The Philosophy of Set Theory: An Historical Introduction to Cantor's Paradise

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Courier Corporation, 2004 - Mathematics - 239 pages
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David Hilbert famously remarked, 'No one will drive us from the paradise that Cantor has created'. This volume offers a guided tour of modern mathematics' Garden of Eden, beginning with perspectives on the finite universe and classes and Aristotelian logic. Author Mary Tiles further examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory; logical objects and logical types; independence results and the universe of sets; and the constructs and reality of mathematical structure. Philosophers and mathematicians will find an abundance of intriguing topics in this text, which is appropriate for undergraduate - and graduate-level courses.
 

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Contents

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