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

Front Cover
Courier Corporation, Jan 1, 2004 - Mathematics - 239 pages
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.
 

Contents

III
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V
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VII
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VIII
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IX
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X
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XI
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XXVII
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XXVIII
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XXIX
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XXX
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XXXII
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XXXIII
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XXXIV
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XXXVI
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XV
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XVI
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XIX
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XXI
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XXII
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XXIII
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XXIV
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XXV
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XXVI
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XXXVII
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XXXVIII
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XXXIX
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XL
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XLI
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XLIII
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XLV
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XLVI
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XLVII
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XLVIII
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XLIX
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L
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LI
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