"If you turn left at the next corner, you will see a blue house at the end of the street." That sentence - a conditional - might be true even though it is possible that you will not see a blue house at the end of the street when you turn left at the next corner. A moving van may block your view; the house may have been painted pink; a crow might swoop down and peck out your eyes. Still, in some contexts, we might ignore these possibilities and correctly assert the conditional. In this book, Christopher Gauker argues that such context-relativity is the key to understanding the semantics of conditionals. Contexts are defined as objective features of the situation in which a conversation takes place, and the semantic properties of sentences - conditionals included - are defined in terms of assertibility in a context.
One of the primary goals of a theory of conditionals has to be to distinguish correctly between valid and invalid arguments containing conditionals. According to Gauker, an argument is valid if the conclusion is assertible in every context in which the premises are assertible. This runs counter to what Gauker sees as a systematic misreading of the data by other authors, who judge arguments to be invalid if they can think of a context in which the premises are judged true and some other context in which the conclusion is judged false. Different schools of thought on conditionals reflect fundamentally different approaches to semantics. Gauker offers his theory as a motive and test case for a distinctive kind of semantics that dispenses with reference relations and possible worlds.
Table of Contents: 1.1 The Context-Relativity of Conditionals 3 1.2 Conversations in the Abstract 9 1.3 Primitive Cotexts 12 1.4 Multicontexts and Conditionals 16 1.5 Indicative Conditionals versus Material Conditionals 24 1.6 Subjuctive Conditionals 25 1.7 Strong Assertibility 31 1.8 Two Stipulations 33 1.9 Foundations 36 1.10 My Argumentative Strategy 45 2 The Concept of Logical Validity 47 2.1 Arguments versus Inferences 49 2.2 Validity as a Matter of Form 52 2.3 The Model-Theoretic Conception of Validity 55 2.4 The Context-Logical Conception of Logical Validity 73 2.5 Does This Conception Do Any Better? 79 2.6 Conditionals as Context-Relative Rules of Inference 82 3 A Catalog of Argument Forms 83 4 Critical Comparisons 127 4.1 The Received View 130 4.2 Stalnaker's Theory 135 4.3 The Barwise-Lycan Theory 162 4.4 Lowe's Theory 170 4.5 Veltman's Theory 172 5 The Core Theory 177 5.1 Definitions and Conditions 177 5.2 Examples 181 5.3 Some Basic Theorems 187 5.4 A Key Result 192 5.5 The Rationales for Certain Features 193 5.6 Some Shortcomings of the Core Theory 203 6 Two Enhancements 205 6.1 Strong Assertibility 205 6.2 Conditional Tautologies 219 7 Subjunctive Conditionals 225 7.1 The Grammatical Distinction 225 7.2 The Formal Theory of Subjunctive Conditionals 241 7.3 Examples 245 7.4 A Couple of Enhancements 249 8 "Even If", et cetera 253 8.1 "Even If" 254 8.2 Quantified Conditionals 272 8.3 "Only If" 277 8.4 Order Effects 280 8.5 Conditionals with Conditional Antecedents 284 9 Decidability 289 9.1 Preliminaries 290 9.2 The Algorithm 298 9.3 Examples 312 9.4 Why the Algorithm Works 314 References Download Chapter as PDF Sample Chapter - Download PDF (45 KB) 325 Index Download Chapter as PDF Sample Chapter - Download PDF (34 KB) 331