94 ROYCE— PRINCIPLES OF THEORETICAL SCIENCE. [April 19, 



Some of Aristotle's anaylses of such principles do show in fact a 

 wonderful instinct for the essential, a logical depth of comprehen- 

 sion, which remains permanently marvelous as well as instructive. 

 So, for instance, his brief but penetrating analysis of the concept of 

 the Continuum touches upon a problem which brings him into close 

 touch with the inquiries even of a Dedekind ; and this fact about 

 Aristotle's view of continuity has well been pointed out by Mr. 

 Peirce. 



But at the best these older analyses labored under one presupposi- 

 tion which was long prominent in philosophical textbooks, which 

 was, however, long since rejected by at least one of the most famous 

 modern philosophers, namely Hegel, and which has now become, as 

 I think, a definitively exposed error, deeply rooted as it still is in the 

 popular mind. This was the presupposition that the first principles 

 of theoretical science, the fundamental concepts upon which all 

 theoretical construction depends, are or can be known to the mind 

 in the form of a list of self-evident principles, or of simply unavoid- 

 able and obviously necessary concepts. I say the older analyses of 

 theoretical science mainly depend upon supposing a list of self-evi- 

 dent principles to be discoverable, and a list of self-evident concepts 

 to be attainable. Even Locke, empiricist as he was, regarded the 

 self-evident concepts and principles as indeed psychologically due to 

 our experience, but as coming to our consciousness, after once our 

 experience had been matured, in a shape which made them shine by 

 their own light. But the modern logician has learned to see, that the 

 feeling of self-evidence which frequently attends the enunciation of 

 a principle, is commonly an indication that one has not yet learned to 

 analyze the principle. In other words, self-evidence is a suspicious 

 sign. It warns you that you do not yet understand the topic. If 

 you cut a strip of paper and bring the two ends of its together to 

 make a ring, it appears self-evident that any strip of paper must 

 have two sides, and that in order to get from the inside of the ring 

 to the outside of the ring by a movement which keeps your finger, 

 or a pencil, in contact with the paper, you have either to go through 

 the paper, or to go over the edge of the paper. All this seems self- 

 evident or to many people may seem so, until someone shows you 



