Deflationists about truth seek to undermine debates about the nature of truth by arguing that the truth predicate is merely a device that allows us to express a certain kind of generality. I argue that a parallel approach is available in the case of logicalconsequence. Just as deflationism about truth offers an alternative to accounts of truth's nature in terms of correspondence or justification, deflationism about consequence promises an alternative to model-theoretic or proof-theoretic accounts of (...) class='Hi'>consequence's nature. I then argue, against considerations put forward by Field and Beall, that Curry's paradox no more rules out deflationism about consequence than the liar paradox rules out deflationism about truth. (shrink)
Compare two conceptions of validity: under an example of a modal conception, an argument is valid just in case it is impossible for the premises to be true and the conclusion false; under an example of a topic-neutral conception, an argument is valid just in case there are no arguments of the same logical form with true premises and a false conclusion. This taxonomy of positions suggests a project in the philosophy of logic: the reductive analysis of the modal (...) conception of logicalconsequence to the topic-neutral conception. Such a project would dispel the alleged obscurity of the notion of necessity employed in the modal conception in favour of the clarity of an account of logicalconsequence given in terms of tractable notions of logical form, universal generalization and truth simpliciter. In a series of publications, John Etchemendy has characterized the model-theoretic definition of logicalconsequence as truth preservation in all models as intended to provide just such an analysis. In this paper, I will argue that Aristotle intends to provide an account of a modal conception of logicalconsequence in topic-neutral terms and so is engaged in a project comparable to the one described above. That Aristotle would be engaged in this sort of project is controversial. Under the standard reading of the Prior Analytics, Aristotle does not and cannot provide an account of logicalconsequence. Rather, he must take the validity of the first figure syllogisms (such as the syllogism known by its medieval mnemonic ‘Barbara’: A belongs to all B; B belongs to all C; so A belongs to all C) as obvious and not needing justification; he then establishes the validity of the other syllogisms by showing that they stand in a suitable relation to the first figure syllogisms. I will argue that Aristotle does attempt to provide an account of logicalconsequence—namely, by appeal to certain mereological theorems. For example, he defends the status of Barbara as a syllogism by appeal to the transitivity of mereological containment. There are, as I will discuss, reasons to doubt the success of this account. But the attempt is not implausible given certain theses Aristotle holds in semantics, mereology and the theory of relations. (shrink)
John Etchemendy (1990) has argued that Tarski's definition of logicalconsequence fails as an adequate philosophical analysis. Since then, Greg Ray (1996) has defended Tarski's analysis against Etchemendy's criticisms. Here, I'll argue that--even given Ray's defense of Tarski's definition--we may nevertheless lay claim to the conditional conclusion that 'if' Tarski intended a conceptual analysis of logicalconsequence, 'then' it fails as such. Secondly, I'll give some reasons to think that Tarski 'did' intend a conceptual analysis of (...)logicalconsequence. (shrink)
It is often claimed that nominalistic programmes to reconstruct mathematics fail, since they will at some point involve the notion of logicalconsequence which is unavailable to the nominalist. In this paper we use an idea of Goodman and Quine to develop a nominalistically acceptable explication of logicalconsequence.
In the present commentary, I argue that Foster has attacked an uncharitable reconstruction of Etchemendy's argument against Tarski's account of the logical properties. I provide an alternative, more charitable reconstruction of that argument that withstands Foster's objections.
Though it is standardly assumed that supervaluationism applied to vagueness is committed to global validity, Achille Varzi (2007) argues that the supervaluationist should take seriously the idea of adopting local validity instead. Varzi’s motivation for the adoption of local validity is largely based on two objections against the global notion: that it brings some counterexamples to classically valid rules of inference and that it is inconsistent with unrestricted higher-order vagueness. In this discussion I review these objections and point out ways (...) to address them not considered in Varzi’s paper. (shrink)
Danilo Suster (2012). Informal Logic and Informal Consequence. In Trobok Majda, Miscevic Nenad & Zarnic Berislav (eds.), Between logic and reality : modeling inference, action and understanding, (Logic, epistemology, and the unity of science, vol. 25). Springer.score: 64.0
What is informal logic, is it ``logic" at all? Main contemporary approaches are briefly presented and critically commented. If the notion of consequence is at the heart of logic, does it make sense to speak about ``informal" consequence? A valid inference is truth preserving, if the premises are true, so is the conclusion. According to Prawitz two further conditions must also be satisfied in the case of classical logicalconsequence: (i) it is because of the (...) class='Hi'>logical form of the sentences involved and not because of their specific content that the inference is truth preserving; (ii) it is necessary that if the premises are true, then so is the conclusion. According to the prevalent criteria of informal logic an argument is cogent if and only if (i) its premises are rationally Acceptable, (ii) its premises are Relevant to its conclusion and (iii) its premises constitute Grounds adequate for accepting the conclusion (the ``ARG" conditions according to Govier). The ARG criteria characterize a certain broad kind of consequence relation. We do not (in general) have truth preservence in cogent arguments but if the premises are acceptable and other criteria are met, then so is the conclusion. We can speak about form in a loose sense and finally, there is rational necessity of the grounding or support relation. So a certain broad notion of logicalconsequence emerges from this comparison. The norms of ARG are norms of elementary scientific methodology in which argument is seen as embodying reasoning within a process of inquiry or of belief formation in subject areas accessible to every informed intellectual. (shrink)
Introduction -- The concept of logicalconsequence -- Tarski's characterization of the common concept of logicalconsequence -- The logicalconsequence relation has a modal element -- The logicalconsequence relation is formal -- The logicalconsequence relation is A priori -- Logical and non-logical terminology -- The meanings of logical terms explained in terms of their semantic properties -- The meanings of logical terms explained in (...) terms of their inferential properties -- Model-theoretic and deductive-theoretic conceptions of logic -- Linguistic preliminaries : the language M -- Syntax of M -- The definition of a well formed formula of M -- Semantics for M -- The sentential connectives are defined -- The notion of satisfaction is introduced and the quantifiers are defined -- Model-theoretic consequence -- Truth in a structure -- Satisfaction revisited -- Formalized definition of truth -- Model-theoretic consequence defined -- The model-theoretic definition and the concept of logicalconsequence -- Does the model theoretic consequence relation reflect the salient features of the common concept of logicalconsequence? -- What is a logical constant? -- Deductive consequence -- Deductive system n -- The deductive theoretic definition and the concept of logicalconsequence -- Tarski's criticism of the deductive theoretic definition -- Is N a correct deductive system? (shrink)
In his classic 1936 essay On the Concept of LogicalConsequence, 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 LogicalConsequence, 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 logicalconsequence 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 logicalconsequence, 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 a series of publications beginning in the 1980s, John Etchemendy has argued that the standard semantical account of logicalconsequence, due in its essentials to Alfred Tarski, is fundamentally mistaken. He argues that, while Tarski's definition requires us to classify the terms of a language as logical or non-logical, no such division is guaranteed to deliver the correct extension of our pre-theoretical or intuitive consequence relation. In addition, and perhaps more importantly, Tarski's account is (...) claimed to be incapable of explaining an essential modal/epistemological feature of consequence, namely, its necessity and apriority. Bernard Bolzano (1781-1848) is widely recognized as having anticipated Tarski's definition in his Wissenschaftslehre (or Theory of Science ) of 1837. Because of the similarities between his account and Tarski's, Etchemendy's arguments have also been extended to cover Bolzano. The purpose of this article is to consider Bolzano's theory in the light of these criticisms. We argue that, due to important differences between Bolzano's and Tarski's theories, Etchemendy's objections do not apply immediately to Bolzano's account of consequence. Moreover, Bolzano's writings contain the elements of a detailed philosophical response to Etchemendy. (shrink)
What is the philosophical significance of the soundness and completeness theorems for first-order logic? In the first section of this paper I raise this question, which is closely tied to current debate over the nature of logicalconsequence. Following many contemporary authors' dissatisfaction with the view that these theorems ground deductive validity in model-theoretic validity, I turn to measurement theory as a source for an alternative view. For this purpose I present in the second section several of the (...) key ideas of measurement theory, and in the third and central section of the paper I use these ideas in an account of the relation between model theory, formal deduction, and our logical intuitions. (shrink)
In Logicalconsequence: A defense of Tarski (Journal of Philosophical Logic, vol. 25, 1996, pp. 617–677), Greg Ray defends Tarski"s account of logicalconsequence against the criticisms of John Etchemendy. While Ray"s defense of Tarski is largely successful, his attempt to give a general proof that Tarskian consequence preserves truth fails. Analysis of this failure shows that de facto truth preservation is a very weak criterion of adequacy for a theory of logicalconsequence (...) and should be replaced by a stronger absence-of-counterexamples criterion. It is argued that the latter criterion reflects the modal character of our intuitive concept of logicalconsequence, and it is shown that Tarskian consequence can be proved to satisfy this criterion for certain choices of logical constants. Finally, an apparent inconsistency in Ray"s interpretation of Tarski"s position on the modal status of the consequence relation is noted. (shrink)
Logic is formal in the sense that all arguments of the same form as logically valid arguments are also logically valid and hence truth-preserving. However, it is not known whether all arguments that are valid in the usual model-theoretic sense are truth-preserving. Tarski claimed that it could be proved that all arguments that are valid (in the sense of validity he contemplated in his 1936 paper on logicalconsequence) are truth-preserving. But he did not offer the proof. The (...) question arises whether the usual model-theoretic sense of validity and Tarski's 1936 sense are the same. I argue in this paper that they probably are not, and that the proof Tarski had in mind, although unusable to prove that model-theoretically valid arguments are truth-preserving, can be used to prove that arguments valid in Tarski's 1936 sense are truth-preserving. (shrink)
In this paper I argue that Bolzano's concept of deducibility and Tarski's concept of logicalconsequence differ with respect to their philosophical intent. I distinguish between epistemic and ontic approaches to logic, and argue that Bolzano's deducibility presupposes an epistemic approach, while Tarski's logicalconsequence presupposes an ontic approach.
This article discusses two coextensive concepts of logicalconsequence 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 logicalconsequence corresponds to the former. Tarski's model-theoretic concept of logicalconsequence 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 logicalconsequence 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. (shrink)
We present a framework that provides a logic for science by generalizing the notion of logical (Tarskian) consequence. This framework will introduce hierarchies of logical consequences, the first level of each of which is identified with deduction. We argue for identification of the second level of the hierarchies with inductive inference. The notion of induction presented here has some resonance with Popper's notion of scientific discovery by refutation. Our framework rests on the assumption of a restricted class (...) of structures in contrast to the permissibility of classical first-order logic. We make a distinction between deductive and inductive inference via the notions of compactness and weak compactness. Connections with the arithmetical hierarchy and formal learning theory are explored. For the latter, we argue against the identification of inductive inference with the notion of learnable in the limit. Several results highlighting desirable properties of these hierarchies of generalized logicalconsequence are also presented. (shrink)
It is often assumed that the supervaluationist theory of vagueness is committed to a global notion of logicalconsequence, in contrast with the local notion characteristic of modal logics. There are, at least, two problems related to the global notion of consequence. First, it brings some counterexamples to classically valid patterns of inference. Second, it is subject to an objection related to higher-order vagueness . This paper explores a third notion of logicalconsequence, and discusses (...) its adequacy for the supervaluationist theory. The paper proceeds in two steps. In the first step, the paper provides a deductive notion of consequence for global validity using the tableaux method. In the second step, the paper provides a notion of logicalconsequence which is an alternative to global validity, and discusses i) whether it is acceptable to the supervaluationist and ii) whether it plays a better role in a theory of vagueness in the face of the problems related to the global notion. (shrink)
The purpose of this paper is to present a thought experiment and argument that spells trouble for “radical” deflationism concerning meaning and truth such as that advocated by the staunch nominalist Hartry Field. The thought experiment does not sit well with any view that limits a truth predicate to sentences understood by a given speaker or to sentences in (or translatable into) a given language, unless that language is universal. The scenario in question concerns sentences that are not understood but (...) are known to be logical consequences of known and understood sentences. Ultimately, the issue turns on the notion of logicalconsequence that is available to various versions of deflationism. (shrink)
The model-theoretic analysis of the concept of logicalconsequence has come under heavy criticism in the last couple of decades. The present work looks at an alternative approach to logicalconsequence where the notion of inference takes center stage. Formally, the model-theoretic framework is exchanged for a proof-theoretic framework. It is argued that contrary to the traditional view, proof-theoretic semantics is not revisionary, and should rather be seen as a formal semantics that can supplement model-theory. Specifically, (...) there are formal resources to provide a proof-theoretic semantics for both intuitionistic and classical logic. We develop a new perspective on proof-theoretic harmony for logical constants which incorporates elements from the substructural era of proof-theory. We show that there is a semantic lacuna in the traditional accounts of harmony. A new theory of how inference rules determine the semantic content of logical constants is developed. The theory weds proof-theoretic and model-theoretic semantics by showing how proof-theoretic rules can induce truth-conditional clauses in Boolean and many-valued settings. It is argued that such a new approach to how rules determine meaning will ultimately assist our understanding of the apriori nature of logic. (shrink)
Abstract: I discuss the account of logicalconsequence advanced in Wittgenstein's Tractatus. I argue that the role that elementary propositions are meant to play in this account can be used to explain two remarkable features that Wittgenstein ascribes to them: that they are logically independent from one another and that their components refer to simple objects. I end with a proposal as to how to understand Wittgenstein's claim that all propositions can be analysed as truth functions of elementary (...) propositions. (shrink)
In the Posterior Analytics (I 6, 75a18–27) Aristotle discusses a puzzle which endangers the possibility of inferring a non-necessary conclusion. His solution relies on the distinction between the necessity of the conclusion's being the case and the necessity of admitting the conclusion once one has admitted the premisses. The former is a factual necessity, whereas the latter is meant to be a normative or deontic necessity that is independent of the facts stated by the premisses and the conclusion. This paper (...) maintains that Aristotle resorts to this distinction because he thinks that, as long as it is conceived as a factual relation, logicalconsequence cannot exist independently of the facts expressed by the premisses and the conclusion. As a corollary, the necessity of such a consequence relation always requires the necessity of these facts. Aristotle holds this factual conception of logicalconsequence responsible for the puzzle, since it cannot account for valid syllogisms with contingent or false premisses. The alternative conception of necessity is then introduced by him in order to make good this deficiency. The distinction between the necessity of being and the necessity of saying was revived by the Oxford logician E. W. B. Joseph, and taken over by Frank Ramsey in his seminal Truth and Probability, but has not received attention from recent interpreters of Aristotle's logic. This paper, however, argues that, in spite of its intrinsic interest, the distinction bore no significant fruit in Aristotle's logical doctrine. (shrink)
The pretheoretical notions of logicalconsequence and of a logical expression are linked in vague and complex ways to modal and pragmatic intuitions. I offer an introduction to the difficulties that these intuitions create when one attempts to give precise characterizations of those notions. Special attention is given to Tarski’s theories of logicalconsequence and logical constancy. I note that the Tarskian theory of logicalconsequence has fared better in the face of (...) the difficulties than the Tarskian theory of logical constancy. Other theories of these notions are explained and criticized. (shrink)
We group the existing variants of the familiar set-theoretical and truth-theoretical paradoxes into two classes: connective paradoxes, which can in principle be ascribed to the presence of a contracting connective of some sort, and structural paradoxes, where at most the faulty use of a structural inference rule can possibly be blamed. We impute the former to an equivocation over the meaning of logical constants, and the latter to an equivocation over the notion of consequence. Both equivocation sources are (...) tightly related, and can be cleared up by adopting a particular substructural logic in place of classical logic. We then argue that our perspective can be justified via an informational semantics of contraction-free substructural logics. (shrink)
It has repeatedly been argued that nominalistic programmes in the philosophy of mathematics fail, since they will at some point or other involve the notion of logicalconsequence which is unavailable to the nominalist. In this paper we will argue that this is not the case. Using an idea of Nelson Goodman andW.V. Quine’s which they developed in Goodman and Quine (1947) and supplementing it with means that should be nominalistically acceptable, we present a way to explicate (...) class='Hi'>logicalconsequence in a nominalistically acceptable way. (shrink)
Gómez-Torrente’s papers have made important contributions to vindicate Tarski’s model-theoretic account of the logical properties in the face of Etchemendy’s criticisms. However, at some points his vindication depends on interpreting the Tarskian account as purportedly modally deflationary, i.e., as not intended to capture the intuitive modal element in the logical properties, that logicalconsequence is (epistemic or alethic) necessary truth-preservation. Here it is argued that the views expressed in Tarski’s seminal work do not support this modally (...) deflationary interpretation, even if Tarski himself was sceptical about modalities. (shrink)
This paper is devoted to show the development of some of the model-theoretic ideas which are clearly present in the main members of the Peano school (Peano himself, Burali-Forti, Pieri and Padoa) asa result of their conception of nominal definitions. Also, their semantic definition of logicalconsequence (Pieri, Padoa) is viewed as one of the outcomes of that conception. Some examples of their use of theexpression “nominal definition” are presented first. Second, the main advantages of this kind of (...) definition, as they saw them, are briefly explained, mainly in a philosophical context. Finally, already in the kernel of the paper, some of the details of the model-theoretic view itself are shown, first in Peano, then in Pieri and Padoa, including in both cases some study of their semantic definitions of logicalconsequence. (shrink)
In this paper, Tarskis notion of LogicalConsequence is viewed as a special case of the more general notion of being a theorem of an axiomatic theory. As was recognized by Tarski, the material adequacy of his definition depends on having the distinction between logical and non logical constants right, but we find Tarskis analysis persuasive even if we dont agree on what constants are logical. This accords with the view put forward in this paper (...) that Tarski indeed captures the more inclusive notion of theoremhood in an axiomatic theory. The approach to logicalconsequence via axiomatic theories leads us to grant centrality to inference schemas rather than to full-fledged arguments and to view the logically valid schemas as a subclass of generally valid schemas. (shrink)
This paper is devoted to show the development of some of the model-theoretic ideas which are clearly present in the main members of the Peano school (Peano himself, Burali-Forti, Pieri and Padoa) asa result of their conception of nominal definitions. Also, their semantic definition of logicalconsequence (Pieri, Padoa) is viewed as one of the outcomes of that conception. Some examples of their use of theexpression “nominal definition” are presented first. Second, the main advantages of this kind of (...) definition, as they saw them, are briefly explained, mainly in a philosophical context. Finally, already in the kernel of the paper, some of the details of the model-theoretic view itself are shown, first in Peano, then in Pieri and Padoa, including in both cases some study of their semantic definitions of logicalconsequence. (shrink)
Timothy Williamson argues against the tactic of criticizing confidence in a theory by identifying a logicalconsequence of the theory whose probability is not raised by the evidence. He dubs it "the consequence fallacy". In this paper we will show that Williamson's formulation of the tactic in question is ambiguous. On one reading of Williamson's formulation, the tactic is indeed a fallacy, but it is not a commonly used tactic; on another reading, it is a commonly used (...) tactic (or at least more often used than the former tactic), but it is not a fallacy. (shrink)
A good argument is one whose conclusions follow from its premises; its conclusions are consequences of its premises. But in what sense do conclusions follow from premises? What is it for a conclusion to be a consequence of premises? Those questions, in many respects, are at the heart of logic (as a philosophical discipline). Consider the following argument: 1. If we charge high fees for university, only the rich will enroll. We charge high fees for university. Therefore, only the (...) rich will enroll. There are many different things one can say about this argument, but many agree that if we do not equivocate (if the terms mean the same thing in the premises and the conclusion) then the argument is valid, that is, the conclusion follows deductively from the premises. This does not mean that the conclusion is true. Perhaps the premises are not true. However, if the premises are true, then the conclusion is also true, as a matter of logic. This entry is about the relation between premises and conclusions in valid arguments. (shrink)
A good argument is one whose conclusions follow from its premises; its conclusions are consequences of its premises. But in what sense do conclusions follow from premises? What is it for a conclusion to be a consequence of premises? Those questions, in many respects, are at the heart of logic (as a philosophical discipline). Consider the following argument: If we charge high fees for university, only the rich will enroll. We charge high fees for university. Therefore, only the rich (...) will enroll. There are many different things one can say about this argument, but many agree that if we do not equivocate (if the terms mean the same thing in the premises and the conclusion) then the argument is valid, that is, the conclusion follows deductively from the premises. This does not mean that the conclusion is true. Perhaps the premises are not true. However, if the premises are true, then the conclusion is also true, as a matter of logic. This entry is about the relation between premises and conclusions in valid arguments. (shrink)
There are different ways we use the expressions “extension” and “intension”. I specify in the first part of this paper two basic senses of this distinction, and try to show that the old metaphysical sense, by means of particular instance vs. universal, is more fundamental than the contemporary sense by means of substitutivity. In the second part, I argue that logic in general is essentially intensional, not only because logic is a rule-guided activity, but because even the extensional definition of (...) a logic system presupposes an intensional notion of logicalconsequence. DOI:10.5007/1808-1711.2010v14n1p111. (shrink)
This paper discusses Fara's so-called 'Paradox of Higher-Order Vagueness' concerning supervaluationism. In the paper I argue that supervaluationism is not committed to global validity, as it is largely assumed in the literature, but to a weaker notion of logicalconsequence I call 'regional validity'. Then I show that the supervaluationist might solve Fara's paradox making use of this weaker notion of logicalconsequence. The paper is discussed by Delia Fara in the same volume.
Paraconsistent approaches have received little attention in the literature on vagueness (at least compared to other proposals). The reason seems to be that many philosophers have found the idea that a contradiction might be true (or that a sentence and its negation might both be true) hard to swallow. Even advocates of paraconsistency on vagueness do not look very convinced when they consider this fact; since they seem to have spent more time arguing that paraconsistent theories are at least as (...) good as their paracomplete counterparts, than giving positive reasons to believe on a particular paraconsistent proposal. But it sometimes happens that the weakness of a theory turns out to be its mayor ally, and this is what (I claim) happens in a particular paraconsistent proposal known as subvaluationism. In order to make room for truth-value gluts subvaluationism needs to endorse a notion of logicalconsequence that is, in some sense, weaker than standard notions of consequence. But this weakness allows the subvaluationist theory to accommodate higher-order vagueness in a way that it is not available to other theories of vagueness (such as, for example, its paracomplete counterpart, supervaluationism). (shrink)
Peacocke proposes a criterion for logical constancy in terms of a priori knowability conditions. An a priori knowability condition, Peacocke claims, meets a condition of adequacy for any criterion of logical constancy: expressions satisfying the criterion are topic-neutral. I’ll raise the objection that certain a posteriori knowability conditions would satisfy this adequacy condition. For the requirement of topic-neutrality is ambiguous between two conceptions. Under one conception, a truth is topic-neutral if it is characterized by its indifference to all (...) worldly facts or its abstraction from all semantic content whatsoever. According to another conception of topic-neutrality, to claim that a truth is topic-neutral is not to characterize it by its abstraction from all content whatsoever but rather to characterize it by its abstraction from the specific identities of things. A posteriori knowability conditions could yield expressions which are topic-neutral in this second sense, and so a priori knowability conditions are unnecessary to yield expressions which are topic-neutral in some sense or other. (shrink)
In a previous paper (see ‘Tolerant, Classical, Strict’, henceforth TCS) we investigated a semantic framework to deal with the idea that vague predicates are tolerant, namely that small changes do not affect the applicability of a vague predicate even if large changes do. Our approach there rests on two main ideas. First, given a classical extension of a predicate, we can define a strict and a tolerant extension depending on an indifference relation associated to that predicate. Second, we can use (...) these notions of satisfaction to define mixed consequence relations that capture non-transitive tolerant reasoning. Although we gave some empirical motivation for the use of strict and tolerant extensions, making use of them commits us to the view that sentences of the form ‘ p∨¬p ’ and ‘ p∧¬p ’ are not automatically valid or unsatisfiable, respectively. Some philosophers might take this commitment as a negative outcome of our previous proposal. We think, however, that the general ideas underlying our previous approach to vagueness can be implemented in a variety of ways. This paper explores the possibility of defining mixed notions of consequence in the more classical super/sub-valuationist setting and examines to what extent any of these notions captures non-transitive tolerant reasoning. (shrink)
In the present paper, we study some properties of matrices for non-structural consequence operators. These matrices were introduced in a former work (see [3]). In sections 1. and 2., general definitions and theorems are recalled; in section 3. a correspondence is studied, among our matrices and Wójcicki's ones for structural operators. In section 4. a theorem is given about operators, induced by submatrices or epimorphic images, or quotient matrices of a given one.Such matrices are used to characterize lattices of (...) non-structural consequence operators, by constructing lattices, antiisomorphic to them (see section 5.). In the last section, a sufficient condition is given for a non-structural operator to be finite. (shrink)
A lógica, considerada como uma disciplina técnica iniciada por Aristóteles e tipicamente representada pela variedade de cálculos lógicos modernos, constitui um esclarecimento e refinamento de uma convicção e prática presentes no senso comum, ou seja, o fato de que os seres humanos crêem que a verdade pode ser adquirida não apenas por evidência imediata, mas também por meio de argumentos. Como uma primeira aproximação, a lógica pode ser vista como um registro “descritivo” das principais formas de argumento presentes no senso (...) comum, mas o fato de que alguns desses padrões possam realmente permitir a derivação de consequências falsas a partir de premissas verdadeiras impõe a tarefa de tornar explícitos que padrões correspondem a um “raciocínio correto” e quais não. Nesse ponto, a lógica (que contém a apresentação de tais padrões) parece ser dotada de uma característica “normativa”. Isso equivale a dizer se pretende que os cálculos lógicos espelhem adequadamente a noção intuitiva de “consequência lógica” e que nesse sentido eles não podem ser totalmente arbitrários ou convencionais, mas devem satisfazer certos requisitos básicos tais como as condições de correção e (tanto quanto possível) de completude semântica. Em tal forma eles são “julgados” de acordo com os requisitos fundamentais presentes no nível do senso comum e aparecem como “idealizações” das espécies de raciocínio praticadas no senso comum. Por essa razão também vários tipos de cálculos lógicos são inteiramente justificados uma vez que tornam explícitos, de uma forma idealizada, os modos concretos de raciocinar que são impostos pelo particular domínio de referência da disciplina na qual são usados e que são basicamente reconhecidos no senso comum. DOI: 10.5007/1808-1711.2011v15n1p15. (shrink)
In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, (...) which we call tolerant truth and strict truth. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague predicates, in particular regarding judgments about borderline cases. (shrink)
In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P , then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of (...) it, which we call tolerant truth and strict truth. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague predicates, in particular regarding judgments about borderline cases. (shrink)
In the present paper I wish to regard constructivelogic as a self-contained system for the treatment ofepistemological issues; the explanations of theconstructivist logical notions are cast in anepistemological mold already from the outset. Thediscussion offered here intends to make explicit thisimplicit epistemic character of constructivism.Particular attention will be given to the intendedinterpretation laid down by Heyting. This interpretation, especially as refined in the type-theoretical work of Per Martin-Löf, puts thesystem on par with the early efforts of Frege andWhitehead-Russell. This (...) quite recent work, however,has proved valuable not only in the philosophy andfoundations of mathematics, but has also foundpractical application in computer science, where thelanguage of constructivism serves as an implementableprogramming language, and within the philosophy oflanguage.\footnote{Nordstr\"{o}m et al. (1990) give an overview of the work in computerscience, whereas Ranta (1995) provides an impressiveconstructivist alternative to Montague Grammar usingthe richer type structure of Martin-L\"{o}f in placeof the simple classical type theory of Church.} Mypresentation will be carried out through a contrastwith standard metamathematical work.\footnote{Troelstra and van <span class='Hi'>Dalen</span> (1988) give an encyclopedictreatment of the metamathematics of constructivism.}In the course of the development I have occasion tooffer some novel considerations (in Sections~6 and 8) on thenature of proof and inference(-acts). (shrink)
This paper is concerned with the claim that supervaluationist consequence is not classical for a language including an operator for definiteness. Although there is some sense in which this claim is uncontroversial, there is a sense in which the claim must be qualified. In particular I defend Keefe's position according to which supervaluationism is classical except when the inference from phi to Dphi is involved. The paper provides a precise content to this claim showing that we might provide complete (...) (and sound) systems of deduction for supervaluationist consequence in which proofs are completely classical with the exception of a single last step (involving the above mentioned inference). (shrink)
The need to distinguish between logical and extra-logical varieties of inference, entailment, validity, and consistency has played a prominent role in meta-ethical debates between expressivists and descriptivists. But, to date, the importance that matters of logical form play in these distinctions has been overlooked. That’s a mistake given the foundational place that logical form plays in our understanding of the difference between the logical and the extra-logical. This essay argues that descriptivists are better positioned (...) than their expressivist rivals to provide the needed account of logical form, and so better able to capture the needed distinctions. This finding is significant for several reasons: First, it provides a new argument against expressivism. Second, it reveals that descriptivists can make use of this new argument only if they are willing to take a controversial—but plausible—stand on claims about the nature and foundations of logic. (shrink)
The theory of imperatives is philosophically relevant since in building it — some of the long standing problems need to be addressed, and presumably some new ones are waiting to be discovered. The relevance of the theory of imperatives for philosophical research is remarkable, but usually recognized only within the field of practical philosophy. Nevertheless, the emphasis can be put on problems of theoretical philosophy. Proper understanding of imperatives is likely to raise doubts about some of our deeply entrenched and (...) tacit presumptions. In philosophy of language it is the presumption that declaratives provide the paradigm for sentence form; in philosophy of science it is the belief that theory construction is independent from the language practice, in logic it is the conviction that logical meaning relations are constituted out of logical terminology, in ontology it is the view that language use is free from ontological commitments. The list is not exhaustive; it includes only those presumptions that this paper concerns. (shrink)
Now we should have to answer the question: when were the questions on Perihermeneias written? Little is known about the chronology of Buridan's works. Even a relative date is difficult to establish. However, some remarks can be made. First, there is the fact that the questions on Perihermeneias are quoted several times in Tractatus I of the Summule (4), in a way that makes it highly probable that the Summule were written after the Questiones on Perihermeneias (5). Now, according to (...) professor Pinborg the first lectura of the Summule may be dated as early as the late 1320es (6), that is at the very beginning of Buridan's career as a teacher of philosophy at the university of Paris. This may be an indication for an early date of the Questiones on Perihermeneias, possibly as early as 1325. There are two other reasons for assuming that the commentary on Perihermeneias is one of Buridan's first works. The first clue is given by the places where Buridan refers to one of his own works: once he refers to his commentary on Porphyry's Isagoge (7), twice to his commentary on Aristotle's Metaphysics (8), and six times to his commentary on the Physics (9). The way in which he refers to these tracts seems also to be significant: the reference to his commentary on Porphyry's Isagoge shows that this work is of an earlier date than the present work. As to the other two works, he only refers to the number of the book in which he is going to treat a particular subject, not to the number of the question. A (cross)reference to the Summule is not given, although, as Pinborg remarks, there is a general doctrinal concordance between the two works. The questions on Metaphysics do not contain a (cross)-reference to the questions on Perihermeneias, at least not on the places where one would expect them. I am not certain about possible references occurring in the commentary on Physics. However, we should be very careful to draw conclusions from the occurrence of references, since it is always possible that we are dealing with a second or third lectura of the text.. (shrink)
This paper argues that logical inferentialists should reject multiple-conclusion logics. Logical inferentialism is the position that the meanings of the logical constants are determined by the rules of inference they obey. As such, logical inferentialism requires a proof-theoretic framework within which to operate. However, in order to fulfil its semantic duties, a deductive system has to be suitably connected to our inferential practices. I argue that, contrary to an established tradition, multiple-conclusion systems are ill-suited for this (...) purpose because they fail to provide a 'natural' representation of our ordinary modes of inference. Moreover, the two most plausible attempts at bringing multiple conclusions into line with our ordinary forms of reasoning, the disjunctive reading and the bilateralist denial interpretation, are unacceptable by inferentialist standards. (shrink)
Arthur Pap’s work played an important role in the development of the analytic tradition. This role goes beyond the merely historical fact that Pap’s views of dispositional and modal concepts were influential. As a sympathetic critic of logical empiricism, Pap, like Quine, saw a deep tension in logical empiricism at its very best in the work of Carnap. But Pap’s critique of Carnap is quite different from Quine’s, and represents the discovery of limits beyond which empiricism cannot go, (...) where there lies nothing other than intuitive knowledge of logic itself. Pap’s arguments for this intuitive knowledge anticipate Etchemendy’s recent critique of the model-theoretic account of logicalconsequence. Pap’s work also anticipates prominent developments in the contemporary neo-Fregean philosophy of mathematics championed by Wright and Hale. Finally, Pap’s major philosophical preoccupation, the concepts of necessity and possibility, provides distinctive solutions and perspectives on issues of contemporary concern in the metaphysics of modality. In particular, Pap’s account of modality allows us to see the significance of Kripke’s well-known arguments on necessity and apriority in a new light. (shrink)
One of the most striking differences between Frege's Begriffsschrift (logical system) and standard contemporary systems of logic is the inclusion in the former of the judgement stroke: a symbol which marks those propositions which are being asserted , that is, which are being used to express judgements . There has been considerable controversy regarding both the exact purpose of the judgement stroke, and whether a system of logic should include such a symbol. This paper explains the intended role of (...) the judgement stroke in a way that renders it readily comprehensible why Frege insisted that this symbol was an essential part of his logical system. The key point here is that Frege viewed logic as the study of inference relations amongst acts of judgement , rather than – as in the typical contemporary view – of consequence relations amongst certain objects (propositions or well-formed formulae). The paper also explains why Frege's use of the judgement stroke is not in conflict with his avowed anti-psychologism, and why Wittgenstein's criticism of the judgement stroke as 'logically quite meaningless' is unfounded. The key point here is that while the judgement stroke has no content , its use in logic and mathematics is subject to a very stringent norm of assertion. (shrink)
Tarski apresentou sua definição de operador de consequência com a intenção de expor as concepções fundamentais da consequência lógica. Um espaço de Tarski é um par ordenado determinado por um conjunto não vazio e um operador de consequência sobre este conjunto. Esta estrutura matemática caracteriza um espaço quase topológico. Este artigo mostra uma visão algébrica dos espaços de Tarski e introduz uma lógica proposicional modal que interpreta o seu operador modal nos conjuntos fechados de algum espaço de Tarski. DOI:10.5007/1808-1711.2010v14n1p47.
This paper concerns voting with logical consequences, which means that anybody voting for an alternative x should vote for the logical consequences of x as well. Similarly, the social choice set is also supposed to be closed under logical consequences. The central result of the paper is that, given a set of fairly natural conditions, the only social choice functions that satisfy social logical closure are oligarchic (where a subset of the voters are decisive for the (...) social choice). The set of conditions needed for the proof include a version of Independence of Irrelevant Alternatives that also plays a central role in Arrow's impossibility theorem. (Published Online July 11 2006) Footnotes1 Much of this article was written while the author was a fellow at the Swedish Collegium for Advanced Study in the Social Sciences (SCASSS) in Uppsala. I want to thank the Collegium for providing me with excellent working conditions. Wlodek Rabinowicz and other fellows gave me valuable comments at a seminar at SCASSS when an early version of the paper was presented. I also want to thank Luc Bovens, Franz Dietrich, Christian List and an anonymous referee for their excellent comments on a later version. The final version was prepared during a stay at Oxford University for which I am grateful to the British Academy. (shrink)
This paper argues that the prominent accounts of logical knowledge have the consequence that they conflict with ordinary reasoning. On these accounts knowing a logical principle, for instance, is having a disposition to infer according to it. These accounts in particular conflict with so-called ‘reasoned change in view’, where someone does not infer according to a logical principle but revise their views instead. The paper also outlines a propositional account of logical knowledge which does not (...) conflict with ordinary reasoning. (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 logicalconsequence 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)
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 logicalconsequence 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 aim of this book is to present the fundamental theoretical results concerning inference rules in deductive formal systems. Primary attention is focused on: admissible or permissible inference rules the derivability of the admissible inference rules the structural completeness of logics the bases for admissible and valid inference rules. There is particular emphasis on propositional non-standard logics (primary, superintuitionistic and modal logics) but general logicalconsequence relations and classical first-order theories are also considered. The book is basically self-contained (...) and special attention has been made to present the material in a convenient manner for the reader. Proofs of results, many of which are not readily available elsewhere, are also included. The book is written at a level appropriate for first-year graduate students in mathematics or computer science. Although some knowledge of elementary logic and universal algebra are necessary, the first chapter includes all the results from universal algebra and logic that the reader needs. For graduate students in mathematics and computer science the book is an excellent textbook. (shrink)
Aristotle was the first and one of the greatest logicians. He not only devised the first system of formal logic, but also raised many fundamental problems in the philosophy of logic. In this book, Dr Lear shows how Aristotle's discussion of logicalconsequence, validity and proof can contribute to contemporary dabates in the philosophy of logic. No background knowledge of Aristotle is assumed.
In 1936 Tarski sketched a rigorous definition of the concept of logicalconsequence which, he claimed, agreed quite well with common usage-or, as he also said, with the common concept of consequence. Commentators of Tarski's paper have usually been elusive as to what this common concept is. However, being clear on this issue is important to decide whether Tarski's definition failed (as Etchemendy has contended) or succeeded (as most commentators maintain). I argue that the common concept of (...)consequence that Tarski tried to characterize is not some general, all-purpose notion of consequence, but a rather precise one, namely the concept of consequence at play in axiomatics. I identify this concept and show that Tarski's definition is fully adequate to it. (shrink)
I argue that Beall and Restall's logical pluralism fails. Beall?Restall pluralism is the claim that there are different, equally correct logicalconsequence relations in a single language. Their position fails for two, related, reasons: first, it relies on an unmotivated conception of the ?settled core? of consequence: they believe that truth-preservation, necessity, formality and normativity are ?settled? features of logicalconsequence and that any relation satisfying these criteria is a logicalconsequence relation. (...) I consider historical evidence and argue that their position relies on an unmotivated conception of the settled features of logicalconsequence. There are many features that are just as settled but which are inconsistent with pluralism. Second, I argue that Beall?Restall pluralism fails to hold in a single language with a single selection of logical constants, which they require for the position to be distinct from Carnap's. I consider various ways in which Beall and Restall can resist this meaning variance, particularly for negation, but argue that the strongest way relies on an unmotivated conception of the settled features of the logical constants. (shrink)
We investigate logicalconsequence in temporal logics in terms of logical consecutions. i.e., inference rules. First, we discuss the question: what does it mean for a logical consecution to be 'correct' in a propositional logic. We consider both valid and admissible consecutions in linear temporal logics and discuss the distinction between these two notions. The linear temporal logic LDTL, consisting of all formulas valid in the frame 〈L, ≤, ≥〉 of all integer numbers, is the prime (...) object of our investigation. We describe consecutions admissible LDTL in a semantic way—via consecutions valid in special temporal Kripke/Hintikka models. Then we state that any temporal inference rule has a reduced normal form which is given in terms of uniform formulas of temporal degree 1. Using these facts and enhanced semantic techniques we construct an algorithm, which recognizes consecutions admissible in LDTL. Also, we note that using the same technique it follows that the linear temporal logic L (N) of all natural numbers is also decidable w.r.t. inference rules. So, we prove that both logics LDTL and L (N) are decidable w.r.t. admissible consecutions. In particular, as a consequence, they both are decidable (Known fact), and the given deciding algorithms are explicit. (shrink)
Fine (2007) argues that Frege’s puzzle and its relatives demonstrate a need for a basic reorientation of the field of semantics. According to this reorientation, the domain of semantic facts would be closed not under the classical consequence relation but only under a stronger relation Fine calls “manifest consequence.” I examine Fine’s informally sketched analyses of manifest consequence, showing that each can be amended to determine a class of strong consequence relations. A best candidate relation emerges (...) from each of the two classes, and I prove that the two candidates extensionally coincide. The resulting consequence relation is of independent interest, for it might be held to constitute a cogent standard of reasoning that proceeds under a deficient grasp on the identity of objects. (shrink)
Two arguments favoring propositionalist accounts of attitude sentences are being revisited: the Church-Langford translation argument and Thomason's argument against quotational theories of indirect discourse. None of them proves to be decisive, thus leaving the option of searching for a developed quotational alternative. Such an alternative is found in an interpreted logical form theory of attitude ascription. The theory differentiates elegantly among different attitudes but it fails to account for logical dependencies among them. It is argued, however, that the (...) concept of logicalconsequence does not well apply to dependencies among belief sentences and that the requirement to account for logical relations among such sentences should be relaxed. (shrink)
Logical pluralism is the view according to which there is more than one relation of logicalconsequence, 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)
We are pluralists about logicalconsequence [1]. We hold that there is more than one sense in which arguments may be deductively valid, that these senses are equally good, and equally deserving of the name deductive validity. Our pluralism starts with our analysis of consequence. This analysis of consequence is not idiosyncratic. We agree with Richard Jeffrey, and with many other philosophers of logic about how logicalconsequence is to be defined. To quote Jeffrey.
In this paper, I distinguish different kinds of pluralism about logicalconsequence. In particular, I distinguish the pluralism about logic arising from Carnap’s Principle of Tolerance from a pluralism which maintains that there are different, equally “good” logicalconsequence relations on the one language. I will argue that this second form of pluralism does more justice to the contemporary state of logical theory and practice than does Carnap’s more moderate pluralism.
