Chapter 28

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.

Liebig's researches, e.g. into the Contagious Influence of Chemical Action, and his Theory of Respiration, are among the finest examples, since Newton's exposition of the law of gravitation, of the use of the deductive method for _explanation_.[2] But the method is as available for explaining mental as physical facts. It is destined to predominate in philosophy. Before Bacon's time deductions were accepted as sufficient, when neither had the premisses been established by proper canons of experimental enquiry, nor the results tested by verification by specific experience. He therefore changed the method of the sciences from deductive to experimental. But, now that the principles of deduction are better understood, it is rapidly reverting from experimental to deductive. Only it must not be supposed that the inductive part of the process is yet complete. Probably, few of the great generalisations fitted to be the premisses for future deductions will be found among truths now known. Some, doubtless, are yet unthought of; others known only as laws of some limited class of facts, as electricity once was. They will probably appear first in the shape of hypotheses, needing to be tested by canons of legitimate induction.

FOOTNOTE:

[2] These, and other illustrations in chap. xiii., cannot be usefully represented in an abridged form.