i9o6] ROVCE— PRINCIPLES OF THEORETICAL SCIENCE. 97 



A similar procedure has now become so common in discussions of 

 this modern type, that it needs no further characterization for those 

 who have examined any such researches. Their interest lies not 

 in the founding of scientific theories upon any set of self-evident 

 principles. The interest lies in showing the connection which exists 

 amongst various concepts and principles, and in bringing to pass 

 a logical analysis of the theory in question and of the concepts 

 which this theory involves. No exclusive significance can be at- 

 tached to any one such investigation. There are numerous, prob- 

 ably very numerous dififerent sets of principles, upon which geo- 

 metrical science could be founded. How far our experience of 

 space bears out any of these principles by confirming their truth 

 is a matter for the science of nature. Why our experience of space 

 has these characters is ultimately a matter for philosophy. What 

 set of geometrical principles it is convenient to use for the purposes 

 of a textbook of geometry, is a pedagogical matter. Geometry is 

 not deducible from self-evident axioms, since there are no self- 

 evident axioms. Geometry is a theoretical science, since we are 

 not confined to particular observations for our knowledge of space 

 relations, but are acquainted with laws which enable to describe and 

 predict our spacial experiences in general terms. The first prin- 

 ciples of this theoretical science can be variously stated. The 

 logical problem lies in understanding the relations that exist 

 amongst these various statements. 



Nevertheless, when a large number of theoretical sciences have 

 been treated in this way, when their various concepts have been 

 analyzed from various points of view, and when as is the case the 

 forms or types of concepts which they contain have been shown to 

 be variations of a comparatively limited number of types, such as 

 the series type, the group type, or to speak of a more special in- 

 stance, the type of the ordinary real numbers, or of the ordinary 

 complex numbers, one is brought in the presence of a further 

 problem which is indeed at the present time the central and char- 

 acteristic problem of logical theory. It is the problem as to the 

 unitv of these forms. Fundamental ideas, in the sense of self- 

 evident concepts and principles, do not exist in scientific 



PROC. AMER. PHIL. SOC, XLV. l82G, PRINTED JUNE 25, I906. 



