Wilfrid Hodges; VIII*—Truth in a Structure, Proceedings of the Aristotelian Society, Volume 86, Issue 1, 1 June 1986, Pages 135–152, https://doi.org/10.1093/ari.

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)

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)

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.

This paper examines from a historical perspective Tarski's 1936 essay, "On the concept of logical consequence." I focus on two main aims. The primary aim is to show how Tarski's definition of logical consequence satisfies two desiderata he himself sets forth for it: (1) it must declare logically correct certain formalizations of the -rule and (2) it must allow for variation of the individual domain in the test for logical consequence. My arguments provide a refutation of some interpreters of Tarski, (...) and notably John Etchemendy, who have claimed that his definition does not satisfy those desiderata. A secondary aim of the paper is to offer some basic elements for an understanding of Tarski's definition in the historical logico-philosophical context in which it was proposed. Such historical understanding provides useful insights on Tarski's informal ideas on logical consequence and their internal cohesion. (shrink)

In his classic 1936 essay "On the Concept of Logical Consequence", Alfred Tarski used the notion of satisfaction to give a semantic characterization of the logical properties. Tarski is generally credited with introducing the model-theoretic characterization of the logical properties familiar to us today. However, in his book, The Concept of Logical Consequence, Etchemendy argues that Tarski's account is inadequate for quite a number of reasons, and is actually incompatible with the standard model-theoretic account. Many of his criticisms are meant (...) to apply to the model-theoretic account as well. In this paper, I discuss the following four critical charges that Etchemendy makes against Tarski and his account of the logical properties: (1) (a) Tarski's account of logical consequence diverges from the standard model-theoretic account at points where the latter account gets it right. (b) Tarski's account cannot be brought into line with the model-theoretic account, because the two are fundamentally incompatible. (2) There are simple counterexamples (enumerated by Etchemendy) which show that Tarski's account is wrong. (3) Tarski committed a modal fallacy when arguing that his account captures our pre-theoretical concept of logical consequence, and so obscured an essential weakness of the account. (4) Tarski's account depends on there being a distinction between the "logical terms" and the "non-logical terms" of a language, but (according to Etchemendy) there are very simple (even first-order) languages for which no such distinction can be made. Etchemendy's critique raises historical and philosophical questions about important foundational work. However, Etchemendy is mistaken about each of these central criticisms. In the course of justifying that claim, I give a sustained explication and defense of Tarski's account. Moreover, since I will argue that Tarski's account and the model theoretic account really do come to the same thing, my subsequent defense of Tarski's account against Etchemendy's other attacks doubles as a defense against criticisms that would apply equally to the familiar model-theoretic account of the logical properties. (shrink)

Alfred Tarski's (1936) semantic account of the logical properties (logical consequence, logical truth and logical consistency) makes essential appeal to a distinction between logical and non-logical terms. John Etchemendy (1990) has recently argued that Tarski's account is inadequate for quite a number of different reasons. Among them is a brief argument which purports to show that Tarski's reliance on the distinction between logical and non-logical terms is in principle mistaken. According to Etchemendy, there are very simple (even first order) languages (...) for which no such distinction can be made. This is a surprising result, and an important one, if true. Since Tarski's account does indeed depend on such a distinction, Etchemendy's argument, if correct, would rule out definitively the received view on logical truth (as well as logical consequence and logical consistency). But his argument is not correct, and it is the job of this paper to show that. (shrink)

I came to the topic of the title in connection with my logical investigations of the Is-Ought problem in multimodal logics . There are infinitely many mathematically possible modal logics. Are they all philosophically serious candidates? Which modal logic the “right” one — does such a question make sense? A similar question can be raised for the infinite variety of propositional logics weaker than classical logics. The Vienna Circle concept of logic was that logic holds merely by form, independently from (...) the facts of the world. Have we lost this concept completely? Is it a matter of arbitrary choice, of mere subjective-practical appropriateness, which logic one chooses? Is Quine right that there is no distinction between analytic and synthetic truth, even if we take “analytic truth” in the narrow sense of “logical truth”? These are the questions which have motivated this paper. (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)