Truth Through Proof: A Formalist Foundation for Mathematics

Title ......Page 1
Copyright ......Page 2
Preface ......Page 3
Dedication ......Page 10
Contents ......Page 11
Introduction ......Page 13
§I Traditional Realism ......Page 24
§II Contemporary Realism ......Page 26
§III Sense, Circumstance, World ......Page 37
§I Projectivism in the SCW Framework ......Page 51
§II Snapshot Dispositions, Correction, Fiction ......Page 59
§III Reduction ......Page 68
§IV A Map of the Terrain ......Page 76
§I An Initial Specification ......Page 80
§II Contentful Language ......Page 89
§III Quantification and Existence ......Page 102
§I Closure ......Page 111
§II Relativism or Pluralism? ......Page 113
§III Incompleteness ......Page 130
§I Conservativeness ......Page 139
§II* Comparison with Fictionalism ......Page 148
§III Theoretical Language ......Page 153
§IV Promises, Promises ......Page 163
§I Tokenism ......Page 164
§II The Spectre of Strict Finitism ......Page 188
§I Idealization ......Page 204
§II The Spectre of Finitism ......Page 221
§I Calculus versus Logic ......Page 234
§II The Basic Semantics Again ......Page 235
§III Logical Consequence ......Page 238
§IV The Conditional ......Page 242
§V* Quantification and Infinitary Logic ......Page 245
§VI Classical Recapture ......Page 247
§VII Really Existing Mathematics ......Page 251
Conclusion ......Page 261
§A.1 Minimax Rules ......Page 264
§A.2 Soundness of Strict Neo-classical Logic ......Page 265
§A.3 Infinitary Rules ......Page 268
§A.4 IS ......Page 269
§A.5 Prime Extensions ......Page 270
§A.6 Limitative Results in Infinitary Logics ......Page 272
Bibliography ......Page 274
Name Index ......Page 285
Subject Index ......Page 289