conclusive, all the modes of the other two are proved at the same time, by means of this operation of reduction. For the rules and manner of this reduction, and the different species of it, called ostensive and per impossibile, I refer to the logicians, that I may not disclose all their mysteries.
The invention contained in these verses is so ingenious, and so great an adminicle to the dexterous management of syllogisms, that I think it very probable that Aristotle had some contrivance of this kind, which was kept as one of the secret doctrines of his school, and handed down by tra dition, until some person brought it to light. This is offered only as a conjecture, leaving it to those who are better acquainted with the most ancient commentators on the Analytics, either to refute or to confirm it.
SECT. 3. On Examples used to illustrate this Theory:
We may observe, that Aristotle hardly ever gives examples of real syllogisms to illustrate his rules. In demonstrating the legitimate modes, he takes