if properly made, it would be conclu- ral tissue of connection unavoidably sive. Here, then, is a general law of weaves itself, by which the whole is nature, inferred without hesitation held together. If A is always acfrom a single instance; an universal companied by D, B by E, and C by proposition from a singular one. Now F, it follows that A B is accompanied mark another case, and contrast it by D E, A C by D F, BC by E F, with this. Not all the instances and finally A B C by D E F; and which have been observed since the thus the general character of regulabeginning of the world in support of rity is produced, which, along with the general proposition that all crows and in the midst of infinite diversity, are black would be deemed a suffi- pervades all nature, cient presumption of the truth of the proposition, to outweigh the testimony of one unexceptionable witness who should affirm that in some region of the earth not fully explored he had caught and examined a crow, and had found it to be grey.

Why is a single instance, in some cases, sufficient for a complete induction, while in others myriads of concurring instances, without a single exception known or presumed, go such a very little way towards establishing an universal proposition? Whoever can answer this question knows more of the philosophy of logic than the wisest of the ancients, and has solved the problem of Induction.

CHAPTER IV.

OF LAWS OF NATURE.

The first point, therefore, to be noted in regard to what is called the uniformity of the course of nature is, that it is itself a complex fact, compounded of all the separate uniformities which exist in respect to single phenomena. These various uniformities, when ascertained by what is regarded as a sufficient induction, we call in common parlance, Laws of Nature. Scientifically speaking, that title is employed in a more restricted sense to designate the uniformities when reduced to their most simple expression. Thus in the illustration already employed, there were seven uniformities: all of which, if considered sufficiently certain, would, in the more lax application of the term, be called laws of nature. of the seven, three alone are properly distinct and independent: these being pre-supposed, the others follow of course. The three first, therefore, according to the stricter acceptation, are called laws of nature; the remainder not; because they are in truth mere cases of the three first: virtually included in them; said, therefore, to result from them: whoever affirms those three has already affirmed all the rest.

But

§ I. IN the contemplation of that uniformity in the course of nature which is assumed in every inference from experience, one of the first observations that present themselves is, that the uniformity in question is not properly uniformity, but uniformities. The general regularity results from the co-existence of partial regularities. The course of nature in general is To substitute real examples for symconstant, because the course of each bolical ones, the following are three uniof the various phenomena that com-formities, or call them laws of nature: pose it is so. A certain fact invari- the law that air has weight, the law that ably occurs whenever certain circum- pressure on a fluid is propagated equally stances are present, and does not in all directions, and the law that presoccur when they are absent; the like sure in one direction, not opposed by is true of another fact; and so on. equal pressure in the contrary direction, From these separate threads of con- produces motion, which does not cease nection between parts of the great until equilibrium is restored. From whole which we term nature a gene- these three uniformities we should

expresses the nature of that regularity a law; as when, in mathematics, we speak of the law of decrease of the successive terms of a converging series. But the expression law of nature has generally been employed with a sort of tacit reference to the original sense of the word law, namely, the expression of the will of a superior. When, therefore, it appeared that any of the uniformities which were observed in nature would result spontaneously from certain other unifor mities, no separate act of creative will being supposed necessary for the production of the derivative unifor

be able to predict another uniformity, namely, the rise of the mercury in the Torricellian tube. This, in the stricter use of the phrase, is not a law of nature. It is the result of laws of nature. It is a case of each and every one of the three laws; and is the only occurrence by which they could all be fulfilled. If the mercury were not sustained in the barometer, and sustained at such a height that the column of mercury were equal in weight to a column of the atmosphere of the same diameter; here would be a case, either of the air not pressing upon the surface of the mercury with the force which is called its weight, or of the downward pres-mities, these have not usually been sure on the mercury not being propagated equally in an upper direction, or of a body pressed in one direction and not in the direction opposite, either not moving in the direction in which it is pressed, or stopping before it had attained equilibrium. If we knew, therefore, the three simple laws, but had never tried the Torricellian experiment, we might deduce its result from those laws. The known weight of the air, combined with the position of the apparatus, would bring the mercury within the first of the three inductions; the first induction would bring it within the second, and the second within the third, in the manner which we characterised in treating of Ratiocination. We should thus come to know the more complex uniformity, independently of specific experience, through our knowledge of the simpler ones from which it results; though, for reasons which will appear hereafter, verification by specific experience would still be desirable, and might possibly be indispensable.

Complex uniformities which, like this, are mere cases of simpler ones, and have, therefore, been virtually affirmed in affirming those, may with propriety be called laws, but can scarcely, in the strictness of scientific speech, be termed Laws of Nature. It is the custom in science, wherever regularity of any kind can be traced, to call the general proposition which

spoken of as laws of nature. According to one mode of expression, the question, What are the laws of nature? may be stated thus: What are the fewest and simplest assumptions, which being granted, the whole existing order of nature would result? Another mode of stating it would be thus: What are the fewest general propositions from which all the uniformities which exist in the universe might be deductively inferred?

Every great advance which marks an epoch in the progress of science has consisted in a step made towards the solution of this problem. Even a simple colligation of inductions already made, without any fresh extension of the inductive inference, is already an advance in that direction. When Kepler expressed the regularity which exists in the observed motions of the heavenly bodies by the three general propositions called his laws, he, in so doing, pointed out three simple suppositions, which, instead of a much greater number, would suffice to construct the whole scheme of the heavenly motions so far as it was known up to that time. A similar and still greater step was made when these laws, which at first did not seem to be included in any more general truths, were discovered to be cases of the three laws of motion, as cbtaining among bodies which mutually tend towards one another with a cer

tain force, and have had a certain | the general order of nature by ascerinstantaneous impulse originally im- taining the particular order of the pressed upon them. After this great occurrence of each one of the phenodiscovery, Kepler's three propositions, though still called laws, would hardly, by any person accustomed to use language with precision, be termed laws of nature: that phrase would be reserved for the simpler and more general laws into which Newton is said to have resolved them.

of induction, or test of the correctness of inductions, unless on the hypothesis that some inductions deserving of reliance have been already made.

There are of course no means of applying such a test as that above described, unless we already possess a general knowledge of the prevalent character of the uniformities existing throughout nature. The indispensable foundation, therefore, of a scientific formula of induction must be a survey of the inductions to which mankind have been conducted in unscientific practice, with the special purpose of ascertaining what kinds of uniformities have been found perfectly invariable, pervading all nature, and what are those which have been found to vary with difference of time, place, or other changeable circumstances.

Let us revert, for instance, to one of our former illustrations, and consider why it is that, with exactly the same amount of evidence, both negative and positive we did not reject the assertion that there are black swans, while we should refuse credence to any testimony which asserted that there were men wearing their heads underneath their shoulders. The first assertion was more credible than the latter. But why more credible? So long as neither phenomenon had been actually witnessed, what reason was there for finding the one harder to be believed than the other? Apparently § 3. The necessity of such a survey because there is less constancy in the is confirmed by the consideration that colours of animals than in the general the stronger inductions are the touchstructure of their anatomy. But how stone to which we always endeavour do we know this? Doubtless, from to bring the weaker. If we find any experience. It appears, then, that we means of deducing one of the less need experience to inform us in what strong inductions from stronger ones, degree, and in what cases, or sorts of it acquires, at once, all the strength of cases, experience is to be relied on. those from which it is deduced; and Experience must be consulted in order even adds to that strength; since the to learn from it under what circum- independent experience on which the stances arguments from it will be weaker induction previously rested valid. We have no ulterior test to becomes additional evidence of the which we subject experience in gene- truth of the better established law in ral; but we make experience its own which it is now found to be included. test. Experience testifies that among We may have inferred, from historical the uniformities which it exhibits or evidence, that the uncontrolled power seems to exhibit, some are more to be of a monarch, of an aristocracy, or of relied on than others; and uniformity, the majority, will often be abused; therefore, may be presumed, from any but we are entitled to rely on this given number of instances, with a generalisation with much greater asgreater degree of assurance, in pro-surance when it is shown to be a portion as the case belongs to a class corollary from still better established in which the uniformities have hitherto facts; the very low degree of eleva been found more uniform. tion of character ever yet attained by the average of mankind, and the little efficacy, for the most part, of the modes of education hitherto practised, in maintaining the predominance of reason and conscience over the selfish propensities. It is at the same time obvious that even these more general facts derive an accession of evidence from the testimony which history bears to the effects of des

This mode of correcting one generalisation by means of another, a narrower generalisation by a wider, which common sense suggests and adopts in practice, is the real type of scientific Induction. All that art can do is but to give accuracy and precision to this process, and adapt it to all varieties of cases, without any essential alteration in its principle.

potism. The strong induction becomes | terrestrial events really depend; and still stronger when a weaker one has been bound up with it.