i88 SCIENCE AND METHOD. 



whether a definition can be regarded as sufficiently 

 simple to be acceptable ? To this question we get no 

 answer except a candid confession of powerlessness. 

 " The axioms as to what functions are predicative 

 have to be exceedingly complicated, and cannot be 

 recommended by any intrinsic plausibility. This is a 

 defect which might be remedied by greater ingenuity, 

 or by the help of some hitherto unnoticed distinction. 

 But hitherto, in attempting to set up axioms for this 

 theory, I have found no guiding principle except the 

 avoidance of contradictions." 



This theory therefore remains very obscure. In the 

 darkness there is a single glimmer, and that is the 

 word zigzag. What Mr. Russell calls zigzagginess is 

 no doubt this special character which distinguishes the 

 argument of Epimenides. 



According to the theory of limitation of size, a 

 class must not be too extensive. It may, perhaps, 

 be infinite, but it must not be too infinite. 



But we still come to the same difficulty. At what 

 precise moment will it begin to be too extensive ? Of 

 course this difficulty is not solved, and Mr. Russell 

 passes to the third theory. 



In the no classes theory all mention of the word 

 class is prohibited, and the word has to be replaced by 

 various periphrases. What a change for the logis- 

 ticians who speak of nothing but class and classes of 

 classes ! The whole of Logistic will have to be re- 

 fashioned. Can we imagine the appearance of a page 

 of Logistic when all propositions dealing with class 

 have been suppressed ? There will be nothing left 

 but a few scattered survivors in the midst of a blank 

 page. Apparent rari nantes in gurgite vasto. 



