For these reasons, it requires much more evidence to establish an exception to one of the more general empirical laws than to the more special ones. We should not have any difficulty in believing that there might be a new Kind of crow; or a new kind of bird resembling a crow in the properties hitherto considered distinctive of that Kind. But it would require stronger proof to convince us of the existence of a Kind of crow having properties at variance with any generally recognized universal property of birds; and a still higher degree if the properties conflict with any recognized universal property of animals. And this is conformable to the mode of judgment recommended by the common sense and general practice of mankind, who are more incredulous as to any novelties in nature, according to the degree of generality of the experience which these novelties seem to contradict.
§ 9. It is conceivable that the alleged properties might conflict with some recognized universal property of all matter. In that case their improbability would be at the highest, but would not even then amount to incredibility. There are only two known properties common to all matter; in other words, there is but one known uniformity of co-existence of properties co-extensive with all physical nature, namely, that whatever opposes resistance to movement gravitates, or, as Professor Bain expresses it, Inertia and Gravity are co-existent through all matter, and proportionate in their amount. These properties, as he truly says, are not mutually implicated; from neither of them could we, on grounds of causation, presume the other. But, for this very reason, we are never certain that a Kind may not be discovered possessing one of the properties without the other. The hypothetical ether, if it exists, may be such a Kind. Our senses can not recognize in it either resistance or gravity; but if the reality of a resisting medium should eventually be proved (by alteration, for example, in the times of revolution of periodic comets, combined with the evidences afforded by the phenomena of light and heat), it would be rash to conclude from this alone, without other proofs, that it must gravitate.
For even the greater generalizations, which embrace comprehensive Kinds containing under them a great number and variety of infimæ species, are only empirical laws, resting on induction by simple enumeration merely, and not on any process of elimination—a process wholly inapplicable to this sort of case. Such generalizations, therefore, ought to be grounded on an examination of all the infimæ species comprehended in them, and not of a portion only. We can not conclude (where causation is not concerned), because a proposition is true of a number of things resembling one another only in being animals, that it is therefore true of all animals. If, indeed, any thing be true of species which differ more from one another than either differs from a third, especially if that third species occupies in most of its known properties a position between the two former, there is some probability that the same thing will also be true of that intermediate species; for it is often, though by no means universally, found, that there is a sort of parallelism in the properties of different Kinds, and that their degree of unlikeness in one respect bears some proportion to their unlikeness in others. We see this parallelism in the properties of the different metals; in those of sulphur, phosphorus, and carbon; of chlorine, iodine, and bromine; in the natural orders of plants and animals, etc. But there are innumerable anomalies and exceptions to this sort of conformity; if indeed the conformity itself be any thing but an anomaly and an exception in nature.
Universal propositions, therefore, respecting the properties of superior Kinds, unless grounded on proved or presumed connection by causation, ought not to be hazarded except after separately examining every known sub-kind included in the larger Kind. And even then such generalizations must be held in readiness to be given up on the occurrence of some new anomaly, which, when the uniformity is not derived from causation, can never, even in the case of the most general of these empirical laws, be considered very improbable. Thus, all the universal propositions which it has been attempted to lay down respecting simple substances, or concerning any of the classes which have been formed among simple substances (and the attempt has been often made), have, with the progress of experience, either faded into inanity, or been proved to be erroneous; and each Kind of simple substance remains, with its own collection of properties apart from the rest, saving a certain parallelism with a few other Kinds, the most similar to itself. In organized beings, indeed, there are abundance of propositions ascertained to be universally true of superior genera, to many of which the discovery hereafter of any exceptions must be regarded as extremely improbable. But these, as already observed, are, we have every reason to believe, properties dependent on causation.[192]
Uniformities of co-existence, then, not only when they are consequences of laws of succession, but also when they are ultimate truths, must be ranked, for the purpose of logic, among empirical laws; and are amenable in every respect to the same rules with those unresolved uniformities which are known to be dependent on causation.[193]
Chapter XXIII.
Of Approximate Generalizations, And Probable Evidence.
§ 1. In our inquiries into the nature of the inductive process, we must not confine our notice to such generalizations from experience as profess to be universally true. There is a class of inductive truths avowedly not universal; in which it is not pretended that the predicate is always true of the subject; but the value of which, as generalizations, is nevertheless extremely great. An important portion of the field of inductive knowledge does not consist of universal truths, but of approximations to such truths; and when a conclusion is said to rest on probable evidence, the premises it is drawn from are usually generalizations of this sort.
As every certain inference respecting a particular case implies that there is ground for a general proposition of the form, every A is B; so does every probable inference suppose that there is ground for a proposition of the form, Most A are B; and the degree of probability of the inference in an average case will depend on the proportion between the number of instances existing in nature which accord with the generalization, and the number of those which conflict with it.
192
Professor Bain (Logic, ii., 13) mentions two empirical laws, which he considers to be, with the exception of the law connecting Gravity with Resistance to motion, “the two most widely operating laws as yet discovered whereby two distinct properties are conjoined throughout substances generally.” The first is, “a law connecting Atomic Weight and Specific Heat by an inverse proportion. For equal weights of the simple bodies, the atomic weight multiplied by a number expressing the specific heat, gives a nearly uniform product. The products, for all the elements, are near the constant number 6.” The other is a law which obtains “between the specific gravity of substances in the gaseous state, and the atomic weights. The relationship of the two numbers is in some instances equality; in other instances the one is a multiple of the other.”
Neither of these generalizations has the smallest appearance of being an ultimate law. They point unmistakably to higher laws. Since the heat necessary to raise to a given temperature the same weight of different substances (called their specific heat) is inversely as their atomic weight, that is, directly as the number of atoms in a given weight of the substance, it follows that a single atom of every substance requires the same amount of heat to raise it to a given temperature; a most interesting and important law, but a law of causation. The other law mentioned by Mr. Bain points to the conclusion, that in the gaseous state all substances contain, in the same space, the same number of atoms; which, as the gaseous state suspends all cohesive force, might naturally be expected, though it could not have been positively assumed. This law may also be a result of the mode of action of causes, namely, of molecular motions. The cases in which one of the numbers is not identical with the other, but a multiple of it, may be explained on the nowise unlikely supposition, that in our present estimate of the atomic weights of some substances, we mistake two, or three, atoms for one, or one for several.
193
Dr. M’Cosh (p. 324 of his book) considers the laws of the chemical composition of bodies as not coming under the principle of Causation; and thinks it an omission in this work not to have provided special canons for their investigation and proof. But every case of chemical composition is, as I have explained, a case of causation. When it is said that water is composed of hydrogen and oxygen, the affirmation is that hydrogen and oxygen, by the action on one another which they exert under certain conditions,
Dr. M’Cosh also complains (p. 325) that I have given no canons for those sciences in which “the end sought is not the discovery of Causes or of Composition, but of Classes; that is, Natural Classes.” Such canons could be no other than the principles and rules of Natural Classification, which I certainly thought that I had expounded at considerable length. But this is far from the only instance in which Dr. M’Cosh does not appear to be aware of the contents of the books he is criticising.