Of course we all know now that mathematics has proved that logic doesn't really make sense, but Etchemendy (philosophy, Stanford Univ.) goes further and challenges the received view of the conceptual underpinnings of modern logic by arguing that Tarski's model-theoretic analysis of logical consequences is wrong. He may have found the soft underbelly of the dead horse. Annotation copyrighted by Book News, Inc., Portland, OR.

This paper examines the question of the extensional correctness of Tarskian definitions of logical truth and logical consequence. I identify a few different informal properties which are necessary for a sentence to be an informal logical truth and look at whether they are necessary properties of Tarskian logical truths. I examine arguments by John Etchemendy and Vann McGee to the effect that some of those properties are not necessary properties of some Tarskian logical truths, and find them unconvincing. I stress (...) the point that since the hypothesis that Tarski's definitions are extensionally correct is deeply entrenched, the burden of proof is still on the shoulders of Tarski's critics, who have not lifted the burden. (shrink)

This paper examines the connection between model-theoretic truth and necessary truth. It is argued that though the model-theoretic truths of some standard languages are demonstrably ''''necessary'''' (in a precise sense), the widespread view of model-theoretic truth as providing a general guarantee of necessity is mistaken. Several arguments to the contrary are criticized.

The main body of this paper assesses a leading recent theory of fairness, a theory put forward by John Broome. I discuss Broome's theory partly because of its prominence and partly because I think it points us in the right direction, even if it takes some missteps. In the course of discussing Broome's theory, I aim to cast light on the relation of fairness to consistency, equality, impartiality, desert, rights, and agreements. Indeed, before I start assessing Broome's theory, I discuss (...) two very popular conceptions of fairness that contrast with his. One of these very popular conceptions identifies fairness with the equal and impartial application of rules. The other identifies fairness with all-things-considered moral rightness. (shrink)

The question, "Which modal logic is the right one for logical necessity?," divides into two questions, one about model-theoretic validity, the other about proof-theoretic demonstrability. The arguments of Halldén and others that the right validity argument is S5, and the right demonstrability logic includes S4, are reviewed, and certain common objections are argued to be fallacious. A new argument, based on work of Supecki and Bryll, is presented for the claim that the right demonstrability logic must be contained in S5, (...) and a more speculative argument for the claim that it does not include S4.2 is also presented. (shrink)

John Broome; V*—Fairness, Proceedings of the Aristotelian Society, Volume 91, Issue 1, 1 June 1991, Pages 87–102, https://doi.org/10.1093/aristotelian/91.1.87.

Logical consequence is a notion that every person who reasons must possess, at least implicitly. To give a precise and accurate characterization of this notion is the fundamental task of logic. In a similar way, the notion of effectivity is a concept that anyone with a basic training in mathematics possesses, and the most fundamental task of a theory of computability is to give a precise characterization of this notion. The problem concerning effectivity was solved in the 1930s, almost as (...) soon as it was raised, by the work of Turing, Church, and others. By contrast, the correct and precise characterization of logical consequence has been hotly contested through the two and a half thousand-year history of logic. (shrink)

In the first section, I consider what several logicians say informally about the notion of logical consequence. There is significant variation among these accounts, they are sometimes poorly explained, and some of them are clearly at odds with the usual technical definition. In the second section, I first argue that a certain kind of informal account—one that includes elements of necessity, generality, and apriority—is approximately correct. Next I refine this account and consider several important questions about it, including the appropriate (...) characterization of necessity, the criterion for selecting logical constants, and the exact role of apriority. I argue, among other things, that there is no need to recognize a special logical sense of necessity and that the selection of terms to serve as logical constants is ultimately a pragmatic matter. In the third section, I consider whether the informal account I have presented and defended is adequately represented by the usual technical definition. I show that it is, and provably so, for certain limited ways of selecting logical constants. In the general case, however, there seems to be no way to be sure that the technical and informal accounts coincide. (shrink)

The main body of this paper assesses a leading recent theory of fairness, a theory put forward by John Broome. I discuss Broome's theory partly because of its prominence and partly because I think it points us in the right direction, even if it takes some missteps. In the course of discussing Broome's theory, I aim to cast light on the relation of fairness to consistency, equality, impartiality, desert, rights, and agreements. Indeed, before I start assessing Broome's theory, I discuss (...) two very popular conceptions of fairness that contrast with his. One of these very popular conceptions identifies fairness with the equal and impartial application of rules. The other identifies fairness with all-things-considered moral rightness. (shrink)