Having established these generals and universals, from them we may extend discovery in what may be termed the DESCENDING SCALE: and here Syllogism, in its common acceptation, has its use. And, as an instrument of invention, Syllogism may in this case supply corollaries; as in the former, Induction might yield discoveries without the help of analogy. Yet a very slight consideration will show, that here also Analogy is the great engine of invention, by which hypotheses or suppositions are supplied; and that in the descending scale Syllogistic Demonstration, as Induction in the ascending, is the grand instrument for confuting, proving, or limiting those hypotheses. But it is said, that, among the ancients, SYLLOGISM was the great engine of discovery. If we examine this matter, we are informed by Aristotle, that Syllogism is a discourse or reasoning, in which, certain things being admitted or supposed, something different from these admitted principles or propositions, necessarily follows, in consequence of their existence.* He tells us, likewise, that Demonstration is a species of Syllogism.† Now it is really of no consequence whether a syllogism is composed of two, three, four, or any number of steps; and, indeed, every mathematical demonstration by synthesis is no other than a chain of Syllogism. If we inquire further of him, how the first principles of all philosophy, and every art and science are to be obtained, from which such demonstrations may depend; he expressly informs us by Induction, by collecting together all the in * Συλλογισμὸς δέ ἐστι λόγος ἐν ᾧ τεθέντων τινῶν, ἕτερόν τι τῶν κειμένων, ἐξ ἀνάγκης συμβαίνει Tų Tauta elvaɩ. I. Pr. Anal. 1-Edit. Casaub. 1590. N.B. there is a great variation in the numbering of the chapters in the different editions of Aristotle. + I. Pr. Anal. 1. I. Pr. Anal. 30-II. Pr. Anal. 1. 23-I. Post. Anal. 1. 10. 14. 18-I. Top. 7-VIII. Top. 1-VIII. Phys. 4-IV. Meteor. 1. dividuals, and drawing the conclusion from them. His logical treatises, indeed, being entirely directed against the sophists of that day, relate solely to syllogistic demonstration. Of course, therefore, he does not investigate the method of obtaining the universals themselves : but he speaks repeatedly of it, that is, of Induction, as the well known and familiar method of obtaining them, through the senses, by experience.* He clearly explains to us the progress of science, both in the ascending and in the descending scale. We learn, says he, only by Induction or Demonstration; by Demonstration from universals to particulars, i. e. in the descending scale; by Induction from particulars to universals, or in the ascending scale. Hence a person, who is defective in any of his senses, cannot use Induction, and therefore can * I. Pr. Anal. 30-I. Post Anal. 10. 15. 27— II. Post. Anal. 18. + I. Top. 10-VIII. Top. 1. not theorize to universals, or by abstraction obtain general propositions: hence, also, his progress in the scale of demonstration must be equally defective with his data.* If we turn to Plato, he throws a new light upon the method of investigation, by requiring some previous hypothesis↑ or idea for examination; and, in the beginning of the Parmenides, lays down the Eleatic or Dialectic method of examin ing it. The method is this-Either, I., The subject is, as it is supposed; or II., it is not. On the first supposition that it is so, we must examine what happens1st. To it with respect to itself: 2d. To it with respect to all other things: 3rd. To all other things with respect to it: 4th. To all other things with respect to * I. Post. Anal. 15. See also the preceding references. + Aristotle uses the word thesis for hypothesis in this sense. His dialectic also differs from that of Plato themselves. Four similar cases will result when we examine what does not happen ; and, according to the exposition of Proclus, four more, when we examine what does, and at the same time does not, happen. Upon the supposition, therefore, that it is so, we must investigate its relations in all their bearings; and we must pursue the same method of investigation upon the second supposition, that it is not so. And if, in so doing, we were guided according to certain categories, a more thorough investigation could not possibly be devised and the method is equally applicable to Experimental philosophy to Intellectual science.* * The ancients, then, professed, in the ascending scale, to work by Hypothesis and Induction; and, in the descending scale, by Syllogistic Demonstration or Deduction from first principles or propo For a method of starting ideas for examination, see a curious description of Socrates, with his hopeful pupil, in the Clouds of Aristophanes. C |