The Wittgensteinian and the ontological (3-dimensional) reaction to the naturalistic challenge
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Edmund Runggaldier
Abstract
Starting with a trustworthy theory T, Galvan (1992) suggests to read off, from the usual hierarchy of theories determined by consistency strength, a finer-grained hierarchy in which theories higher up are capable of ‘explaining’, though not fully justifying, our commitment to theories lower down. One way to ascend Galvan’s ‘hierarchy of explanation’ is to formalize soundness proofs: to this extent it often suffices to assume a full theory of truth for the theory T whose soundness is at stake. In this paper, we investigate the possibility of an extension of this method. Our ultimate goal will be to extend T not only with truth axioms, but with a combination of axioms for predicates for truth and necessity.We first consider two alternative strategies for providing possibleworlds semantics for necessity as a predicate, one based on classical logic, the other on a supervaluationist interpretation of necessity. We will then formulate a deductive system of truth and necessity in classical logic that is sound with respect to the given (nonclassical) semantics.
Abstract
Starting with a trustworthy theory T, Galvan (1992) suggests to read off, from the usual hierarchy of theories determined by consistency strength, a finer-grained hierarchy in which theories higher up are capable of ‘explaining’, though not fully justifying, our commitment to theories lower down. One way to ascend Galvan’s ‘hierarchy of explanation’ is to formalize soundness proofs: to this extent it often suffices to assume a full theory of truth for the theory T whose soundness is at stake. In this paper, we investigate the possibility of an extension of this method. Our ultimate goal will be to extend T not only with truth axioms, but with a combination of axioms for predicates for truth and necessity.We first consider two alternative strategies for providing possibleworlds semantics for necessity as a predicate, one based on classical logic, the other on a supervaluationist interpretation of necessity. We will then formulate a deductive system of truth and necessity in classical logic that is sound with respect to the given (nonclassical) semantics.
Chapters in this book
- Frontmatter I
- Contents VII
- Preface IX
- Hilbert’s τ and ϵ in Proof Theory: a proof-theoretical representation of universal and existential statements 1
- Truths in Contemporary Set Theory 23
- Gödel, Searle, and the Computational Theory of the (Other) Mind 41
- Naïve Proof and Curry’s Paradox 61
- Exploring and extending the landscape of conjunctive approaches to verisimilitude 69
- Mental Causation and Nonreductive Physicalism, an Unhappy Marriage? 89
- On Grounding Arithmetic 103
- Risk vs Logic. Karl Barth and Heinrich Scholz on Faith and Reason 119
- On the Ontology of Biological Species 135
- Who is Afraid of Subjective Probability? 151
- Agent-causation and Its Place in Nature 159
- Quantified Modal Justification Logic with Existence Predicate 179
- The Case for Conceptualism 195
- Two days in the life of a genius 207
- Multiple Religious Belonging: A Logico-Philosophical Approach 241
- Definitions by Abstraction in the Peano School 261
- Intelligible Worlds 289
- Necessary Truths and Supervaluations 309
- The Wittgensteinian and the ontological (3-dimensional) reaction to the naturalistic challenge 331
- Measure-Entailment and Support in the Logic of Approximate Generalizations 341
- Bibliography 373
Chapters in this book
- Frontmatter I
- Contents VII
- Preface IX
- Hilbert’s τ and ϵ in Proof Theory: a proof-theoretical representation of universal and existential statements 1
- Truths in Contemporary Set Theory 23
- Gödel, Searle, and the Computational Theory of the (Other) Mind 41
- Naïve Proof and Curry’s Paradox 61
- Exploring and extending the landscape of conjunctive approaches to verisimilitude 69
- Mental Causation and Nonreductive Physicalism, an Unhappy Marriage? 89
- On Grounding Arithmetic 103
- Risk vs Logic. Karl Barth and Heinrich Scholz on Faith and Reason 119
- On the Ontology of Biological Species 135
- Who is Afraid of Subjective Probability? 151
- Agent-causation and Its Place in Nature 159
- Quantified Modal Justification Logic with Existence Predicate 179
- The Case for Conceptualism 195
- Two days in the life of a genius 207
- Multiple Religious Belonging: A Logico-Philosophical Approach 241
- Definitions by Abstraction in the Peano School 261
- Intelligible Worlds 289
- Necessary Truths and Supervaluations 309
- The Wittgensteinian and the ontological (3-dimensional) reaction to the naturalistic challenge 331
- Measure-Entailment and Support in the Logic of Approximate Generalizations 341
- Bibliography 373
