This paper deals with the adequacy of the model-theoretic definition of logical consequence. Logical consequence is commonly described as a necessary relation that can be determined by the form of the sentences involved. In this paper, necessity is assumed to be a metaphysical notion, and formality is viewed as a means to avoid dealing with complex metaphysical questions in logical investigations. Logical terms are an essential part of the form of sentences and thus have a crucial role in determining logical (...) consequence. Gila Sher and Stewart Shapiro each propose a formal criterion for logical terms within a model-theoretic framework, based on the idea of invariance under isomorphism. The two criteria are formally equivalent, and thus we have a common ground for evaluating and comparing Sher and Shapiro philosophical justification of their criteria. It is argued that Shapiro's blended approach, by which models represent possible worlds under interpretations of the language, is preferable to Sher’s formal-structural view, according to which models represent formal structures. The advantages and disadvantages of both views’ reliance on isomorphism are discussed. (shrink)

The Logic Manual is a clear and concise introduction to logic for beginning philosophy students.

I ON THE PRIMITIVE TERM OF LOGISTICf IN this article I propose to establish a theorem belonging to logistic concerning some connexions, not widely known, ...

There are quite a few theses about logic that are in one way or another pluralist: they hold (i) that there is no uniquely correct logic, and (ii) that because of this, some or all debates about logic are illusory, or need to be somehow reconceived as not straightforwardly factual. Pluralist theses differ markedly over the reasons offered for there being no uniquely correct logic. Some such theses are more interesting than others, because they more radically affect how we are (...) initially inclined to understand debates about logic. Can one find a pluralist thesis that is high on the interest scale, and also true? (shrink)

I argue that recent defenses of the view that in 1936 Tarski required all interpretations of a language to share one same domain of quantification are based on misinterpretations of Tarski’s texts. In particular, I rebut some criticisms of my earlier attack on the fixed-domain exegesis and I offer a more detailed report of the textual evidence on the issue than in my earlier work. I also offer new considerations on subsisting issues of interpretation concerning Tarski’s views on the logical (...) correctness of certain omega-arguments, on the Tarskian proof that Etchemendy took to be modal and fallacious, and on Tarski’s appeals to the “common concept of consequence”. (shrink)

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

The essays can be seen as addressing Tarski's seminal treatment of four basic questions about logical consequence. (1) How are we to understand truth, one of ...

Beall and Restall argue for a pluralistic conception of logic, which may be called Background Pluralism. In the first part of this paper, I outline the core tenets of Beall and Restall's position. In the second part I consider a particular line of criticism presented in Read and Priest. Finally, in the last part of the paper, I develop a new argument which is directed against the fundamental thesis of Beall and Restall's pluralistic theory. Since the argument attempts to show (...) that the fundamental thesis incorporates a self-defeating feature, it will be called the Instability Argument. (shrink)

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 article identifies problems with regard to providing criteria that regulate the matching of logical formulae and natural language. We then take on to solve these problems by defining a necessary and sufficient criterion of adequate formalization. On the basis of this criterion we argue that logic should not be seen as an ars iudicandi capable of evaluating the validity or invalidity of informal arguments, but as an ars explicandi that renders transparent the formal structure of informal reasoning.

Consequence is at the heart of logic, and an account of consequence offers a vital tool in the evaluation of arguments. This text presents what the authors term as 'logical pluralism' arguing that the notion of logical consequence doesn't pin down one deductive consequence relation; it allows for many of them.

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)

Revised and reprinted; originally in Dov Gabbay & Franz Guenthner (eds.), Handbook of Philosophical Logic, Volume IV. Kluwer 133-251. -- Two sorts of property theory are distinguished, those dealing with intensional contexts property abstracts (infinitive and gerundive phrases) and proposition abstracts (‘that’-clauses) and those dealing with predication (or instantiation) relations. The first is deemed to be epistemologically more primary, for “the argument from intensional logic” is perhaps the best argument for the existence of properties. This argument is presented in the (...) course of discussing generality, quantifying-in, learnability, referential semantics, nominalism, conceptualism, realism, type-freedom, the first-order/higher-order controversy, names, indexicals, descriptions, Mates’ puzzle, and the paradox of analysis. Two first-order intensional logics are then formulated. Finally, fixed-point type-free theories of predication are discussed, especially their relation to the question whether properties may be identified with propositional functions. (shrink)

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)

Logical pluralism is the view according to which there is more than one relation of logical consequence, even within a given language. A recent articulation of this view has been developed in terms of quantification over different cases: classical logic emerges from consistent and complete cases; constructive logic from consistent and incomplete cases, and paraconsistent logic from inconsistent and complete cases. We argue that this formulation causes pluralism to collapse into either logical nihilism or logical universalism. In its place, we (...) propose a modalist account of logical pluralism that is independently well motivated and that avoids these collapses. (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)

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)

Logik ist nach dem traditionellen Verständnis eine ars iudicandi, eine Kunst, die Gültigkeit von Schlüssen zu prüfen. Da mit die normalen Mittel der modernen Logik zu diesem Zweck eingesetzt werden können, müssen erst Formeln an die Stelle von Sätzen treten: umgangssprachliche Schlüsse müssen adäquat formalisiert werden. Die richtige Formel entwickelt ein theoretisches Konzept des Formalisierens und praktisch anwendbare Adäquatheitskriterien für Formalisierungen. Dabei werden zentrale Fragen der Philosophie der Logik unter dem Gesichtspunkt des Zusammenspiels von Umgangssprache und Formalismus untersucht. Die ausführliche (...) und systematische Diskussion von Formalisierungstests bietet eine wichtige Ergänzung zu den traditionellen Logiklehrbüchern. (shrink)

I reject the contention that an important theoretical difference exists between formal and natural languages.

We investigate a construction schema for first-order logical systems, called “form logic”. Form logic allows us to overcome the dualistic commitment of predicate logic to individual constants and predicates. Dualism is replaced by a pluralism of terms of different “logical forms”. Individual form-logical systems are generated by the determination of a range of logical forms and of the formbased syntax rules for combining terms into formulas. We develop a generic syntax and semantics for such systems and provide a completeness proof (...) for them. To illustrate the idea of form logic, and the possibilities it facilitates, we discuss three particular systems, one of which is the form-logical reconstruction of standard first-order predicate logic. (shrink)

Logical Forms explains both the detailed problems involved in finding logical forms and also the theoretical underpinnings of philosophical logic. In this revised edition, exercises are integrated throughout the book. The result is a genuinely interactive introduction which engages the reader in developing the argument. Each chapter concludes with updated notes to guide further reading.

Logical pluralism is the claim that different accounts of validity can be equally correct. Beall and Restall have recently defended this position. Validity is a matter of truth-preservation over cases, they say: the conclusion should be true in every case in which the premises are true. Each logic specifies a class of cases, but differs over which cases should be considered. I show that this account of logic is incoherent. Validity indeed is truth-preservation, provided this is properly understood. Once understood, (...) there is one true logic, relevance logic. The source of Beall and Restall’s error is a recent habit of using a classical metalanguage to analyse non-classical logics generally, including relevance logic. (shrink)

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 book presents modern logic as the formalization of reasoning that needs and deserves a semantic foundation. Chapters on propositional logic; parsing propositions; and meaning, truth and reference give the reader a basis for establishing criteria that can be used to judge formalizations of ordinary language arguments. Over 120 worked examples illustrate the scope and limitations of modern logic, as analyzed in chapters on identity, quantifiers, descriptive names, and functions. The chapter on second-order logic shows how different conceptions of predicates (...) and propositions do not lead to a common basis for quantification over predicates, as they do for quantification over things. Notable for its clarity of presentation and supplemented by many exercises, this volume will be invaluable for philosophers, linguists, mathematicians, and computer scientists who wish to better understand the tools they use in formal reasoning. (shrink)

A natural language argument may be valid in at least two nonequivalent senses: it may be interpretationally or representationally valid (Etchemendy in The concept of logical consequence. Harvard University Press, Cambridge, 1990). Interpretational and representational validity can both be formally exhibited by classical first-order logic. However, as these two notions of informal validity differ extensionally and first-order logic fixes one determinate extension for the notion of formal validity (or consequence), some arguments must be formalized by unrelated nonequivalent formalizations in order (...) to formally account for their interpretational or representational validity, respectively. As a consequence, arguments must be formalized subject to different criteria of adequate formalization depending on which variant of informal validity is to be revealed. This paper develops different criteria that formalizations of an argument have to satisfy in order to exhibit the latter’s interpretational or representational validity. (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)

The article addresses two closely related questions: What are the criteria of adequacy of logical formalization of natural language arguments, and what gives logic the authority to decide which arguments are good and which are bad? Our point of departure is the criticism of the conception of logical formalization put forth, in a recent paper, by M. Baumgartner and T. Lampert. We argue that their account of formalization as a kind of semantic analysis brings about more problems than it solves. (...) We also argue that the criteria of adequate formalization need not be based on truth conditions associated with logical formulas; in our view, they are better based on structural (inferential) grounds. We then put forward our own version of the criteria. The upshot of the discussion that follows is that the quest for an adequate formalization in a suitable logical language is best conceived of as the search for a Goodmanian reflective equilibrium. (shrink)

In his 1936 paper,On the Concept of Logical Consequence, Tarski introduced the celebrated definition oflogical consequence: “The sentenceσfollows logicallyfrom the sentences of the class Γ if and only if every model of the class Γ is also a model of the sentenceσ.” [55, p. 417] This definition, Tarski said, is based on two very basic intuitions, “essential for the proper concept of consequence” [55, p. 415] and reflecting common linguistic usage: “Consider any class Γ of sentences and a sentence which (...) follows from the sentences of this class. From an intuitive standpoint it can never happen that both the class Γ consists only of true sentences and the sentenceσis false. Moreover, … we are concerned here with the concept of logical, i.e.,formal, consequence.” [55, p. 414] Tarski believed his definition of logical consequence captured the intuitive notion: “It seems to me that everyone who understands the content of the above definition must admit that it agrees quite well with common usage. … In particular, it can be proved, on the basis of this definition, that every consequence of true sentences must be true.” [55, p. 417] The formality of Tarskian consequences can also be proven. Tarski's definition of logical consequence had a key role in the development of the model-theoretic semantics of modern logic and has stayed at its center ever since. (shrink)