David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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History and Philosophy of Logic 1 (1-2):61-93 (1980)
This paper is concerned with the influence that the set theory of georg cantor (1845-1918) bore upon the mathematical logic of bertrand russell (1872-1970). In some respects the influence is positive, And stems directly from cantor's writings or through intermediary figures such as peano: but in various ways negative influence is evident, For russell adopted alternative views about the form and foundations of set theory. After an opening biographical section, Six sections compare and contrast their views on matters of common interest: irrational numbers, Infinitesimals, Cardinal and ordinal numbers, The axiom of infinity, The paradoxes, And the axioms of choice. Two further sections compare the two men over more general questions: the role of logic and the philosophy of mathematics. In a final section I draw some conclusions
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I. Grattan-Guinness (1982). Psychology in the Foundations of Logic and Mathematics: The Cases of Boole, Cantor and Brouwer. History and Philosophy of Logic 3 (1):33-53.
Francisco Rodríguez Consuegra (1987). Russell's Logicist Definitions of Numbers, 1898–1913: Chronology and Significance. History and Philosophy of Logic 8 (2):141-169.
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