David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Dover Publications (1989)
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|
|Categories||categorize this paper)|
|Buy the book||$6.55 used (57% off) $7.48 new (50% off) $13.18 direct from Amazon (12% off) Amazon page|
|Call number||QA8.4.T54 2004|
|Through your library||Configure|
References found in this work BETA
No references found.
Citations of this work BETA
B. H. Slater (2006). Grammar and Sets. Australasian Journal of Philosophy 84 (1):59 – 73.
Similar books and articles
Christopher Menzel (1984). Cantor and the Burali-Forti Paradox. The Monist 67 (1):92-107.
John Mayberry (1994). What is Required of a Foundation for Mathematics? Philosophia Mathematica 2 (1):16-35.
Edward G. Belaga, From Traditional Set Theory – That of Cantor, Hilbert , Gödel, Cohen – to Its Necessary Quantum Extension.
J. Ferreiros (2004). The Motives Behind Cantor’s Set Theory: Physical, Biological and Philosophical Questions. Science in Context 17 (1/2):1–35.
Edward G. Belaga (forthcoming). Retrieving the Mathematical Mission of the Continuum Concept From the Transfinitely Reductionist Debris of Cantor’s Paradise. Extended Abstract. International Journal of Pure and Applied Mathematics.
Peter Schreiber (1996). Mengenlehre—Vom Himmel Cantors Zur Theoria Prima Inter Pares. NTM International Journal of History and Ethics of Natural Sciences, Technology and Medicine 4 (1):129-143.
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.
Added to index2009-01-28
Total downloads53 ( #25,161 of 1,088,389 )
Recent downloads (6 months)1 ( #69,601 of 1,088,389 )
How can I increase my downloads?