Reflections on Consequence

In The Concept of Logical Consequence (CLC) [13], I presented an extended argument that the standard, Tarskian analysis of logical consequence and logical truth is wrong. In the years since its publication, over a score of authors have written reviews, articles, or portions of books criticizing various arguments I gave in the book.1 Nearly all have presented what the authors considered devastating replies to some or all of my arguments. Many of the replies are very thoughtful and contain much with which I entirely agree. Other authors misunderstood crucial parts of my argument, no doubt because I expressed them poorly. But all in all, the attention the book has gotten is gratifying. My only regret is that due to an onerous administrative appointment at my university, I was unable to reply to individual articles as they came out. This paper is not meant to be a “reply to my critics.” Such a reply would be of very little interest to any one reader, inasmuch as the critics themselves disagree so sharply on fundamental points, and so the lines of criticism are often at odds with one another. Instead, the paper is meant to be a rethinking of my overall argument in light of what I have learned from the various critiques, in particular what I have learned about ways in which CLC was confusing, incomplete, or otherwise misleading. Where appropriate, I indicate in footnotes how points made in this paper relate to specific criticism that has appeared in print. Let me say at the outset that I still believe that all of the significant points made in the book are essentially correct. Indeed, I am confident that most readers will not need my help answering some of the criticism that has been offered in the literature. A fair amount of that criticism has centered on historical questions about Tarski’s 1936 paper “On the Concept of Logical Consequence” [37], which I took as the philosophical locus of the standard analysis. Tarski’s short paper is remarkably puzzling in many ways, but as I said in the book, and as most commentators agree, the important issue is not what Tarski was