sentences:  The totality of all logical objects, or of all propositions, involves, it would seem a fundamental logical difficulty.What the complete solution of the difficulty may be, I have not succeeded in discovering; but as it affects the very foundations of reasoning..."
  
  By the time of his 1908 "Mathematical logic as based on the theory of types" Russell had studied "the contradictions" (among them the Epimenides paradox, the Burali-Forti paradox, and Richard's paradox) and concluded that "In all the contradictions there is a common characteristic, which we may describe as self-reference or reflexiveness".In 1903, Russell defined "predicative" functions as those whose order is one more than the highest-order function occurring in the expression of the function.