The Philosophy Of Set Theory: An Historical Introduction To Cantor's Paradise (Dover Books On Mathematics)

an historical introduction to Cantor's paradise

Plot

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.