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

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, and more. 1989 edition. Includes 32 figures. 1. The Finite Universe 2. Classes and Aristotelian Logic 3. Permutations, Combinations and Infinite Cardinalities 4. Numbering the Continuum 5. Cantor's Transfinite Paradise 6. Axiomatic Set Theory 7. Logical Objects and Logical Types 8. Independence Results and the Universe of Sets 9. Mathematical Structure--Construct and Reality Further Reading Bibliography Glossary of Symbols Index