1906] 



ROYCE— PRINCIPLES OF THEORETICAL SCIENCE. 95 



the now well-known one-sided paper ring, made of an ordinary strip 

 of paper, but so made that the two sides form but a single side. In 

 this case the very strip of paper which has but one side, now has 

 but one edge. And thus a universal principle which might, but for 

 such an example, have seemed self-evident, namely the principle that 

 a ring strip of paper must have two sides and two edges, becomes 

 in the light of this principle, simply false ; and one's geometrical 

 ideas are hereby enlarged. So long, then, as it is self-evident to you 

 that any ring strip of paper must have two sides, you simply do 

 not understand the forms in question. Another case now very fam- 

 iliar in discussion, another case, I say, of a principle long regarded 

 as self-evident, is the principle that the whole of a collection, must 

 exceed in multitude any part of that collection which may be formed 

 by leaving some of the members of the collection out. But the 

 modern theory of infinite collections is founded upon supposing this 

 principle to be, as it actually is, false for such collections. Thus 

 there are as many powers of two as there are whole numbers, an 

 assertion which follows directly from the definition of a power of 

 two, and from the definition of whole numbers. Yet the powers 

 of two are themselves whole numbers, and are but a portion of the 

 whole numbers, and may be viewed as an extremely small portion in 

 case one judges its size merely by considering what whole numbers 

 are omitted from this collection. Upon self-evidence, then, no theory 

 of the scope of theoretical science can be built up. I do not hesitate 

 to say that there are no self-evident principles. And as myself, in 

 philosophy, what is called an absolutist, that is a believer in the exist- 

 ence of absolute truth, I utter this assertion not in the interests of 

 skepticism, but in the interests of truth. Single truths do not pos- 

 sess self-evidence, just because there are many truths which form 

 a system, wherein each element is dependent for its nature upon its 

 relations to the others. In general the assertion of the self-evidence 

 of single principles has repeatedly been a foe to the progress of civil- 

 ization, as it is hostile to a genuinely logical understanding of the 

 nature of truth. The assertion of self-evidence has been used to 

 defend almost any bulwark of tyranny from the questionings of 

 beneficent reformers. Not upon self-evidence, therefore, nor upon a 

 list of fundamental verities, each of which shines merely by its 



