SECTION IV. OF THE REMAINING PART OF THE FIRST BOOK. THE resolution of syllogisms requires no other principles, but those before laid down for constructing them. However it is treated of largely, and rules laid down for reducing reasoning to syllogisms, by supplying one of the premises when it is understood, by rectifying inversions and putting the propositions in the proper order. Here he speaks also of hypothetical syllogisms; which he acknowledges cannot be resolved into any of the figures, although there be many kinds of them which ought diligently to be observed; and which he promises to handle afterward. But this promise is not fulfilled, as far as I know, in any of his works that are extant. SECTION V. OF THE SECOND BOOK OF THE FIRST ANALYTICS. THE second book treats of the powers of syllogisms, and shows, in twenty-seven chapters, how we may perform many feats by them, and what figures and modes are adapted to each. Thus, in some syllogisms, several distinct conclusions may be drawn from the same premises: in some, true conclusions 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 syllogistical 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 disputing syllogistically, instead of the rhetorical disputations which the sophists were wont to use in more ancient times. CHAPTER IV. REMARKS. SECTION I. OF THE CONVERSION OF PROPOSITIONS. WE have given a summary view of the theory of pure syllogisms as delivered by Aristotle, a theory of which he claims the sole invention. And I believe it will be difficult, in any science, to find so large a system of truths of so very 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 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 В 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 should 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 un dergo 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. SECTION II. ON ADDITIONS MADE TO ARISTOTLE'S THEORY. ALTHOUGH the logicians have enlarged the first and second parts of logic, by explaining some technical words and distinctions which Aristotle had omitted, and by giving names to some kinds of propositions which he overlooks; yet in what concerns 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 shown, 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 he might think that there was no occasion to multiply the modes of syllogism upon their account. 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 categoricalsyllogisms, seems to be the invention of those technical names given to the legitimate modes, by which they may be easily re membered, and which have been comprised in these barbarous verses. Barbara, Celarent, Darii, Ferio, dato prima; 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 mysteries 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 impossible, 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 tradition, until somebody 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. SECTION III. ON EXAMPLES USED TO ILLUSTRATE THIS THEORY. WE E may observe, that Aristotle hardly ever gives examples of real syllogisms to illustrate his rules. In demonstrating the legitimate modes, he takes A, B, C, for the terms of the syllogism. Thus, the first mode of the first figure is demonstrated by him in this manner. "For," says he, "if A is attributed to every B, and B to every C, it follows necessarily, that A may be attributed to every C." For disproving the illegitimate modes, he uses the same manner; with this difference, that he commonly for an example gives three real terms, such as bonum, habitus, prudentia; of which three terms you are to make up a syllogism of the figure and mode in question, which will appear to be inconclusive. The commentators, and systematical writers in logic, have supplied this defect; and given us real examples of every legitimate mode in all the figures. This we must acknowledge to be charitably done, to assist the imagination in the conception of matters so very abstract; 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; and has contributed much to bring it into contempt: for when one considers the silly and uninstructive reasonings that have been brought forth by this grand organ of science, he can hardly forbear crying out, Parturiunt montes, et nascitur ridiculus mus. Many of the writers of logic are acute and ingenious, and much practised in the syllogistical art; and there must be some reason why the examples they have given of syllogisms are so lean. We shall speak of the reason afterward; and shall now give a syllogism in each figure as an example. No work of God is bad; The natural passions and appetites of men are the work of God; Therefore none of them is bad. In this syllogism, the middle term, work of God, is the subject of the major and the predicate of the minor; so that the syllogism is of the first figure. The mode is that called Celarent; the major and conclusion being both universal negatives, and the minor an universal affirmative. It agrees to the rules of the figure, as the major is universal, and the minor affirmative; it is also agreeable to all the general rules; so that it maintains its character in every trial. And to show of what ductile materials syllogisms are made, we may, by converting simply the major proposition, reduce it to a good syllogism of the second figure, and of the mode Casare, thus: Whatever is bad is not the work of God; All the natural passions and appetites of men are the work of God. Therefore they are not bad. Another example: Every thing virtuous is praise-worthy; Some pleasures are not praise-worthy; Therefore some pleasures are not virtuous. Here the middle term praise-worthy being the predicate of both premises, the syllogism is of the second figure; and seeing it is made up of the propositions, A, O, O, the mode is Baroco. It will be found to agree both with the general and special rules and it |