This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11-page 1936 Tarski consequence-definition paper is based on a monistic fixed-universe framework?like Begriffsschrift and Principia Mathematica. Monistic fixed-universe frameworks, common in pre-WWII logic, keep the range of the individual variables fixed as the class of all individuals. The contrary alternative is that the definition is predicated on a pluralistic multiple-universe framework?like the 1931 Gödel incompleteness paper. A pluralistic multiple-universe framework recognizes multiple (...) universes of discourse serving as different ranges of the individual variables in different interpretations?as in post-WWII model theory. In the early 1960s, many logicians?mistakenly, as we show?held the ?contrary alternative? that Tarski 1936 had already adopted a Gödel-type, pluralistic, multiple-universe framework. We explain that Tarski had not yet shifted out of the monistic, Frege?Russell, fixed-universe paradigm. We further argue that between his Principia-influenced pre-WWII Warsaw period and his model-theoretic post-WWII Berkeley period, Tarski's philosophy underwent many other radical changes. (shrink)

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)

Owen Griffiths has recently argued that Etchemendy’s account of logical consequence faces a dilemma. Etchemendy claims that we can be sure that his account does not overgenerate, but that we should expect it to undergenerate. Griffiths argues that if we define the relationship between formal and natural language as being dependent on logical consequence, then Etchemendy’s claims are not true; and if we define the relationship as being independent of logical consequence, then we cannot assess the truth of the claims (...) without further information. I argue that Griffiths misconstrues Etchemendy’s theory and overstates the first horn of the dilemma: Etchemendy does see the relationship as being dependent on logical consequence, but that does not mean that his claims are not true. (shrink)

In John Etchemendy's book, The Concept of Logical Consequence, several arguments are put forth against the standard model‐theoretic account of logical consequence and logical truth. I argue in this article that crucial parts of Etchemendy's attack depend on a failure to distinguish two senses of logic and two correlative senses of being something a logical question. According to one of these senses, the logic of a language, L, is the set of logical truths of L. In the other sense, logic (...) is a theoretical discipline whose aim is to characterize logical properties and it can be identified with the set of sentences on what, and why, the extension of the set of logical truths of a particular language is. Some particular claims by Etchemendy about the status assigned to the axiom of infinity in the model‐theoretic account are criticized and shown to be erroneous because of that conflation. (shrink)