P751 | 3258 | Barwise

Topic: Logical Consequence Note: This course carries 4 credit hours. The central topic of the seminar will be that of logical consequence. What does it mean for one sentence to be a logical consequence of another? The standard answer to this is usually taken to be given to Tarski's famous analysis of the notion. We will start by reading Tarski's analysis. A few years ago, John Etchemendy published the book The Concept of Logical Consequence, where he argued that Tarski's famous analysis is wrong on conceptual grounds. This book had recently been reprinted and so is now available again. The central portion of the course will be devoted to going through Etchemendy's argument. Since the publication of Etchemendy's book, many authors have published attacks on Etchemendy's argument, attempts to salvage Tarski's analysis by finding an error in the argument. Interestingly, they seem to find the error in very different places. We will read a selection of these rebuttals. Etchemendy has recently written a follow-up article, based on his failure to be convinced by any of the rebuttals. In this paper he both summarizes his argument against the Tarskian account, in light of what he takes to be misunderstandings of it, ang goes on to sketch his positive view of how to develop a theory of logical consequence. We will also read this paper. If time permits, we will also read some other related papers. Students will be expected to lead seminar discussions and to write a term paper on a topic closely related to that of the seminar. Prerequisites: Elementary set theory and first-order logic (up through the completeness theorem). Students who have successfully completed P505 meet the prerequisite.