tion the laws of two causes: first, the force of primitive impulsion in the direction of the tangent; next, an accelerative attracting force. From these inductive laws we deduce by calculation the motion of a body submitted to their combined influence; and satisfying ourselves that the planetary motions observed coincide exactly with the predicted movements, we conclude that the two forces in question are actually the causes of the planetary motions. "To the Deductive Method," says Mill," the human mind is indebted for its most conspicuous triumphs in the investigation of nature. To it we owe all the theories by which vast and complicated phenomena are embraced under a few simple laws." Our deviations have led us further than the direct path; we have derived efficiency from imperfection. Section X.-Comparison of the Methods of Induction and Deduction If we now compare the two methods, their aptness, function, and provinces, we shall find, as in an abstract, the history, divisions, hopes, and limits of human science. The first appears at the beginning, the second at the end. The first, necessarily, gained ascendancy in Bacon's time,1 and now begins to lose it; the second, necessarily, lost ascendancy in Bacon's time, and now begins to regain it. So that science, after having passed from the deductive to the experimental state, is now passing from the experimental to the deductive. Induction has for its province phenomena which are capable of being decomposed, and on which we can experiment. Deduction has for its province indecomposable phenomena, or those on which we cannot experiment. The first is efficacious in physics, chemistry, zoölogy, and botany, in the earlier stages of every science, and also whenever phenomena are but slightly complicated, within our reach, capable of being modified by means at our disposal. The second is efficacious in astronomy, in the higher branches of physics, in physiology, history, in the higher grades of every science, whenever phenomena are very complicated, as in animal and social life, or lie beyond our reach, as the motions of the heavenly bodies and the changes 1 Mill's "Logic," i. 526. of the atmosphere. When the proper method is not employed, science is at a stand-still: when it is employed, science progresses. Here lies the whole secret of its past and its present. If the physical sciences remained stationary till the time of Bacon, it is because men used deduction when they should have used induction. If physiology and the moral sciences are now making slow progress, it is because we employ induction when deduction should be used. It is by deduction, and according to physical and chemical laws, that we shall be enabled to explain physiological phenomena. It is by deduction, and according to mental laws, that we shall be enabled to explain historical phenomena. And that which has become the instrument of these two sciences, it is the object of all the others to employ. All tend to become deductive, and aim at being summed up in certain general propositions, from which the rest may be deduced. The less numerous these propositions are, the more science advances. The fewer suppositions and postulates a science requires, the more perfect it is become. Such a reduction is its final condition. Astronomy, acoustics, optics, present its models; we shall know nature when we shall have deduced her millions of facts from two or three laws. I venture to say that the theory which you have just heard is perfect. I have omitted several of its characteristics, but you have seen enough to recognize that induction has nowhere been explained in so complete and precise a manner, with such an abundance of fine and just distinctions, with such extensive and exact applications, with such a knowledge of the practical methods and ascertained results of science, with so complete an exclusion of metaphysical principles and arbitrary suppositions, and in a spirit more in conformity with the rigorous procedure of modern experimental science. You asked me just now, what Englishmen have effected in philosophy; I answer, the theory of Induction. Mill is the last of that great line of philosophers, which begins at Bacon, and which, through Hobbes, Newton, Locke, Hume, Herschel, is continued down to our own times. They have carried our national spirit into philosophy; they have been positive and practical; they have See chapter 9, book vi. v. 2, 478, on The Physical or Concrete Deductive Method as applied to Sociology; and chapter 13, book ii., for explanations, after Liebig, of Decomposition, Respi ration, the Action of Poisons, etc. A whole book is devoted to the logic of the moral sciences; I know no better treatise on the subject. not soared above facts; they have not attempted out-of-theway paths; they have cleared the human mind of its illusions, presumptions, and fancies. They have employed it in the only direction in which it can act; they only wished to mark out and light up the already well-trodden ways of the progressive sciences. They have not been willing to spend their labor vainly in other than explored and verified paths; they have aided in the great modern work, the discovery of applicable laws; they have contributed, as men of special attainments do, to the increase of man's power. Can you find many philosophers who have done as much? Section XI.-Limits of Our Knowledge You will tell me that our philosopher has clipped his wings, in order to strengthen his legs. Certainly; and he has acted wisely. Experience limits the career which it opens to us; it has given us our goal, but also our boundaries. We have only to observe the elements of which our experience is composed, and the facts from which it sets out, to understand that its range is limited. Its nature and its method confine its progress to a few steps. And, in the first place,1 the ultimate laws of nature cannot be less numerous than the several distinct species of our sensations. We can easily reduce a movement to another movement, but not the sensation of heat to that of smell, or of color, or of sound, nor either of these to a movement. We can easily connect together phenomena of different degrees, but not phenomena differing in species. We find distinct sensations at the bottom of all our knowledge, as simple indecomposable elements, separated absolutely one from another, absolutely incapable of being reduced one to another. Let experience do what she will, she cannot suppress these diversities which constitute her foundation. On the other hand, experience, do what she will, cannot escape from the conditions under which she acts. Whatever be her province, it is bounded by time and space; the fact which she observes is limited and influenced by an infinite number of other facts to which she cannot attain. She is obliged to suppose or recognize some primordial condition from whence she starts, Mill's "Logic," ii. 4. and which she does not explain. Every problem has its accidental or arbitrary data: we deduce the rest from these, but there is nothing from which these can be deduced. The sun, the earth, the planets, the initial impulse of the heavenly bodies, the primitive chemical properties of substances, are such data.3 If we possessed them all we could explain everything by them, but we could not explain these themselves. Mill says: "Why these particular natural agents existed originally and no others, or why they are commingled in such and such proportions, and distributed in such and such a manner throughout space, is a question we cannot answer. More than this: we can discover nothing regular in the distribution itself; we can reduce it to no uniformity, to no law. There are no means by which, from the distribution of these causes, or agents, in one part of space, we could conjecture whether a similar distribution prevails in another." 4 And astronomy, which just now afforded us the model of a perfect science, now affords us an example of a limited science. We can predict the numberless positions of all the planetary bodies; but we are obliged to assume, beside the primitive impulse and its amount, not only the force of attraction and its law, but also the masses and distances of all the bodies in question. We understand millions of facts, but it is by means of a hundred facts which we do not comprehend; we arrive at necessary results, but it is only by means of accidental ante 2" There exists in nature a number of Permanent Causes, which have subsisted ever since the human race has been in existence, and for an indefinite and probably an enormous length of time previous. The sun, the earth, and planets, with their various constituents, air, water, and the other distinguishable substances, whether simple or compound, of which nature is made up, are such Permanent Causes. They have existed, and the effects or consequences which they were fitted to produce have taken place (as often as the other conditions of the production met), from the very beginning of our perience. But we can give no account of the origin of the Permanent Causes themselves."-Mill's Logic," i. 378. ex "The resolution of the laws of the heavenly motions established the previously unknown ultimate property of a mutual attraction between all bodies: the resolution, so far as it has yet proceeded, of the laws of crystallization, or chemical composition, electricity, magnetism, etc., points to various polarities, ultimately inherent in the cedents; so that if the theory of our universe were completed there would still remain two great voids: one at the commencement of the physical world, the other at the beginning of the moral world; the one comprising the elements of being, the other embracing the elements of experience; one containing primary sensations, the other primitive agents. “Our knowledge," says Royer-Collard, "consists in tracing ignorance as far back as possible." Can we at least affirm that these irreducible data are so only in appearance, and in relation to our mind? Can we say that they have causes, like the derived facts of which they are the causes? Can we conclude that every event, always and everywhere, happens according to laws, and that this little world of ours, so well-regulated, is a sort of epitome of the universe? Can we by aid of the axioms, quit our narrow confines, and affirm anything of the universe? In no wise; and it is here that Mill pushes his principles to their furthest consequences: for the law which attributes a cause to every event, has to him no other foundation, worth, or scope, than what it derives from experience. It has no inherent necessity; it draws its whole authority from the great number of cases in which we have recognized it to be true; it only sums up a mass of observations; it unites two data, which, considered in themselves, have no intimate connection; it joins antecedents generally to consequents generally, just as the law of gravitation joins a particular antecedent to a particular consequent; it determines a couple, as do all experimental laws, and shares in their uncertainty and in their restrictions. Listen to this bold assertion: "I am convinced that anyone accustomed to abstraction and analysis, who will fairly exert his faculties for the purpose, will, when his imagination has once learnt to entertain the notion, find no difficulty in conceiving that in some one, for instance, of the many firmaments into which sidereal astronomy now divides the universe, events may succeed one another at random, without any fixed law; nor can anything in our experience, or in our mental nature, constitute a sufficient, or indeed any, reason for believing that this is nowhere the case. The grounds, therefore, which warrant us in rejecting such a supposition with respect to any of the phenomena of which we have experience, must be sought elsewhere than in any supposed necessity of our intellectual faculties." 5 Mill's "Logic,” ii. 95. |