Everything, more or less : a defence of generality relativism / J.P. Studd.

Format:

Book

Author/Creator:

Studd, James, 1982- author.

Series:

Oxford philosophical monographs

Language:

English

Subjects (All):

Relativity.

Physical Description:

xii, 279 pages ; 24 cm.

Edition:

First edition.

Place of Publication:

Oxford : Oxford University Press, 2019.

Summary:

Almost no systematic theorizing is generality-free. Scientists test general hypotheses; set theorists prove theorems about every set; metaphysicians espouse theses about all things regardless of their kind. But how general can we be and do we ever succeed in theorizing about absolutely everything? Not according to generality relativism. 0In its most promising form, this kind of relativism maintains that what 'everything' and other quantifiers encompass is always open to expansion: no matter how broadly we may generalize, a more inclusive 'everything' is always available. The importance of the issue comes out, in part, in relation to the foundations of mathematics. Generality relativism opens the way to avoid Russell's paradox without imposing ad hoc imitations on which pluralities of items may be encoded as a set. On the other0hand, generality relativism faces numerous challenges: What are we to make of seemingly absolutely general theories? What prevents our achieving absolute generality simply by using 'everything' unrestrictedly? How are we to characterize relativism without making use of exactly the kind of generality this view foreswears?0This book offers a sustained defence of generality relativism that seeks to answer these challenges. Along the way, the contemporary absolute generality debate is traced through diverse issues in metaphysics, logic, and the philosophy of language; some of the key works that lie behind the debate are reassessed; an accessible introduction is given to the relevant mathematics; and a relativist-friendly motivation for Zermelo-Fraenkel set theory is developed.

Contents:

1 Absolutism and Relativism p. 1

1.1 Absolutism p. 1

1.2 The argument from sortal restriction p. 4

1.3 The argument from metaphysical realism p. 6

1.4 The argument from indefinite extensibility p. 10

1.5 The objection from mysteriousness p. 15

1.6 The objection from ineffability p. 18

2 Russell, Zermelo, and Dummett p. 21

2.1 Self-reproductive processes and classes p. 22

2.2 The vicious-circle principle p. 31

2.3 Zermelo-Fraenkel set theory p. 40

2.4 The open-ended hierarchy p. 47

2.5 Indefinite extensibility p. 54

3 Quantifiers p. 61

3.1 MT-semantics for the language of set theory p. 62

3.2 MT-semantics for the language of generalized quantifiers p. 63

3.3 Intended MT-interpretations? p. 69

3.4 P-semantics for the language of set theory p. 73

3.5 SP-semantics for the language of generalized quantifiers p. 75

3.6 Semantics for Quineans p. 79

4 Restrictionism and Expansionism p. 87

4.1 Domains and universes p. 88

4.2 Restrictionism p. 91

4.3 The objection from semantic theorizing p. 99

4.4 Expansionism p. 102

4.5 The objection from kind-generalizations p. 110

5 Schemas p. 120

5.1 The objection from ineffability p. 120

5.2 Open-ended schemas p. 125

5.3 Relativism schematized p. 128

5.4 Systematic ambiguity p. 131

5.5 The objection from side-conditions p. 135

6 Modal Operators p. 142

6.1 Modal generality p. 142

6.2 Modalization: first-order theories p. 153

6.3 Modalization: plural theories p. 157

6.4 Set theory for relativists p. 163

6.5 Objections from unintelligibility p. 171

6.6 Hybrid relativism p. 176

7 Russell Reductio Redux p. 178

7.1 The schematic argument p. 179

7.2 The modal argument p. 184

7.3 Uncollectability p. 186

7.4 Instability p. 195

7.5 Non-comprehensibility p. 201

8 How Universes Expand p. 214

8.1 The explanatory challenge p. 215

8.2 The Quantification Question p. 217

8.4 The Expansion Question p. 231

8.5 Idealization p. 237.

Notes:

Includes bibliographical references and index.

ISBN:

9780198719649

0198719647

OCLC:

1061819226