Everything, more or less: A defence of generality relativism (Oxford Philosophical Monographs)

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? Do we ever succeed in theorizing about ABSOLUTELY EVERYTHING in some interestingly final, all-caps-worthy sense of ‘absolutely everything’? Not according to generality relativism. In 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 limitations on which pluralities of items may be encoded as a set. On the other hand, 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? This 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. Cover Everything, More or Less: A Defence of Generality Relativism Copyright Dedication Preface Contents Acknowledgements 1: Absolutism and Relativism 1.1 Absolutism 1.2 The argument from sortal restriction 1.3 The argument from metaphysical realism 1.4 The argument from indefinite extensibility Collection The russell reductio Interpretation The williamson-russell reductio The naivety rejoinder 1.5 The objection from mysteriousness 1.6 The objection from ineffability 2: Russell, Zermelo, and Dummett 2.1 Self-reproductive processes and classes A template for paradox The Dummettian argumentThe naivety rejoinder redux 3: Quantifiers 3.1 MT-semantics for the language of set theory 3.2 MT-semantics for the language of generalized quantifiers The language of generalized quantifiers: syntax The language of generalized quantifiers: MT-semantics 3.3 Intended MT-interpretations? 3.4 P-semantics for the language of set theory 3.5 SP-semantics for the language of generalized quantifiers The language of generalized quantifiers: SP-semantics Interpreting superplural quantifiers 3.6 Semantics for Quineans The Williamson-Russell paradox Semantic optimism Whither Quinean absolutism?4: Restrictionism and Expansionism 4.1 Domains and universes 4.2 Restrictionism The indexical account Tacit nominal variables Pragmatic restriction Contextual restrictionism 4.3 The objection from semantic theorizing 4.4 Expansionism Procedural postulationism Interpretational expansionism The objection from creationism The objection from crypto-restrictionism The objection from semantic theorizing 4.5 The objection from kind-generalizations Kind-generalizations An intensional gap? A hyperintensional gap? AvoidingWilliamson's regress Expressive issues revisited5: Schemas 5.1 The objection from ineffability Absolutism stated Is relativism self-defeating? 5.2 Open-ended schemas 5.3 Relativism schematized 5.4 Systematic ambiguity 5.5 The objection from side-conditions 6: Modal Operators 6.1 Modal generality Beyond schematic generality Non-circumstantial modality Interpretational modality: a bimodal account 6.2 Modalization: first-order theories Invariance and Mirroring 6.3 Modalization: plural theories Adding plural resources Indefinite extensibility Relativism stated 6.4 Set theory for relativists "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." -- Oxford Scholarship Online Presentación del editor: "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." 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. In 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 Limitations On Which Pluralities Of Items May Be Encoded As A Set. On The Other Hand, 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? This 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. Almost no systematic theorizing is generality-free. Scientists test general hypotheses; set theorists prove theorems about every set; metaphysicians espouse theses about all things of any kind. But do we ever succeed in theorizing about absolutely everything? Not according to generality relativism, which J.P. Studd defends in this book.