The Philosophy of Set Theory: An Historical Introduction to Cantor's ParadiseDavid 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. |
Contents
III | 6 |
V | 10 |
VI | 12 |
VII | 22 |
VIII | 32 |
IX | 33 |
X | 39 |
XI | 47 |
XXVII | 107 |
XXVIII | 111 |
XXIX | 114 |
XXX | 118 |
XXXII | 121 |
XXXIII | 134 |
XXXIV | 138 |
XXXVI | 146 |
Other editions - View all
The Philosophy of Set Theory: An Historical Introduction to Cantor's Paradise Mary Tiles Limited preview - 2012 |
Common terms and phrases
absolutely infinite actual infinite algebraic applications Aristotelian Aristotle arithmetic assumption axiom of choice axiom of reducibility axiomatization belong Cantor classical finitist constructible sets contains continuum hypothesis defined definition denumerable distinction division domain elements EQUATIONS existence expression extension extensional figure finite number Frege geometrical intuition Gödel inaccessible cardinal infinite cardinal infinite ordinal numbers infinite sequence infinite sets infinity inner model introduction kind language of ZF limit logic mathematical mathematician means model of ZF natural numbers negation nominalist notion number of points objects one-one correspondence ordinal number paradoxes philosophical physical possible potentially infinite power set predicative functions principle problem proof propositional functions proved quantifiers question rational numbers real numbers relation Russell's sense sequences of rationals set axiom set of points set theory space structure subset theoretical things tion transfinite transfinite numbers true variable whole given Zeno's paradoxes ZF axioms