i9o6] ROYCE— PRINCIPLES OF THEORETICAL SCIENCE. 83 



a science the premature prominence of theoretical constructions leads 

 to a neglect of facts or to a too easy contentment with an insufficient 

 collection of facts. When a science, however, is already highly 

 developed but is also rapidly growing, the search for new facts is 

 commonly guided by more or less highly developed theoretical inter- 

 ests, and is directel by presuppositions, by hypotheses, by questions, 

 which have come to mind in consequence of reasonings due to 

 theories. 



In the normal case of a science in which theories play an im- 

 portant part, a scientific theory takes the form, first, of the state- 

 ment of a set of principles, or of relatively fundamental proposi- 

 tions, which the theory treats, at least provisionally, as true. Sec- 

 ondly, the theory consists of the logical development of a set of 

 consequences, which follow from these principles and so will be true 

 in case the latter are true. These consequences may be reached, 

 and in the case of the most highly developed theories, are reached, 

 by mathematical computations. In its application to the work of 

 the science, the theory becomes useful, in so far as its results can 

 be compared with the particular facts of experience, or can be tested 

 by seeing how far they lead to successful predictions. 



A theory whose results disagree with facts has to be amended 

 accordingly, but in many cases may be adjusted to the facts by alter- 

 ations which leave its main principles intact, and which involve only 

 minor modifications. When a theory succeeds up to a certain point, 

 but leaves some facts indeterminate, it frequently gives rise to 

 hypotheses concerning phenomena as yet imobserved, and in this 

 sense may prove a guide to investigation. There are well known 

 and important cases where a theoretical computation disagrees for 

 a time with actually observed facts, but where the discrepancy can 

 be shown to be due to the non-recognition of certain facts which, so 

 soon as you take them into account, enable the original theory to 

 apply with reasonable accuracy to the whole system of facts in ques- 

 tion. In some cases improved methods of calculation, or other 

 purely logical developments of theory itself, suffice to remove dis- 

 crepancies ; and such cases furnish very persuasive tests of the value 

 of the theory in question. 



If you look towards the world of facts, as experience shows them 



