1906] 



ROYCE -PRINCIPLES OF THEORETICAL SCIENCE. 85 



true. It must then develop the consequences of these principles. 

 It must be logically accurate, and as full in its development of con- 

 sequences as the application which is to be made of the theory seems 

 to require. This, it would seem, can in general be said. But with 

 this vague generality the theory of what constitutes a good theory 

 would appear at first sight to be completed. 



Yet a moment's thought will show, that we all pretend to know 

 more about the structure towards which highly developed theories 

 tend, than this first generalization would make manifest. For in- 

 stance, it is a comment which has become commonplace, that, wher- 

 ever quantitative conceptions are possible, theories whose first prin- 

 ciples can be expressed in quantitative form, have a formal advantage 

 over theories which have to be expressed in non-quantitative terms. 

 Some portions of our empirical world are subject to measurement. 

 Measurement in practice gives results w^hich vary within the limits 

 of error, and which are therefore inexact. A theory which is to be 

 just to any highly advanced state of knowledge regarding measur- 

 able facts, must make use of principles which involve provisionally 

 assumed relations of quantities. One advantage which a quantita- 

 tive theory can then possess lies in the very fact that its provisionally 

 assumed principles may be stated with an exactness which empiri- 

 cal measurements never reach. In other words, the very incapacity 

 of our theory to account for the variations, and for the inexactness 

 of any single process of measurement, may be an advantage in the 

 development and in the further application of the theory. Assum- 

 ing exact relations, and invariant relations, where the actual meas- 

 urements of observers show a considerable range of uncontrollable 

 variation, the theory may enable computations to be made, in terms 

 of which the work of measurement may be guided, and the essen- 

 tial and unessential elements of" experience may be distinguished. 

 Cases of this sort suggest that the structure of theories is subject to 

 certain logically definable laws which are somewhat independent of 

 the precise degree to which in a given case the theory in question 

 can be verified. In other words, while the true theory, in the sense 

 of the theory that agrees with the observed facts, is indeed the ideal, 

 one may be able to judge the value of a theory in advance of know- 

 ing whether it is true of not, in so far, for instance, as a quantitative 



