Florida Philosophical Review 12 (1):83-92 (2011)

Authors
Burkay Ozturk
Texas State University
Abstract
This paper deploys a Cantor-style diagonal argument which indicates that there is more possible mathematical content than there are propositional functions in Russell and Whitehead's Principia Mathematica and similar formal systems. This technical result raises a historical question: "How did Russell, who was himself an expert in diagonal arguments, not see this coming?" It turns out that answering this question requires an appreciation of Russell's understanding of what logic is, and how he construed the relationship between logic and Principia Mathematica.
Keywords Principia Mathematica  expressive completeness  incompleteness  cantor  diagonalization  Godel  Russell  Whitehead
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My Philosophical Development.B. RUSSELL - 1958 - Hibbert Journal 57:2.
My Philosophical Development.Morris Weitz & Bertrand Russell - 1961 - Philosophical Review 70 (1):112.

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