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

Dover Publications (1989)
Abstract
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. 1989 ed. 32 figures.
Keywords Mathematics Philosophy  Set theory
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Reprint years 2004
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Call number QA8.4.T54 2004
ISBN(s) 0486435202   9780486435206  
DOI 10.2307/2219596
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B. H. Slater (2006). Grammar and Sets. Australasian Journal of Philosophy 84 (1):59 – 73.
Dougal Blyth (2000). Platonic Number in the Parmenides and Metaphysics XIII. International Journal of Philosophical Studies 8 (1):23 – 45.

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