Proof and Falsity: A Logical Investigation

Description

Provides an original analysis of negation - a central concept of logic - and how to define its meaning in proof-theoretic semantics. This book argues that the meaning of negation, perhaps the most important logical constant, cannot be defined within the framework of the most comprehensive theory of proof-theoretic semantics, as formulated in the influential work of Michael Dummett and Dag Prawitz. Nils Kürbis examines three approaches that have attempted to solve the problem - defining negation in terms of metaphysical incompatibility; treating negation as an undefinable primitive; and defining negation in terms of a speech act of denial - and concludes that they cannot adequately do so. He argues that whereas proof-theoretic semantics usually only appeals to a notion of truth, it also needs to appeal to a notion of falsity, and proposes a system of natural deduction in which both are incorporated. Offering new perspectives on negation, denial and falsity, his book will be important for readers working on logic, metaphysics and the philosophy of language. Nils Kürbis is a research fellow in the Department of Philosophy at University College London. He has published articles in the Journal of Philosophical Logic, Logique et Analyse and Grazer Philosophische Studien. Cover Summary Title Page Contents Acknowledgements Introduction 1 Meaning 1.1 Meaning, Use and Logic 1.2 Linguistic Knowledge 1.3 Truths and Rules of Logic 1.4 Definitions 1.5 The Theory of Meaning 1.6 Realism and Anti-Realism 2 Logic 2.1 Logical Constants 2.2 Gentzen’s Natural Deduction 2.3 Molecularity and Complexity of Rules 2.4 Dissonance 2.5 Gentzen’s Thesis and Three Kinds of Harmony 2.6 Two Inversion Principles 2.7 Grounds and Consequences Again 2.8 Stability and Harmony Defined 2.9 Loose Ends 2.10 Formalities 3 Negation 3.1 Introduction 3.2 Tertium Non Datur 3.3 The Rules of Classical Logic 3.4 Ex Falso Quodlibet 3.5 Final Remarks on Dummett on ⊥ 3.6 Conclusion 4 Nothing 4.1 The Problem of Negation 4.2 Primitive Incompatibility 4.3 The Epistemology and Metaphysics of Negation 4.4 Concluding Reflections 5 Not 5.1 Primitive Negation 5.2 Against Primitive Negation 5.3 Conclusion 6 No 6.1 Primitive Denial 6.2 Formal Bilateralism 6.3 Informal Bilateralism 6.4 Conclusion 7 Falsity 7.1 Primitive Falsity 7.2 Truth, Falsity and Negation in the Metalanguage 7.3 The Intuitionist Route 7.4 The Bi-Intuitionist Route 7.5 The Classicist Route 7.6 Conclusion Bibliography Index