Concept Of Logical Consequence Research Articles

A Formal Explication of Blanchette's Conception of Fregean Consequence

Over the past decades, Patricia Blanchette has developed a sophisticated account of Frege's conception of logic and his views on logical consequence. One of the central components of her interpretation is the idea that Frege's conception of logical consequence is ‘semantically laden’ and not purely formal. The aim of the present paper is to provide precise explications of this as well as related ideas that inform her account, and to discuss their significance for the philosophy of logic in general and Frege's philosophy in particular.

Time and Indexicality in Buridan’s Concept of Logical Consequence

Jean Buridan developed his theory of consequence within a semantical framework compatible with what we now call token-based semantics. In his Treatise on Consequences and Sophismata, Buridan showed that the notion of consequence accepted by the logicians of his time (that the antecedent cannot be true without the consequent being true) fails when we consider inferences such as: (1) ‘No proposition is negative, therefore, no ass is running’; and (2) ‘Every proposition is affirmative, therefore, no proposition is negative’. Our analysis of Buridan’s semantic and logical theory shows that: (a) for Buridan, time was a fundamental needed concept to adequately define the notion of consequence; (b) sentences like ‘No proposition is negative’ — appearing in (1) and (2) — are temporal indexicals; (c) these indexicals appealed to Buridan because they suggest a new type of validity, that has been called contextual validity by Blackburn and Jørgensen, and which was originally discussed by Kamp and Kaplan in the twentieth century. Finally, we offer a reconstruction of Buridan’s theory of consequence in terms of a contextual hybrid logic, a logical-symbolic apparatus that allows us to assess Buridan’s logical and philosophical contributions in contemporary terms and contribute to the current discussion on the topic.

Logical pluralism, indeterminacy and the normativity of logic

According to the form of logical pluralism elaborated by Beall and Restall there is more than one relation of logical consequence. Since they take the relation of logical consequence to reside at the very heart of a logical system, different relations of logical consequence yield different logics. In this paper, we are especially interested in understanding what are the consequences of endorsing Beall and Restall’s version of logical pluralism vis-à-vis the normative guidance that logic is taken to provide to reasoners. In particular, the aim of this paper is threefold. First, in Sections 2 and 3, we offer an exegesis of Beall and Restall’s logical pluralism as a thesis of semantic indeterminacy of our concept of logical consequence – i.e. understood as indeterminacy logical pluralism. Second, in Sections 4 and 5, we elaborate and critically scrutinize three models of semantic indeterminacy that we think are fit to capture Beall and Restall’s indeterminacy logical pluralism. Third, in Section 6, following Beall and Restall’s assumption that the notion of logical consequence has normative significance for deductive reasoning, we raise a series of normative problems for indeterminacy logical pluralism. The overall conclusion that we aim to establish is that Beall and Restall’s indeterminate logical pluralism cannot offer an adequate account of the normative guidance that logic is taken to provide us with in ordinary contexts of reasoning.

Modern approaches of the understanding of ad-arguments and criteria for their eligibility

In this article the term appellant argument (ad-argument) is considered in terms of current approaches (Pragma-dialectic, informal logic, formal dialectic) on the study of the theory of argumentation. Considering the grounds on which such arguments were recognized as incorrect in argumentation for a long time. The informal nature of such arguments is the main ground for understanding them as a way of sophistic argument. In addition, it is established that critics of such arguments is possible not only by the form but also by the content. A review of the position of the subjective nature of such arguments has been performed and it has been stated that by the way of understanding the truth in terms of its communicative nature, the problem is solved by matching the arguments of the thesis based on the consent of the participants. The concept of logical consequence and the concepts of the consequence in the argumentation are being distinguished. Based on this distinction it is concluded that in contrast to the logical consequence in logic, that provides a form of communication between base and conclusions, the consequence in the argumentation is closely associated with the concept of substantiation. The acceptability of ad-arguments is determined to be possible in case of the relationship between the thesis of a dialogue and a subject area, based on such arguments that does not belong to the subject area of the dialogue. A method of the critical issues and method of universalization of ad-arguments as a method for the verification of the relevance of such arguments are proposed.

Витгенштейн о логическом следовании

Витгенштейн о логическом следовании

The overgeneration argument(s): A succinct refutation

The overgeneration argument attempts to show that accepting second-order validity as a sound formal counterpart of logical truth has the unacceptable consequence that the Continuum Hypothesis is either a logical truth or a logical falsehood. The argument was presented and vigorously defended in John Etchemendy’s The Concept of Logical Consequence and it has many proponents to this day. Yet it is nothing but a seductive fallacy. I demonstrate this by considering five versions of the argument; as I show, each is either unsound or lacks a troubling conclusion.

Exhibiting interpretational and representational validity

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.

Fixed‐ versus Variable‐domain Interpretations of Tarski’s Account of Logical Consequence

AbstractIn this article I describe and evaluate the debate that surrounds the proper interpretation of Tarski’s account of logical consequence given in his classic 1936 article ‘On the concept of logical consequence’. In the late 1980s Etchemendy argued that the familiar model theoretic account of logical consequence is not to be found in Tarski’s original article. Whereas the contemporary account of logical consequence is a variable‐domain conception – in that it calls for a reinterpretation of the domain of variation of the quantifiers when evaluating logical consequence –, no such reinterpretation is found in Tarski’s original account, which was rather based on a ‘fixed‐domain’ conception. Etchemendy’s claims have sparked a debate on Tarski’s conception of logical consequence with important contributions by, among others, Bach, Bays, Corcoran, Gómez‐Torrente, Mancosu, Ray, Sagüillo, and Sher.

Methodological Practice and Complementary Concepts of Logical Consequence: Tarski's Model-Theoretic Consequence and Corcoran's Information-Theoretic Consequence

This article discusses two coextensive concepts of logical consequence that are implicit in the two fundamental logical practices of establishing validity and invalidity for premise-conclusion arguments. The premises and conclusion of an argument have information content (they ‘say’ something), and they have subject matter (they are ‘about’ something). The asymmetry between establishing validity and establishing invalidity has long been noted: validity is established through an information-processing procedure exhibiting a step-by-step deduction of the conclusion from the premise-set. Invalidity is established by exhibiting a countermodel satisfying the premises but not the conclusion. The process of establishing validity focuses on information content; the process of establishing invalidity focuses on subject matter. Corcoran's information-theoretic concept of logical consequence corresponds to the former. Tarski's model-theoretic concept of logical consequence formulated in his famous 1936 no-countermodels definition corresponds to the latter. Both are found to be indispensable for understanding the rationale of the deductive method and each complements the other. This study discusses the ontic question of the nature of logical consequence and the epistemic question of the human capabilities presupposed by practical applications of these two concepts as they make validity and invalidity accessible to human knowledge.

エチメンディのモデル理論的帰結批判

In his book, The Concept of Logical Consequence, Etchemendy claims that the currently standard model-theoretic account of logical consequence is "the interpretational semantics" and does not capture logicality. The purpose of this paper is to defend the model-theoretic account from Etchemendy's criticisms. Through comparison with Sher's "Tarskian logic" and her model-theoretic definition of logical constants, I aim to demonstrate that the basis of Etchemendy's arguments are mistaken. I then explain that the model-theoretic account of logical consequence guarantees its logicality by the semantic functions of logical constants.

A Fallacy about the Modal Status of Logic⋆

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 (and the extension of the relation of logical consequence) of a particular language (or of a certain class of languages) 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.

Tarski On Logical Notions

We try to explain Tarski's conception of logical notions, as it emerges from alecture of his, delivered in 1966 and published posthumously in 1986 (Historyand Philosophy of Logic 7, 143–154), a conception based on the idea ofinvariance. The evaluation of Tarski's proposal leads us to consider an interesting(and neglected) reply to Skolem in which Tarski hints at his own point of view onthe foundations of set theory. Then, comparing the lecture of 1966 with Tarski'slast work and with an earlier paper written with Lindenbaum, it is shown thatTarski's conception of logical notions, with its essentially type-theoretic character,did not undergo any significant modifications throughout his life. A remark onTarski's prudential attitude on the topic in the famous paper on the concept oflogical consequence (and elsewhere) concludes our paper.

On tarski on models

Abstract.This paper concerns Tarski's use of the term “model” in his 1936 paper “On the Concept of Logical Consequence.” Against several of Tarski's recent defenders. I argue that Tarski employed a non-standard conception of models in that paper. Against Tarski's detractors. I argue that this nonstandard conception is more philosophically plausible than it may appear. Finally, I make a few comments concerning the traditionally puzzling case of Tarski's ω-rule example.

John Etchemendy. The concept of logical consequence. An unaltered republication of JSL LVII 254. The David Hume series of philosophy and cognitive science reissues. Center for the Study of Language and Information, Stanford 1999, also distributed by Cambridge University Press, New York, vii + 174 pp.

John Etchemendy. <b>The concept of logical consequence</b>. An unaltered republication of JSL LVII 254. The David Hume series of philosophy and cognitive science reissues. Center for the Study of Language and Information, Stanford 1999, also distributed by Cambridge University Press, New York, vii + 174 pp.

Model Theory and Validity

Take a formula of first-order logic which is a logical consequence of some other formulae according to model theory, and in all those formulae replace schematic letters with English expressions. Is the argument resulting from the replacement valid in the sense that the premisses could not have been true without the conclusion also being true? Can we reason from the model-theoretic concept of logical consequence to the modal concept of validity? Yes, if the model theory is the standard one for sentential logic; no, if it is the standard one for the predicate calculus; and yes, if it is a certain model theory for free logic. These conclusions rely inter alia on some assumptions about possible worlds, which are mapped into the models of model theory. Plural quantification is used in the last section, while part of the reasoning is relegated to an appendix that includes a proof of completeness for a version of free logic.

What Anit‐realist Intuitionism Could Not Be

One of the two major parts of Dummett’s defense of intuitionism is the rejection of classical in favor of intuitionistic reasoning in mathematics, given that mathematical discourse is anti‐realist. While there have been illuminating discussions of what Dummett’s argument for this might be, no consensus seems to have emerged about its overall form. In this paper I give an account of this form, starting by investigating a fundamental, but little discussed question: to what view of the relation between deductive principles and meaning is anti‐realism committed? The result of this investigation is a constraint on meaning theoretic assessments of logical laws. Given this constraint, I show that, surprisingly, a consistent anti‐realist critique of classical logic could not rely on the rejection of bivalence. Moreover, a consistent anti‐realist defense of intuitionism must begin with a radical rejection of the very conception of logical consequence that underlies realist classical logic. It follows from these conclusions that anti‐realist intuitionism seems committed to proceeding by proof theoretic means.

On a fallacy attributed to tarski

The purpose of this paper is to examine some passages of Tarski‘s paper ’On the concept of logical consequence’ and to show that some recent readings of those passages are wrong. John Etchemendy has claimed that in those passages Tarski gave an argument purporting to show that the notion of logical consequence defined by him (as opposed to some pretheoretic notion of logical consequence) possesses certain modal properties. Etchemendy further claims that the argument he attributes to Tarski is fallacious. Some of Etchemendy’s critics have granted him that Tarski did give an argument purporting to show that the defined notion possesses certain modal properties ; but they have claimed that Tarski’s argument was not a fallacious one. I will show that both Etchemendy and his critics are wrong; in the relevant passages, Tarski did not offer (nor did he intend to offer) an argument that the defined notion of logical consequence possesses any modal properties

The Concept of Logical Consequence

There is broad agreement among logicians about the technical definition of the notion of logical consequence, especially as it applies to extensional first-order languages. The definition most logicians accept is the familiar one framed in terms of assignments of truth values to sentence letters, denotations to individual constants, and extensions to predicates, these assignments being relative to some nonempty set of objects. There is less agreement, however, on the pre-theoretic notion this technical definition is supposed to represent, and very little discussion of whether it actually does represent it adequately.' This paper will be concerned with the latter two points, primarily as they arise in the context of extensional first-order languages. 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 (subsection 2. 1) that a certain kind of informal account-one that includes elements of necessity, generality, and apriority-is approximately correct. Next (subsection 2.2) 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. (Subsection 2.2.1 contains my fully developed account of the informal notion of logical consequence; subsection 2.2.2 includes criticism of recent work by Sher and Etchemendy.) In the third section, I consider whether the informal

Logical consequence: A defense of Tarski

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.

Did Tarski commit “Tarski's fallacy”?

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.