Philosophy of Set Theory (eBook)

An Historical Introduction to Cantor's Paradise

Mary Tiles (Autor)

eBook Download: EPUB

2012
Dover Publications (Verlag)
978-0-486-13855-8 (ISBN)

Infos

Beginning with perspectives on the finite universe and classes and Aristotelian logic, the author examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory, and more.

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A century ago, Georg Cantor demonstrated the possibility of a series of transfinite infinite numbers. His methods, unorthodox for the time, enabled him to derive theorems that established a mathematical reality for a hierarchy of infinities. Cantor's innovation was opposed, and ignored, by the establishment; years later, the value of his work was recognized and appreciated as a landmark in mathematical thought, forming the beginning of set theory and the foundation for most of contemporary mathematics. As Cantor's sometime collaborator, David Hilbert, remarked, "e;No one will drive us from the paradise that Cantor has created."e; 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; and independence results and the universe of sets. She concludes with views of the constructs and reality of mathematical structure. Philosophers with only a basic grounding in mathematics, as well as mathematicians who have taken only an introductory course in philosophy, will find an abundance of intriguing topics in this text, which is appropriate for undergraduate-and graduate-level courses.

Inhalt

1. The Finite Universe2. Classes and Aristotelian Logic3. Permutations, Combinations and Infinite Cardinalities4. Numbering the Continuum5. Cantor's Transfinite Paradise6. Axiomatic Set Theory7. Logical Objects and Logical Types8. Independence Results and the Universe of Sets9. Mathematical Structure--Construct and RealityFurther ReadingBibliographyGlossary of SymbolsIndex

Produkt-Details

• Erscheint lt. Verlag: 8.3.2012
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Gewicht: 299 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• ISBN-10: 0-486-13855-0 / 0486138550
• ISBN-13: 978-0-486-13855-8 / 9780486138558