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  1. What is the Normative Role of Logic?Hartry Field - 2009 - Aristotelian Society Supplementary Volume 83 (1):251-268.
    The paper tries to spell out a connection between deductive logic and rationality, against Harman's arguments that there is no such connection, and also against the thought that any such connection would preclude rational change in logic. One might not need to connect logic to rationality if one could view logic as the science of what preserves truth by a certain kind of necessity (or by necessity plus logical form); but the paper points out a serious obstacle to any such (...)
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  • Validity and Truth-Preservation.Lionel Shapiro & Julien Murzi - 2015 - In D. Achourioti, H. Galinon & J. Martinez (eds.), Unifying the Philosophy of Truth. Springer. pp. 431-459.
    The revisionary approach to semantic paradox is commonly thought to have a somewhat uncomfortable corollary, viz. that, on pain of triviality, we cannot affirm that all valid arguments preserve truth (Beall2007, Beall2009, Field2008, Field2009). We show that the standard arguments for this conclusion all break down once (i) the structural rule of contraction is restricted and (ii) how the premises can be aggregated---so that they can be said to jointly entail a given conclusion---is appropriately understood. In addition, we briefly rehearse (...)
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  • Logical consequence: Models and modality.Stewart Shapiro - 1998 - In Matthias Schirn (ed.), The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993. Oxford, England: Clarendon Press. pp. 131--156.
  • Doubt truth to be a liar.Graham Priest - 2006 - New York: Oxford University Press.
    Dialetheism is the view that some contradictions are true. This is a view which runs against orthodoxy in logic and metaphysics since Aristotle, and has implications for many of the core notions of philosophy. Doubt Truth to Be a Liar explores these implications for truth, rationality, negation, and the nature of logic, and develops further the defense of dialetheism first mounted in Priest's In Contradiction, a second edition of which is also available.
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  • Truth without contra(di)ction.Elia Zardini - 2011 - Review of Symbolic Logic 4 (4):498-535.
    The concept of truth arguably plays a central role in many areas of philosophical theorizing. Yet, what seems to be one of the most fundamental principles governing that concept, i.e. the equivalence between P and , is inconsistent in full classical logic, as shown by the semantic paradoxes. I propose a new solution to those paradoxes, based on a principled revision of classical logic. Technically, the key idea consists in the rejection of the unrestricted validity of the structural principle of (...)
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  • Naive Modus Ponens.Elia Zardini - 2013 - Journal of Philosophical Logic 42 (4):575-593.
    The paper is concerned with a logical difficulty which Lionel Shapiro’s deflationist theory of logical consequence (as well as the author’s favoured, non-deflationist theory) gives rise to. It is argued that Shapiro’s non-contractive approach to solving the difficulty, although correct in its broad outlines, is nevertheless extremely problematic in some of its specifics, in particular in its failure to validate certain intuitive rules and laws associated with the principle of modus ponens. An alternative non-contractive theory is offered which does not (...)
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  • Failures of Categoricity and Compositionality for Intuitionistic Disjunction.Jack Woods - 2012 - Thought: A Journal of Philosophy 1 (4):281-291.
    I show that the model-theoretic meaning that can be read off the natural deduction rules for disjunction fails to have certain desirable properties. I use this result to argue against a modest form of inferentialism which uses natural deduction rules to fix model-theoretic truth-conditions for logical connectives.
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  • Conceptual truth.Timothy Williamson - 2006 - Aristotelian Society Supplementary Volume 80 (1):1–41.
    The paper criticizes epistemological conceptions of analytic or conceptual truth, on which assent to such truths is a necessary condition of understanding them. The critique involves no Quinean scepticism about meaning. Rather, even granted that a paradigmatic candidate for analyticity is synonymy with a logical truth, both the former and the latter can be intelligibly doubted by linguistically competent deviant logicians, who, although mistaken, still constitute counterexamples to the claim that assent is necessary for understanding. There are no analytic or (...)
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  • Blind Reasoning.Timothy Williamson - 2003 - Supplement to the Proceedings of the Aristotelian Society 77 (1):249-293.
    [Paul Boghossian] The paper asks under what conditions deductive reasoning transmits justification from its premises to its conclusion. It argues that both standard externalist and standard internalist accounts of this phenomenon fail. The nature of this failure is taken to indicate the way forward: basic forms of deductive reasoning must justify by being instances of ’blind but blameless’ reasoning. Finally, the paper explores the suggestion that an inferentialist account of the logical constants can help explain how such reasoning is possible. (...)
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  • Boghossian and Casalegno on Understanding and Inference.Timothy Williamson - 2012 - Dialectica 66 (2):237-247.
    In response to Paul Boghossian's objections in ‘Inferentialism and the epistemology of logic’, this paper defends counterexamples offered by Paolo Casalegno and the author to an inferentialist account of what it is to understand a logical constant, on which Boghossian had relied in his explanation of our entitlement to reason according to basic logical principles. The importance for understanding is stressed of non-inferential aspects of the use of logical constants. Boghossian's criteria for individuating concepts are also queried.
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  • Doxastic Correctness.Ralph Wedgwood - 2013 - Aristotelian Society Supplementary Volume 87 (1):217-234.
    If beliefs are subject to a basic norm of correctness—roughly, to the principle that a belief is correct only if the proposition believed is true—how can this norm guide believers in forming their beliefs? Answer: this norm guides believers indirectly: believers are directly guided by requirements of rationality—which are themselves explained by this norm of correctness. The fundamental connection between rationality and correctness is probabilistic. Incorrectness comes in degrees; for beliefs, these degrees of incorrectness are measured by quadratic scoring rules, (...)
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  • What are logical notions?Alfred Tarski - 1986 - History and Philosophy of Logic 7 (2):143-154.
    In this manuscript, published here for the first time, Tarski explores the concept of logical notion. He draws on Klein's Erlanger Programm to locate the logical notions of ordinary geometry as those invariant under all transformations of space. Generalizing, he explicates the concept of logical notion of an arbitrary discipline.
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  • Why Conclusions Should Remain Single.Florian Steinberger - 2011 - Journal of Philosophical Logic 40 (3):333-355.
    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 (...)
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  • Squeezing arguments.P. Smith - 2011 - Analysis 71 (1):22-30.
    Many of our concepts are introduced to us via, and seem only to be constrained by, roughand-ready explanations and some sample paradigm positive and negative applications. This happens even in informal logic and mathematics. Yet in some cases, the concepts in question – although only informally and vaguely characterized – in fact have, or appear to have, entirely determinate extensions. Here’s one familiar example. When we start learning computability theory, we are introduced to the idea of an algorithmically computable function (...)
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  • Rejection and valuations.Luca Incurvati & Peter Smith - 2010 - Analysis 70 (1):3 - 10.
    Timothy Smiley’s wonderful paper ‘Rejection’ (1996) is still perhaps not as well known or well understood as it should be. This note first gives a quick presentation of themes from that paper, though done in our own way, and then considers a putative line of objection – recently advanced by Julien Murzi and Ole Hjortland (2009) – to one of Smiley’s key claims. Along the way, we consider the prospects for an intuitionistic approach to some of the issues discussed in (...)
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  • Rejection.Timothy Smiley - 1996 - Analysis 56 (1):1–9.
  • A general logic.John Slaney - 1990 - Australasian Journal of Philosophy 68 (1):74 – 88.
  • Sets, classes and extensions: A singularity approach to Russell's paradox.K. Simmons - 2000 - Philosophical Studies 100 (2):109-149.
  • Multiple Conclusion Logic.D. J. Shoesmith & Timothy Smiley - 1978 - Cambridge, England / New York London Melbourne: Cambridge University Press. Edited by T. J. Smiley.
    Multiple -conclusion logic extends formal logic by allowing arguments to have a set of conclusions instead of a single one, the truth lying somewhere among the conclusions if all the premises are true. The extension opens up interesting possibilities based on the symmetry between premises and conclusions, and can also be used to throw fresh light on the conventional logic and its limitations. This is a sustained study of the subject and is certain to stimulate further research. Part I reworks (...)
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  • Did Tarski commit "Tarski's fallacy"?Gila Sher - 1996 - Journal of Symbolic Logic 61 (2):653-686.
    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 (...)
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  • Logical consequence, proof theory, and model theory.Stewart Shapiro - 2005 - In Oxford Handbook of Philosophy of Mathematics and Logic. Oxford University Press. pp. 651--670.
    This chapter provides broad coverage of the notion of logical consequence, exploring its modal, semantic, and epistemic aspects. It develops the contrast between proof-theoretic notion of consequence, in terms of deduction, and a model-theoretic approach, in terms of truth-conditions. The main purpose is to relate the formal, technical work in logic to the philosophical concepts that underlie reasoning.
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  • Foundations without foundationalism: a case for second-order logic.Stewart Shapiro - 1991 - New York: Oxford University Press.
    The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed description of higher-order logic, including a comprehensive discussion of its semantics. He goes on to demonstrate the prevalence of second-order concepts in mathematics and the extent to which mathematical ideas can be formulated in higher-order logic. He also shows how first-order languages are often insufficient to codify (...)
  • Deflating logical consequence.Lionel Shapiro - 2011 - Philosophical Quarterly 61 (243):320-342.
    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 logical consequence. 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 consequence's nature. I then (...)
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  • Validity Concepts in Proof-theoretic Semantics.Peter Schroeder-Heister - 2006 - Synthese 148 (3):525-571.
    The standard approach to what I call “proof-theoretic semantics”, which is mainly due to Dummett and Prawitz, attempts to give a semantics of proofs by defining what counts as a valid proof. After a discussion of the general aims of proof-theoretic semantics, this paper investigates in detail various notions of proof-theoretic validity and offers certain improvements of the definitions given by Prawitz. Particular emphasis is placed on the relationship between semantic validity concepts and validity concepts used in normalization theory. It (...)
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  • The categorical and the hypothetical: a critique of some fundamental assumptions of standard semantics.Peter Schroeder-Heister - 2012 - Synthese 187 (3):925-942.
    The hypothetical notion of consequence is normally understood as the transmission of a categorical notion from premisses to conclusion. In model-theoretic semantics this categorical notion is 'truth', in standard proof-theoretic semantics it is 'canonical provability'. Three underlying dogmas, (I) the priority of the categorical over the hypothetical, (II) the transmission view of consequence, and (III) the identification of consequence and correctness of inference are criticized from an alternative view of proof-theoretic semantics. It is argued that consequence is a basic semantical (...)
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  • Knowledge by deduction.Ian Rumfitt - 2008 - Grazer Philosophische Studien 77 (1):61-84.
    It seems beyond doubt that a thinker can come to know a conclusion by deducing it from premisses that he knows already, but philosophers have found it puzzling how a thinker could acquire knowledge in this way. Assuming a broadly externalist conception of knowledge, I explain why judgements competently deduced from known premisses are themselves knowledgeable. Assuming an exclusionary conception of judgeable content, I further explain how such judgements can be informative. (According to the exclusionary conception, which I develop from (...)
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  • Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.
    This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning---one which takes meaning to be constituted by assertibility and deniability conditions---and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory of meaning to present and motivate a logical system---ST---that conservatively extends classical (...)
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  • General-Elimination Harmony and the Meaning of the Logical Constants.Stephen Read - 2010 - Journal of Philosophical Logic 39 (5):557-576.
    Inferentialism claims that expressions are meaningful by virtue of rules governing their use. In particular, logical expressions are autonomous if given meaning by their introduction-rules, rules specifying the grounds for assertion of propositions containing them. If the elimination-rules do no more, and no less, than is justified by the introduction-rules, the rules satisfy what Prawitz, following Lorenzen, called an inversion principle. This connection between rules leads to a general form of elimination-rule, and when the rules have this form, they may (...)
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  • Harmony and autonomy in classical logic.Stephen Read - 2000 - Journal of Philosophical Logic 29 (2):123-154.
    Michael Dummett and Dag Prawitz have argued that a constructivist theory of meaning depends on explicating the meaning of logical constants in terms of the theory of valid inference, imposing a constraint of harmony on acceptable connectives. They argue further that classical logic, in particular, classical negation, breaks these constraints, so that classical negation, if a cogent notion at all, has a meaning going beyond what can be exhibited in its inferential use. I argue that Dummett gives a mistaken elaboration (...)
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  • Logical consequence: A defense of Tarski.Greg Ray - 1996 - Journal of Philosophical Logic 25 (6):617 - 677.
    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 (...)
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  • Absolute generality.Agustín Rayo & Gabriel Uzquiano (eds.) - 2006 - New York: Oxford University Press.
    The problem of absolute generality has attracted much attention in recent philosophy. Agustin Rayo and Gabriel Uzquiano have assembled a distinguished team of contributors to write new essays on the topic. They investigate the question of whether it is possible to attain absolute generality in thought and language and the ramifications of this question in the philosophy of logic and mathematics.
  • The Runabout Inference-Ticket.A. N. Prior - 1960 - Analysis 21 (2):38-39.
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  • The logic of paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
  • Etchemendy and Logical Consequence.Graham Priest - 1995 - Canadian Journal of Philosophy 25 (2):283 - 292.
    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 (...)
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  • The epistemic significance of valid inference.Dag Prawitz - 2012 - Synthese 187 (3):887-898.
    The traditional picture of logic takes it for granted that "valid arguments have a fundamental epistemic significance", but neither model theory nor traditional proof theory dealing with formal system has been able to give an account of this significance. Since valid arguments as usually understood do not in general have any epistemic significance, the problem is to explain how and why we can nevertheless use them sometimes to acquire knowledge. It is suggested that we should distinguish between arguments and acts (...)
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  • On the idea of a general proof theory.Dag Prawitz - 1974 - Synthese 27 (1-2):63 - 77.
  • Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
    This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics.
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  • Meaning Approached Via Proofs.Dag Prawitz - 2006 - Synthese 148 (3):507-524.
    According to a main idea of Gentzen the meanings of the logical constants are reflected by the introduction rules in his system of natural deduction. This idea is here understood as saying roughly that a closed argument ending with an introduction is valid provided that its immediate subarguments are valid and that other closed arguments are justified to the extent that they can be brought to introduction form. One main part of the paper is devoted to the exact development of (...)
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  • New foundations for logic.Karl Popper - 1947 - Mind 56 (223):193-235.
  • New essays on Tarski and philosophy.Douglas Patterson (ed.) - 2008 - New York: Oxford University Press.
    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 ...
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  • Quine and Slater on paraconsistency and deviance.Francesco Paoli - 2003 - Journal of Philosophical Logic 32 (5):531-548.
    In a famous and controversial paper, B. H. Slater has argued against the possibility of paraconsistent logics. Our reply is centred on the distinction between two aspects of the meaning of a logical constant *c* in a given logic: its operational meaning, given by the operational rules for *c* in a cut-free sequent calculus for the logic at issue, and its global meaning, specified by the sequents containing *c* which can be proved in the same calculus. Subsequently, we use the (...)
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  • Some remarks on the notion of proof.John Myhill - 1960 - Journal of Philosophy 57 (14):461-471.
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  • The inexpressibility of validity.Julien Murzi - 2014 - Analysis 74 (1):65-81.
    Tarski's Undefinability of Truth Theorem comes in two versions: that no consistent theory which interprets Robinson's Arithmetic (Q) can prove all instances of the T-Scheme and hence define truth; and that no such theory, if sound, can even express truth. In this note, I prove corresponding limitative results for validity. While Peano Arithmetic already has the resources to define a predicate expressing logical validity, as Jeff Ketland has recently pointed out (2012, Validity as a primitive. Analysis 72: 421-30), no theory (...)
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  • Manifestability and Epistemic Truth.Julien Murzi - 2012 - Topoi 31 (1):17-26.
    I argue that the standard anti-realist argument from manifestability to intuitionistic logic is either unsound or invalid. Strong interpretations of the manifestability of understanding are falsified by the existence of blindspots for knowledge. Weaker interpretations are either too weak, or gerrymandered and ad hoc. Either way, they present no threat to classical logic.
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  • Curry’s Paradox.Robert K. Meyer, Richard Routley & J. Michael Dunn - 1979 - Analysis 39 (3):124 - 128.
  • XIII*—Two Problems with Tarski's Theory of Consequence.Vann McGee - 1992 - Proceedings of the Aristotelian Society 92 (1):273-292.
    Vann McGee; XIII*—Two Problems with Tarski's Theory of Consequence, Proceedings of the Aristotelian Society, Volume 92, Issue 1, 1 June 1992, Pages 273–292, htt.
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  • Tarski on Logical Consequence.Mario Gómez-Torrente - 1996 - Notre Dame Journal of Formal Logic 37 (1):125-151.
    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, (...)
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  • Logical Consequence and the Paradoxes.Edwin Mares & Francesco Paoli - 2014 - Journal of Philosophical Logic 43 (2-3):439-469.
    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, (...)
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  • Logical constants.John MacFarlane - 2008 - Mind.
    Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...)
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  • Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
    A formal theory of truth, alternative to tarski's 'orthodox' theory, based on truth-value gaps, is presented. the theory is proposed as a fairly plausible model for natural language and as one which allows rigorous definitions to be given for various intuitive concepts, such as those of 'grounded' and 'paradoxical' sentences.
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