1

"1

to be here a new and peculiar kind of inference of which deductive logic knows nothing. Professor Davis says "Induction is an immediate synthetic inference generalizing from and beyond experience.” But this does not appear to be a correct analysis. When there is an inference we necessarily look about for propositions which can be syllogistically combined. Professor Davis claims that we intuitively know the Uniformity of Nature, and he unconsciously makes this his major premise. But the uniformity of nature can be known and defined only inductively, not intuitively. It is a discovery of induction, not the basis of it.

No if there is a permanent or recurring fact in nature, we ascertain it simply by generalization, not by inference.

How do we know that the mill is standing by the river? We cannot be looking at it all of the time. Having seen it a hundred or a thousand times we have come to believe in its permanence. How do we know that the water is flowing over the mill-dam? We have seen it often and have come to think it continuous. Here is a permanent fact — the mill, and a uniformity -the flow of the water; how do we come to feel assured of them? Not by any process of inference, but simply by generalization. We have not reasoned about the future or the unknown, but about the present and the known. Whether the world will come to an end to-night, and the river and the mill be annihilated, we cannot predict from our observations upon them; all that we know is that this permanence - the mill, and this uniformity the flow of the stream, are facts of

1 Inductive Logic, p. 6.

the existing order; and since it would be irrational to act, without evidence, upon the supposition of the cessation of the existing order, we keep on carrying grist to the mill.

A primary induction does not rest upon a process of inference any more than does our belief in any permanent fact. That the cliffs of England are white is a permanent fact; that the crows of England are black is a uniformity. We cannot be looking at the cliffs all the time, and we cannot examine all the crows; but having looked at the cliffs frequently, and having seen a large number of crows, we rest in the assurance that we know the existing order. Should we wake up some morning and find the cliffs blackened, we should simply recognize that the order had changed. Should we find in visiting a remote part of the kingdom a flock of white crows, we should simply observe that we had passed beyond the former area of observation. If our expectation of finding the cliffs white and the crows black at the next observation rested upon any logical necessity, our not finding them so would require a doubt of our own sanity.

The suggestion has been made that we base our belief in the truth of a primary induction upon our faith in the veracity of God. But surely such an induction as that "the Cretans are always liars" cannot be based upon the veracity of God; it rests merely upon observation of the uniform mendacity of those depraved people.

The sort of induction we are now describing has been known, since Bacon's time, as Inductio per Enumerationem Simplicem, Induction by Simple Count.

"It

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." 991

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."

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.