OCTOBEE 24, 1913] 



SCIENCE 



581 



deducing the consequences of a given hy- 

 pothesis. This may involve computations 

 of all degrees of complexity. You also 

 need training in the art of taking a fair 

 sample of consequences for your test; for 

 a given hypothesis may involve numerous 

 consequences that are already known, from 

 previous experience, to be true. And such 

 consequences furnish you with no crucial 

 tests. In case of success, your hypothesis 

 may become very highly probable. But 

 induction never renders it altogether cer- 

 tain. 



Classic instances of this method of induc- 

 tion exist in the physical sciences. In the 

 organic sciences the process of testing hy- 

 potheses is frequent, but is less highly 

 organized, and generally less exact than in 

 the great eases that occur in the inorganic 

 sciences. No theory of the consequences of 

 any hypothesis in the organic sciences has 

 ever yet reached the degree of precision 

 attained by the kinetic theory of gases, or 

 by the theory of gravitation. 



So much for the two great inductive 

 methods, as Peirce defines them. But now 

 does successful scientific method wholly 

 reduce to these two processes, viz., (1) 

 sampling the constitution of classes of phe- 

 nomena; and (2) sampling the theoretical 

 consequences of hypotheses? Many stu- 

 dents of the subject seem to think so. I 

 think that the history of science shows us 

 otherwise. 



As a fact, I think that the progress of 

 science largely depends upon still another 

 factor, viz., upon the more or less provi- 

 sional choice and use of what I have already 

 called, in this paper, leading ideas. 



A leading idea is, of course, in any given 

 natural science, an hypothesis. But it is an 

 hypothesis which decidedly differs from 

 those hypotheses that you directly test by 

 the observations and experiments of the 

 particular research wherein you are en- 



gaged. Unlike them, it is a hypothesis that 

 you use as a guide, or in Kant's phrase, as 

 a regulative principle of your research, 

 even although you do not in general intend 

 directly to test it by your present scientific 

 work. It is usually of too general a nature 

 to be tested by the means at the disposal of 

 your special investigation. Yet it does 

 determine the direction of your labors, and 

 may be highly momentous for you. 



Such a leading idea, for instance, is the 

 ordinary hypothesis that even in the most 

 confused or puzzling regions of the natural 

 world law actually reigns, and awaits the 

 coming of the discoverer. "We can not say 

 that our science has already so fairly 

 sampled natural phenomena as to have 

 empirically verified this assumption, so as 

 to give it a definite inductive probability. 

 For as a fact, science usually pays small 

 attention to phenomena unless there ap- 

 pears to be a definable prospect of reduc- 

 ing them to some sort of law within a rea- 

 sonable time; and chaotic natural facts, if 

 there were such, would probably be pretty 

 stubbornly neglected by science, so far as 

 such neglect was possible. On the other 

 hand, the leading idea that law is to be 

 found if you look for it long enough and 

 carefully enough is one of the great motive 

 powers not only of science but of civiliza- 

 tion. 



It may interest you to know that the 

 modern study of the so-called axioms of 

 geometry, as pursued by the mathemati- 

 cians themselves, has shown that such prin- 

 ciples as the ordinary postulate about the 

 properties of parallel lines (as Euclid de- 

 fines that postulate) are simply leading 

 ideas. What the text-books of geometry 

 usually assert to be true about the funda- 

 mental properties of parallel lines is a 

 principle that is neither self-evident, nor 

 necessarily true, nor even an inductively 

 assured truth of experience. It turns out, 



