BERTRAND RUSSELL AND THE ORIGIN OF THE SET-THEORETIC PARADOXES

The main goal of this thesis is to study the role played by Bertrand Russell in the origin and development of the paradoxes of set theory.; First, I describe what I call 'a standard interpretation of the origins of the set theoretic paradoxes'. This chapter describes the explanation of other historians of how the paradoxes were discovered. I also present a discussion of the major reasons why this interpretation--with all its small variants--has to be discarded.; Second, I analyze Russell's early philosophical and mathematical background to his writing of The Principles of Mathematics. I try to show how his study of Kant, Hegel, Cantor, among others, is related to how Russell became interested in philosophical antinomies, and how he originally studied the relations between mathematics and logic. Throughout this analysis, I describe the stages of early drafts of The Principles, and the influence of Georg Cantor which most historians influenced by Russell's own later recollections have overlooked.; I next describe how Russell discovered Cantor's paradox; his own paradox; and how he formulated the elements that would provoke the discovery of yet another paradox, the Burali-Forti paradox. Russell's correspondence, especially with Louis Couturat, and the comparison between the manuscript of The Principles with the printed version are used to support my analysis. I maintain that Russell himself discovered at least two of the three most famous paradoxes of the theory of sets--and set forth the elements to provoke another one; that there are some inconsistencies contained in The Principles related to the paradoxes; and, that Russell's later recollections of these developments are inaccurate.; Fourth, I finally discuss the emergence of the nowadays called 'semantic paradoxes'. The description of the polemics and debates concerning the Well-Ordering Theorem help clarify how these paradoxes originated and spread. I attempt to show that, contrary to the previously described standard interpretation, these paradoxes did not develop as an immediate and reasonable consequence of the origin of the 'logical' ones. I try to prove that it was the polemic surrounding the Well-Ordering Theorem that dominated the whole outlook.