On the Philosophy of Discovery, Chapters Historical and Critical. William Whewell
Timæus, as the portions of a theological view of the universe—such as has been called a Theodicæa, a justification of God. In the former passage of Plato, the sciences enumerated are Arithmetic, Plane Geometry, Solid Geometry, Astronomy and Harmonics8. In the Timæus we have a further notice of many other subjects, in a way which is intended, I conceive, to include such knowledge as Plato had then arrived at on the various parts of the universe. The subjects there referred to are, as I have elsewhere stated9, these: light and heat, water, ice, gold, gems, rust and other natural objects:—odours, taste, hearing, lights, colour, and the powers of sense in general:—the parts and organs of the body, as the bones, the marrow, the brain, flesh, muscles, tendons, ligaments and nerves; the skin, the hair, the nails; the veins and arteries; respiration; generation; and in short, every obvious point of physiology. But the opinions thus delivered in the Timæus on the latter subject have little to do with the progress of real knowledge. The doctrines, on the other hand, which depend upon geometrical and arithmetical relations are portions or preludes of the sciences which the fulness of time brought forth.
5. I may, as further bearing upon the Platonic notion of science, notice Plato's view of the constitution of the human mind. According to him the Ideas which are the constituents of science form an Intelligible World, while the visible and tangible things which we perceive by our senses form the Visible World. In the visible world we have shadows and reflections of actual objects, and by these shadows and reflections we may judge of the objects, even when we cannot do so directly; as when men in a dark cavern judge of external objects by the shadows which they cast into the cavern. In like manner in the Intelligible World there are conceptions which are the usual objects of human thought, and about which we reason; but these are only shadows and reflections of the Ideas which are the real sources of truth. And the Reasoning Faculty, the Discursive Reason, the Logos, which thus deals with conceptions, is subordinate to the Intuitive Faculty, the Intuitive Reason, the Nous, which apprehends Ideas10. This recognition of a Faculty in man which contemplates the foundations—the Fundamental Ideas—of science, and by apprehending such Ideas, makes science possible, is consentaneous to the philosophy which I have all along presented, as the view taught us by a careful study of the history and nature of science. That new Fundamental Ideas are unfolded, and the Intuitive Faculty developed and enlarged by the progress of science and by an intimate acquaintance with its reasonings, Plato appears to have discerned in some measure, though dimly. And this is the less wonderful, inasmuch as this gradual and successive extension of the field of Intuitive Truth, in proportion as we become familiar with a larger amount of derived truth, is even now accepted by few, though proved by the reasonings of the greatest scientific discoverers in every age.
The leading defect in Plato's view of the nature of real science is his not seeing fully the extent to which experience and observation are the basis of all our knowledge of the universe. He considers the luminaries which appear in the heavens to be not the true objects of astronomy, but only some imperfect adumbration of them;—mere diagrams which may assist us in the study of a higher truth, as beautiful diagrams might illustrate the truths of geometry, but would not prove them. This notion of an astronomy which is an astronomy of Theories and not of Facts, is not tenable, for Theories are Facts. Theories and Facts are equally real; true Theories are Facts, and Facts are familiar Theories. But when Plato says that astronomy is a series of problems suggested by visible things, he uses expressions quite conformable to the true philosophy of science; and the like is true of all other sciences.
CHAPTER IV.
Aristotle
The views of Aristotle with regard to the foundations of human knowledge are very different from those of his tutor Plato, and are even by himself put in opposition to them. He dissents altogether from the Platonic doctrine that Ideas are the true materials of our knowledge; and after giving, respecting the origin of this doctrine, the account which we quoted in the last chapter, he goes on to reason against it. "Thus," he says11, "they devised Ideas of all things which are spoken of as universals: much as if any one having to count a number of objects, should think that he could not do it while they were few, and should expect to count them by making them more numerous. For the kinds of things are almost more numerous than the special sensible objects, by seeking the causes of which they were led to their Ideas." He then goes on to urge several other reasons against the assumption of Ideas and the use of them in philosophical researches.
Aristotle himself establishes his doctrines by trains of reasoning. But reasoning must proceed from certain First Principles; and the question then arises, Whence are these First Principles obtained? To this he replies, that they are the result of Experience, and he even employs the same technical expression by which we at this day describe the process of collecting these principles from observed facts;—that they are obtained by Induction. I have already quoted passages in which this statement is made12. "The way of reasoning," he says13, "is the same in philosophy, and in any art or science: we must collect the facts (τὰ ὑπὰρχοντα), and the things to which the facts happen, and must have as large a supply of these as possible, and then we must examine them according to the terms of our syllogisms." … "There are peculiar principles in each science; and in each case these principles must be obtained from experience. Thus astronomical observation supplies the principles of astronomical science. For the phenomena being rightly taken, the demonstrations of astronomy were discovered; and the same is the case with any other Art or Science. So that if the facts in each case be taken, it is our business to construct the demonstrations. For if in our natural history (κατὰ τὰν ἱστορί αν) we have omitted none of the facts and properties which belong to the subject, we shall learn what we can demonstrate and what we cannot." And again14, "It is manifest that if any sensation be wanting, there must be some knowledge wanting, which we are thus prevented from having. For we acquire knowledge either by Induction (ἐπαγωγῆ) or by Demonstration: and Demonstration is from universals, but Induction from particulars. It is impossible to have universal theoretical propositions except by Induction: and we cannot make inductions without having sensation; for sensation has to do with particulars."
It is easy to show that Aristotle uses the term Induction, as we use it, to express the process of collecting a general proposition from particular cases in which it is exemplified. Thus in a passage which we have already quoted15, he says, "Induction, and Syllogism from Induction, is when we attribute one extreme term to the middle by means of the other." The import of this technical phraseology will further appear by the example which he gives: "We find that several animals which are deficient in bile are long-lived, as man, the horse, the mule; hence we infer that all animals which are deficient in bile are long-lived."
We may observe, however, that both Aristotle's notion of induction, and many other parts of his philosophy, are obscure and imperfect, in consequence of his refusing to contemplate ideas as something distinct from sensation. It thus happens that he always assumes the ideas which enter into his proposition as given; and considers it as the philosopher's business to determine whether such propositions are true or not: whereas the most important feature in induction is, as we have said, the introduction of a new idea, and not its employment when once introduced. That the mind in this manner gives unity to that which is manifold,—that we are thus led to speculative principles which have an evidence higher than any others,—and that a peculiar sagacity in some men seizes upon the conceptions by which the facts may be bound into true propositions,—are doctrines which form no essential part of the philosophy of the Stagirite, although such views are sometimes recognized, more or less clearly, in his expressions. Thus he says16, "There can be no knowledge when the sensation does not continue in the mind. For this purpose, it is necessary both to perceive, and to have some unity in the mind (αἰσθανομένοις εχειν ἔν τι
See Appendix, Essay B.
See these views further discussed in the Appendix, Essay C.