consists in ascribing the character of general truths to all propositions which are true in every instance that we happen to know of." Mr. Mill's attitude toward such inductions in the first edition of his Logic was curious. Although holding that the uniformity of Nature, the law of Causation, and the axioms of Mathematics are established only in this way, he yet inclined to deny to the process even the name of induction. He said: "This is the kind of induction, if it deserves the name, which is natural to the mind when unaccustomed to scientific methods." Later Mr. Mill omitted the clause "if it deserves the name"; but his disparaging tone continued and infected logical writers. Thus, Dr. Fowler says: "But not only is the Inductio per Enumerationem Simplicem the mode of generalization natural to immature and uninstructed minds; it is the method which, till the time of Bacon, or at least till the era of those great discoveries which shortly preceded the time of Bacon, was almost universal." "When men first begin to argue from their experience of the past to their expectation of the future, or from the observation of what immediately surrounds them to the properties of distant objects, they seem naturally to fall into this unscientific and unreflective mode of reasoning." 1 Bacon himself seems responsible for this sneer; he says: "Inductio quae procedit per enumerationem simplicem, res puerilis est, et precario concludit, et periculo exponitur ab instantia contradictoria, et plerumque secundum pauciora quam par est, et his tantum modo quae praesto sunt pronunciat." 2 Still there remains an inconsistency in Mr. Mill's doctrine; for he says most justly : 1 Inductive Logic, pp. 280, 281. 2 Novum Organum, lib. 1, aph. cv. "Experience must be consulted in order to learn from it under what circumstances arguments from it will be valid. We have no ulterior test to which we subject experience in general; but we make experience its own test. Experience testifies, that among the uniformities which it exhibits or seems to exhibit, some are more to be relied on than others; and uniformity, therefore, may be presumed from any given number of instances, with a greater degree of assurance, in proportion as the case belongs to a class in which the uniformities have hitherto been found more uniform. This mode of correcting one generalization by another, a narrower generalization by a wider, which common sense suggests and adopts in practice, is the real type of scientific induction." 1 The truth could not be better set forth than in the foregoing accurate and discriminating statement; after all, the "real type of scientific induction" is merely an inductio per enumerationem simplicem, carefully made. Experience gives us not only uniformities, but uniformities among uniformities. Not only does this ox uniformly chew the cud, but all oxen uniformly chew the cud, and all other sorts of animals with similar structure uniformly chew the cud. Not only does this piece of lead maintain a uniform specific gravity of 11.4, but there is a uniformity in specific gravity among all pieces of lead, and, moreover, every different substance maintains a uniform specific gravity. What we call the "Principle of the Uniformity of Nature" is merely the wide primary induction that the various limited uniformities of nature persist. There is no other sense in which nature is uniform. It is not meant, of course, that every object is like every other object, and every event like every other event. 1 Logic, p. 232. "Every person's consciousness assures him that he does not always expect uniformity in the course of events; he does not always believe that the unknown will be similar to the known, that the future will resemble the past. Nobody believes that the succession of rain and fine weather will be the same in every future year as in the present. Nobody expects to have the same dreams repeated every night. On the contrary everybody mentions it as something extraordinary, if the course of nature is constant, and resembles itself in these particulars. To look for constancy where constancy is not to be expected, as for instance that a day which has once brought good fortune will always be a fortunate day, is justly accounted superstition." 1 The assurance with which a primary induction is held, depends upon the number of instances from which it is generalized. If the number is small, the assurance is imperfect: if the number of instances is practically infinite, the assurance is practically complete. Belief shades thus from faint presumption, by imperceptible increments, into positiveness. When at last we have examined all the instances, the induction is complete and we know. To quote Mr. Mill: — "Induction by simple enumeration in other words, generalization of an observed fact from the mere absence of any known instance to the contrary affords in general a precarious and unsafe ground of assurance; for such generalizations are incessantly discovered, on further experience, to be false. Still, however, it affords some assurance, sufficient, in many cases, for the ordinary guidance of conduct. It would be absurd to say, that the generalizations arrived at by mankind in the outset of their experience, such as these food nourishes, fire burns, water drowns, - were unworthy of reliance. There is a scale of trustworthiness in the results of the original unscientific induction; and on this diversity (as observed in the fourth chapter of the present 1 Mill's Logic, p. 226. book) depend the rules for the improvement of the process. The improvement consists in correcting one of these inartificial generalizations by means of another. As has been already pointed out, this is all that art can do. To test a generalization, by showing that it follows from or conflicts with some stronger induction, some generalization resting on a broader foundation of experience, is the beginning and end of the logic of induction." 1 Quite a different view from the foregoing has, however, been often taken. The name induction has been denied to the generalization of experience, and has been reserved exclusively for statements in regard to the unobserved. Professor Bain speaks as follows: "Induction is the arriving at General Propositions, by means of Observation or Fact. "In an induction there are three essentials: (1) the result must be a proposition an affirmation of concurrence or non-concurrence as opposed to a Notion; (2) the Proposition must be general, or applicable to all cases of a given kind; (3) the method must be an appeal to observation of fact. "The Propositions established by induction are general. A single individual concurrence, as 'the wind is shaking the tree,' is in its statement a proposition, but not an induction. On such individual statements we base inductions, but one is not enough. If the coincidence recurs, we mark the recurrence; we are affected by the shock or flash of identity, a very important step in our knowledge. If, pursuing the suggestion, we remark that as often as the wind is high, the trees are shaken; that the two things have concurred within the whole course of our observation; that the same concurrence has been uniform in the observation of all other persons whose experience we have been informed of, - we are then entitled to make a still wider sweep, and to say, 'every time that a high wind has been observed, a waving of the trees has also been observed.' "Still, with all this multitude and uniformity of observations, 1 Logic, p. 401. there is no proper Induction. What then remains? The answer is, the extension of the concurrence from the observed to the unobserved cases to the future which has not yet come within observation, to the past before observation began, to the remote where there has been no access to observe. This is the leap, the hazard of Induction, which is necessary to complete the process. Without this leap our facts are barren; they teach us what has been, after the event; whereas we want knowledge that shall instruct us before the event, that shall impart what we have no means of observing. A complete induction, then, is a generalization that shall express what is conjoined everywhere, and at all times, superseding forever the labor of fresh observation. "We thus contrast Induction with that species of 'Induction improperly so-called,' where a general statement merely sums up the observed particulars. "If, after observing that each one of the planets shines by the sun's light, we affirm that all the planets shine by the sun's light,' we make a general proposition to appearance, but it falls short of an induction in the full sense of the term. The general statement is merely another way of expressing the particulars; it does not advance beyond them. But without such advance there is no real inference, no march of information, no addition to our knowledge. Induction is the instrument of multiplying and extending knowledge; it teaches us how, from a few facts observed, to affirm a great many that have not been observed. If, from the observation of the planets now discovered, we make an assertion respecting all that have yet to be discovered, we make the leap implied in real or inductive inference. If the assertion had been made when only six planets were known, actual observation would have been the guarantee for those six, induction for the remaining hundred or upwards. "The sole method of attaining Inductive truths being the observation and comparison of particulars, the sole evidence for such truths is Universal Agreement. "A permanent or uniform concurrence can be established, in the last resort, only by the observation of its uniformity. That unsupported bodies fall to the ground, is a conjunction suggested by the observation of mankind, and proved by the unanimity of all |