(4) We may have included among the data of our reasonings agents or circumstances that do not exist or do not affect the phenomenon in question.  In the early days of science purely fanciful powers were much relied upon:  such as the solid spheres that carried the planets and stars; the influence of the planets upon human destiny; the tendency of everything to seek “its own place,” so that fire rises to heaven, and solids fall to the earth; the “plastic virtue” of the soil, which was once thought to have produced fossils.  When, however, such conceptions hindered the progress of explanation, it was not so much by vitiating the deductive method as by putting men off from exact inquiries.  More to our present purpose were the supposed cataclysms, or extraordinary convulsions of the earth, a belief in which long hindered the progress of Geology.  Again, in Biology, Psychology, and Sociology many explanations have depended upon the doctrine that any improvement of structure or faculty acquired by an individual may be inherited by his descendants:  as that, if an animal learns to climb trees, his offspring have a greater aptitude for that mode of life; that if a man tries to be good, his children find it easier to be virtuous; that if the inhabitants of a district carry on cloth-work, it becomes easier for each successive generation to acquire dexterity in that art.  But now the inheritability of powers acquired by the individual through his own efforts, is disputed; and, if the denial be made good, all such explanations as the above must be revised.

If, then, the premises of a deductive argument be vitiated in any of these four ways, its conclusion will fail to agree with the results of observation and experiment, unless, of course, one kind of error happen to be cancelled by another that is ‘equal and opposite.’  We now come to a variation of the method of combining Induction with Deduction, so important as to require separate treatment.

Sec. 5.  The Inverse or Historical Method has of late years become remarkably fruitful.  When the forces determining a phenomenon are too numerous, or too indefinite, to be combined in a direct deduction, we may begin by collecting an empirical law of the phenomenon (as that ’the democracies of City-States are arbitrary and fickle’), and then endeavour to show by deductions from “the nature of the case,” that is, from a consideration of the circumstances and forces known to be operative (of which, in the above instance, the most important is sympathetic contagion), that such a law was to be expected.  Deduction is thus called in to verify a previous induction; whereas in the ’Physical Method’ a deduction was verified by comparing it with an induction or an experiment; hence the method now to be discussed has been named the Inverse Deductive Method.