Philosophy 142

“Philosophical logic” includes both (a) the philosophical investigation of the fundamental concepts of logic and (b) the deployment of logical methods in the service of philosophical ends. We’ll tackle five interconnecting topics in philosophical logic:

1. Quantifiers: You may think you learned everything there is to know about quantifiers in Philosophy 12A. But in fact, there are quite a few quantificational idioms that we can’t understand in terms of the quantification theory you learned. We’ll look at the logic of identity, numerical quantifiers, generalized quantifiers, definite descriptions, substitutional quantifiers, and plural quantifiers.

2. Modal logic: In addition to talking about what is the case, we talk about what might have been the case and what could not have been otherwise. Modal logic gives us tools to analyze reasoning involving these notions. We’ll get a basic grasp on some of the fundamentals of propositional modal logic, and then delve into some hairy conceptual problems surrounding quantified modal logic, explored by Quine, Kripke, and others. We’ll also look at the famous “slingshot argument,” which was used by Quine and Davidson to reject modal logic and correspondence theories of truth. At this point our work on definite descriptions will come in handy!

3. Logical consequence: If you ask what logic is about, a reasonable (though not completely satisfactory) answer is that it’s the study of what follows from what, that is, of logical consequence. But how should we think of this relation? We’ll start by looking at Tarski’s account of logical consequence, which has become the orthodox account. On this account, logical consequence is a matter of truth preservation: P follows from Q if there is no model on which P is true and Q false. We’ll talk about how this account relates to the older idea that P follows from Q if it is impossible for P to be true and Q false. Then we’ll consider some alternatives. One alternative is to define consequence in terms of proof. We’ll look at a version of this idea by Dag Prawitz, which yields a nonclassical logic called “intuitionistic logic.” We’ll then look at the suggestion that relevance in addition to truth preservation is required for logical consequence. We’ll see how one might develop a nonclassical “relevance logic,” and we’ll consider some technical and philosophical issues that speak for and against a requirement of relevance. Finally, we’ll consider how, exactly, logic relates to reasoning.

4. Conditionals: In Philosophy 12A you were taught to translate English conditionals using the “material conditional,” a truth-functional connective. This leads to some odd results: for example, “If I am currently on Mars, then I am a hippopotamus” comes out true (since the antecedent is false). We’ll start by considering some attempts to defend the material-conditional analysis of indicative conditionals in English. Then we’ll consider some alternatives, inculding Edgington’s view that indicative conditionals have no truth-conditions, Stalnaker’s elegant modal account, and the view that indicative conditionals should be understood as conditional assertions. Finally, we’ll look at McGee’s “counterexample to modus ponens,” and consider whether this sacrosanct inference rule is actually invalid!

5. Vagueness: Finally we’ll turn to the “sorites paradox,” or paradox of the heap, which argues: five thousand grains of sand make a heap; taking one grain away from a heap still leaves you with a heap; so…one grain of sand makes a heap. Philosophical logicians have suggested that it is a mistake to use classical logic and semantics in analyzing this argument, and they have proposed a number of alternatives. We’ll consider three of them: (a) a three-valued logic, (b) a continuum-valued (or fuzzy) logic, and (c) a supervaluational approach that preserves classical logic (mostly) but not classical semantics. If there’s time, we’ll also look at a short argument by Gareth Evans that purports to show that vagueness must be a semantic phenomenon: that is, that there is no vagueness “in the world.”

Requirements will include both papers and problem sets.

Prerequisites: Philosophy 12A or equivalent, and at least one other course in philosophy. The course covers some technical material, but knowledge of logic beyond 12A will not be assumed.

Books: Course Reader.