84 ROYCE— PRINCIPLES OF THEORETICAL SCIENCE. [April 19 



to you, the principal use of a theory seems to He in two things. 

 First, a theory, if successful, enables you to give an economical 

 description of a vast number of facts. Secondly, a theory usefully 

 guides your search after new facts, and in particular your predic- 

 tions, and the practical activities by means of which you apply your 

 science to the study of new cases. The common mind often opposes 

 theory and practice. But every enlightened student is aware how 

 large a part theory plays, in those cases where theory is possible, as 

 a means towards guiding the practical applications of a science to 

 the various arts. Thus without astronomical theory the application 

 of astronomy to navigation would remain very limited; because one 

 who has to apply observations of the heavenly bodies to the work 

 of the navigator must accomplish his application by means of defi- 

 nite processes of computation. Such computations can be reduced 

 to precise rules only by means of considerations which belong to the 

 theoretical side of the science. So long as, for the Babylonian as- 

 trologers, astronomy remained a mysterious branch of empirical nat- 

 ural history, computations could have only a limited scope. It is 

 astronomical theory, not to be sure the whole of astronomical theory, 

 but a certain limited portion of it, which gives to the navigator's 

 computations a uniform and controlable character. Economical 

 description, controlable application to the search for new facts, and 

 to the practical uses of a science, these are the characters which a 

 scientific theory must possess in order to meet the requirements 

 •which the real world makes upon it. 



But these requirements cannot be met unless the theory possesses 

 a certain coherent logical structure. This structure might in gen- 

 eral be possessed, almost or quite equally, by a great number of 

 different theories whereof only one happened to be true to the facts. 

 Nevertheless, although the internal logical finish of the structure of 

 a theory is by itself no guarantee that the theory is useful in describ- 

 ing or predicting facts, such logical structure is a condition sine qua 

 non of a good theory. A natural question arises as to what con- 

 stitutes this internal logically coherent structure to which a highly 

 developed theory must conform. The question so stated may appear 

 at first sight very vague and indeterminate. A theory, you will say, 

 must make use of principles which it provisionally assumes to be 



