اجزای کلاس‌ها

Does the notion of part and whole have any application to classes? Lewis argues that it does, and that the smallest parts of any class are its one-membered "singleton" subclasses. That results in a reconception of set theory. The set-theoretical making of one out of many is just the composition of one whole out of many parts. But first, one singleton must be made out of its one member - this is the distinctively set-theoretical primitive operation. Thus set theory is entangled, with mereology: the theory of parts and wholes. Title ......Page 1 Copyright ......Page 2 Contents ......Page 3 Preface ......Page 5 1.1 Fusions and Classes ......Page 9 1.2 Classes and their Subclasses ......Page 11 1.3 Are there any other Parts of Classes? ......Page 14 1.4 The Null Set ......Page 18 1.5 Consequences of the Main Thesis ......Page 23 1.6 More Redefinitions ......Page 25 1.7 Sethood and Proper Classes ......Page 26 1.8 A Map of Reality ......Page 27 1.9 Nominalistic Set Theory Revisited ......Page 29 2.1 Mysterious Singletons ......Page 37 2.2 Van Inwagen's Tu Quoque ......Page 43 2.3 On Relations that Generate ......Page 46 2.4 Quine on Urelements and Singletons ......Page 49 2.5 The Lasso Hypothesis ......Page 50 2.6 Ramsifying out the Singleton Function ......Page 53 2.7 Metaphysics to the Rescue? ......Page 62 2.8 Credo ......Page 63 3.1 Desiderata for a Framework ......Page 69 3.2 Plural Quantification ......Page 70 3.3 Choice ......Page 79 3.4 Mereology ......Page 80 3.5 Strife over Mereology ......Page 83 3.6 Composition as Identity ......Page 89 3.7 Distinctions of Size ......Page 96 4.1 The Size of Reality ......Page 101 4.2 Mereologized Arithmetic ......Page 103 4.3 Four Theses Regained ......Page 106 4.4 Set Theory Regained ......Page 108 4.5 Ordinary Arithmetic and Mereologized Arithmetic ......Page 115 4.6 What's in a Name? ......Page 117 4.7 Intermediate Systems ......Page 120 4.8 Completeness of Mereologized Arithmetic ......Page 121 Appendix on Pairing ......Page 129 Index ......Page 159 Aimed at philosophers of logic, set theory and mathematics, this philosophical treatise argues that the notion of part and whole - the theory of mereology - has application to classes because of one-membered "singleton" subclasses, thus resulting in a reconception of set theory. David Lewis ; With An Appendix By John P. Burgess, A.p. Hazen, And David Lewis. Includes Bibliographical References And Index.