86 ROYCE— PRINCIPLES OF THEORETICAL SCIENCE. 



1 April 19, 



theory is preferable to a non-quantitative one, and in so far as exact 

 theoretical interpretations are preferable to inexact ones. 



This very commonplace instance suggests where lies the logical 

 problem regarding the internal structure of theories. What does 

 one mean, for instance, by a quantitative theory? In order to ans- 

 wer this question one must know what one means by quantity. Why 

 are quantitative ideas more useful than non-quantitative ideas? 

 Wherein lies the logical difference between conceptions of quantity 

 and other conceptions? Is the notion that quantitative conceptions 

 stand alone amongst possible scientific conceptions, in their peculiar 

 possession of exactness, and of a capacity to be submitted to precise 

 and entensive processes of deduction, is this presupposition itself well 

 founded ? Are there other concepts which are logically as exact as 

 the quantitative concepts, which are as capable of being subjected 

 to elaborate processes of a deductive character? If so, are there 

 other regions than those of the sciences of measurement in which 

 highly developed theoretical finish is possible? May the science of 

 the future come to use other than quantitative theories in dealing 

 with regions of nature or of mind where measurement proves to 

 be unattainable, or inexact ? How will the non-quantitative theories, 

 in so far as they can be developed, stand related to the quantitative 

 theories ? What is it that makes certain concepts adapted to furnish 

 a wide range of unexpected results, which can be reached deduc- 

 tively, and by exact devices of thinking, although these results can- 

 not readily be seen at a glance, by merely inspecting the conceptions 

 in question? How can mere deduction lead to an infinite number 

 of unexpected results, as is often the case in the exact sciences ? Do 

 the possible conceptions which the human mind can frame, and can 

 lay at the basis of theoretical constructions, form anything like a 

 closed system? In other words, is the range over which our theo- 

 retical constructions vary simply limitless, and indeterminate, or is 

 it, even if infinite, still in some way itself determinate, so that one 

 can name certain fundamental concepts which every theory must 

 use, or from which every theoretical construction must make a selec- 

 tion, even in defining its provisionally assumed principles? In 

 other words, are there first principles of scientific theory? Are the 

 ideas which we can use in defining our provisional hypotheses, in 



