The Role of CBT in Russell’s Paradox

  • Arie HinkisEmail author
Part of the Science Networks. Historical Studies book series (SNHS, volume 45)


Russell tells in his 1903 “The principles of mathematics” (POM p 101) that he “was led to it [his paradox] in the endeavor to reconcile Cantor’s proof that there can be no greatest cardinal number with the very plausible supposition that the class of all terms … has necessarily the greatest possible number of members”. Cantor’s proof mentioned here is the proof of Cantor’s Theorem (1892) which, Russell says (p 362), “is found to state that, if u be a class, the number of classes contained in u is greater than the number of terms of u”. The class of all terms thus appeared to Russell as a refutation to Cantor’s Theorem. Russell’s Paradox was thus obtained within a Lakatosian proof-analysis.


Relation Counterpart Hide Assumption Diagonal Argument Gestalt Switch Equal Domain 
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© Springer Basel 2013

Authors and Affiliations

  1. 1.The Cohn Institute for the History and Philosophy of Science and IdeasTel Aviv UniversityTel AvivIsrael

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