1906] 



ROYCE— PRINCIPLES OF THEORETICAL SCIENCE. 89 



already their place in certain of the sciences, while other exact, and 

 equally fruitful, although non-quantitative theories, are likely to be- 

 come of definite use in the science of the future. We are. therefore, 

 already on the way vastly to enlarge, but on the other hand much 

 more precisely to define our concept of what constitutes an exact 

 scientific theory. We are on the way towards understanding why 

 some theoretical concepts permit of such a vast range of deduction, 

 wdiile others are less significant in this respect. We are becoming 

 able to face as never before the logical question as to what we mean 

 when we define facts as being quantitative at all. And as our view 

 of the forms of conceptual structure which are possible for the 

 human mind not only enlarges, but becomes more exact, we are 

 coming nearer to the point where we can profitably study w^hat the 

 conditions are upon which the formation of exact concepts depends. 



III. 



The researches to w^hich I refer are wtU known to all students 

 of modern logic. They have come, to a considerable extent, from the 

 mathematical side. They have been suggested, however, not only 

 by mathematical science, but by the logical analysis of the exact 

 physical sciences, and to some extent by the analysis of the concepts 

 W'hich lie at the basis of the study of the humanities, and of the his- 

 torical sciences. The interest in formal logic which received a new 

 impetus from the researches of Boole, has added itself to these other 

 motives. As examples of inquiry of the type that I here have in 

 mind, one may mention the well known works of Mach, and of 

 Pearson, on the concepts and methods of physical and of statistical 

 science, the recent books of Ostwald and of Poincare, the various 

 lectures on the concepts and methods of science, w^hich were called 

 out by the St. Louis Congress, the varied and extensive investigations 

 of our principal American logician, Mr. Charles Peirce, the great 

 literature which has now grown up about the theory of assemblages 

 wihch Cantor initiated, the investigations of Dedekind upon the 

 concepts of arithmetic, the lectures and essays of Helmholtz regard- 

 ing the concepts of the exact natural science, the extensive inquiries 

 into principles of geometry, the modern effort to formulate the con- 

 cepts and purposes of historical science, the manifold controversies 



