These complex effects must be investigated by deducing the law of the effect from the laws of the separate causes on the combination of which it depends. No inductive method is conclusive in such cases (e.g. in physiology, or à fortiori, in politics and history), whether it be the method of simple observation, which compares instances, whether positive or negative, to see if they agree in the presence or the absence of one common antecedent, or the empirical method, which proceeds by directly trying different combinations (either made or found) of causes, and watching what is the effect. Both are inconclusive; the former, because an effect may be due to the concurrence of many causes, and the latter, because we can rarely know what all the coexisting causes are; and still more rarely whether a certain portion (if not all) of the total effect is not due to these other causes, and not to the combination of causes which we are observing.
CHAPTER XI.
THE DEDUCTIVE METHOD.
The deductive method is the main source of our knowledge of complex phenomena, and the sole source of all the theories through which vast and complicated facts have been embraced under a few simple laws. It consists of processes of Induction, Ratiocination, and Verification. First, by one of the four inductive methods, the simple laws (whence may be deduced the complex) of each separate cause which shares in producing the effect, must be first ascertained. This is difficult, when the causes or rather tendencies cannot be observed singly. Such is the case in physiology, since the different agencies which make up an organized body cannot be separated without destroying the phenomenon; consequently there our sole resource is to produce experimentally, or find (as in the case of diseases), pathological instances in which only one organ at a time is affected. Secondly, when the laws of the causes have been found, we calculate the effect of any given combination of them by ratiocination, which may have (though not necessarily) among its premisses the theorems of the sciences of number and geometry. Lastly, as it might happen that some of the many concurring agencies have been unknown or overlooked, the conclusions of ratiocination must be verified; that is, it must be explained why they do not, or shown that they do, accord with observed cases of at least equal complexity, and (which is the most effectual test) that the empirical laws and uniformities, if any, arrived at by direct observation, can be deduced from and so accounted for by them, as, e.g. Kepler's laws of the celestial motions by Newton's theory.
CHAPTERS XII. AND XIII.
THE EXPLANATION AND EXAMPLES OF THE EXPLANATION OF LAWS OF NATURE.
The aim, in the deductive method, is either to discover the law of the effect, or to account for it by explaining it, that is, by pointing out some more general phenomenon (though often less familiar to us) of which this is a case and a partial exemplification, or some laws of causation which produce it by their joint or successive action. This explanation may be made, either—1. By resolving the laws of the complex effect into its elements, which consist as well of the separate laws of the causes which share in producing it, as also of their collocation, i.e. the fact that these separate laws have been so combined; or—2. By resolving the law which connects two links, not proximate, in a chain of causation, into the laws which connect each link with the intermediate links; or—3. By the subsumption or gathering up of several laws under one which amounts to the sum of them all, and which is the recognition of the same sequence in different sets of instances. In the first two of the processes, laws are resolved into others, which both extend to more cases, i.e. are more general, and also, as being laws of nature, of which the complex laws are but results, are more certain, i.e. more unconditional and more universally true. In the third process, laws are resolved into others which are indeed more general, but not more certain, since they are in fact the same laws, and therefore, subject to the same exceptions.