Logic Without Gaps or Gluts: How to Solve the Paradoxes Without Sacrificing Classical Logic

Description

This book offers a defense against non-classical approaches to the paradoxes. The author argues that, despite appearances, the paradoxes give no reason at all to reject classical logic. In fact, he believes classical solutions fare better than non-classical ones with respect to key tests like Curry’s Paradox, a Liar-like paradox that dialetheists are forced to solve in a way totally disjoint from their solution to the Liar. Graham Priest’s In Contradiction was the first major work that advocated the use of non-classical approaches. Since then, these views have moved into the philosophical mainstream. Much of this movement is fueled by a widespread sense that these logically heterodox solutions get to the real nub of the issue. They lack the ad hoc feel of many other solutions to the paradoxes. The author believes that it's long past time for a response to these attacks against classical orthodoxy. He presents a non-logically-revisionary solution to the paradoxes. This title offers a literal way of cashing out the disquotation metaphor. While the details of the view are novel, the idea has a pre-history in the relevant literature. The author examines objections in detail. He rejects each in turn and concludes by comparing the virtues of his logically orthodox approach with those of the paraconsistent and paracomplete competition. Contents Chapter 1: Logic and the Liar Paradox 1.1 The T-Schema and the Laws of Logic 1.2 Capture and Release 1.3 Paraconsistent and Paracomplete Options 1.4 Comparing Dialetheism to Paracompleteness 1.5 Varieties of Gaps and Gluts 1.6 Once More on the Comparative Plausibility of Restricting the T-Schema and Rejecting Classical Logic 1.7 Summary of the Chapters Chapter 2: Graham Priest and Dialetheism 2.1 Three Priests Walk Into A Bar: What´s Funny About Dialetheism 2.2 The Paradoxes of Motion and Change 2.3 Russell´s Paradox and the Inclosure Schema 2.4 A Bishop and a Priest Walk Into a Bar (Berkeley´s Master Argument) 2.5 Inconsistent Laws and Norms Chapter 3: How to Solve Priest´s Paradoxes Without Sacrificing Classical Logic 3.1 Normative Dilemmas Without Normative Contradictions 3.2 How to Solve the Paradoxes of Naïve Set Theory 3.3 How to Solve the Paradoxes of Motion and Change 3.4 Where Berkeley and Priest (and Max Black!) Go Wrong 3.5 What Has Not Been Solved Chapter 4: Dialetheism and the Laws of Logic 4.1 Dialetheism and Validity 4.2 Dialetheism and the Status of Reductio Ad Absurdum and Modus Tollens 4.3 Alan Weir on Dialetheism and Falsity Preservation 4.4 Why Successful Classical Recapture Is Vital to the Dialetheic Project 4.5 The Failure of Classical Recapture, Part I (The Failure of Principle R) Chapter 5: Dialetheism, Rejection, and Curry´s Paradox 5.1 The Broader Importance of the Failure of Principle R (I: Curry´s Paradox) 5.2 Why Priest Rejected Principle R (and JC Beall Should Too) 5.3 Is the Classical Logician Entitled to Principle R? 5.4 Re-Examining the Relationship Between Dialetheism and (Even ``Informal´´) Reductio Arguments in Light of the Failure of Pr... 5.5 The Broader Importance of the Failure of Principle R (II: Rejection-Talk in Beall and Field) 5.6 Francesco Berto´s Critique of Dialetheist Rejection-Talk Chapter 6: Dialetheism, Rejection, and Probability Theory 6.1 Probability and Quasi-Validity 6.2 Dialetheism and the Consistency of the Empirical World 6.3 Priest´s Case for the Consistency of the Empirical World, Part I (The Argument from Pierre and the Conjunction Principle) 6.4 Priest´s Case for the Consistency of the Empirical World, Part II (The Argument from Perceptual Illusions) 6.5 Why LPm, Logical Pluralism, and Local Validity Cannot Save Us 6.6 The Failure of Classical Recapture, Part II (The Failure of the Probabilistic Strategy) 6.7 Francesco Berto on Negation, Exclusion, and NOT Chapter 7: Hartry Field and Paracompleteness 7.1 Paracompleteness and Truth Preservation 7.2 Paracompleteness and Ordinary Reasoning 7.3 Paracompleteness and Probability 7.4 Paracompleteness and Rejection 7.5 Paracompleteness and Revenge 7.6 Paracompleteness and Hierarchies: Field Vs. Tarski and Maudlin 7.7 Paracompleteness and the Exhaustive Characterization Project 7.8 Paracompleteness and Properties: Field Solution to Russell´s Paradox and Mine Chapter 8: How to Solve the Liar Paradox Without Sacrificing Classical Logic 8.1 Some Preliminary Points About Propositions 8.2 More Preliminaries: Disquotationalism and Inferentialism 8.3 How To Cash Out the Disquotation Analogy and Solve the Liar Paradox in the Bargain: Content Inheritance Disquotationalism 8.4 Comparing CID With Other Disquotationalisms 8.5 Objections and Replies 8.6 Comparing the Solutions: The Principle of Uniform Solution 8.7 Conclusion: Vagueness, Quantum Weirdness, and Other Loose Ends References Index