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Analysis 22 (6):130-134 (1962)

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  1. Notions of Proof and Refutation in ‘Gentzensemantik’: Franz von Kutschera as an Early Proponent of (Bilateralist) Proof-Theoretic Semantics.Sara Ayhan - forthcoming - History and Philosophy of Logic:1-7.
    This is a comment on a translation of Franz von Kutschera's paper ‘Ein verallgemeinerter Widerlegungsbegriff für Gentzenkalküle’, which was published in German in 1969. The paper is an important predecessor of what is nowadays called ‘proof-theoretic semantics’, which describes the view that the meaning of logical connectives is determined by the rules governing their use in a proof system. Von Kutschera adopts this view in this paper, and more specifically, a bilateralist view on this subject in that his aim is (...)
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  • Making Meaning: A study in foundational semantics.Jaakko Reinikainen - 2024 - Dissertation, Tampere University
    This is a work in the philosophy of language and metasemantics. Its purpose is to help answer the question about how words acquire their meanings. The work is divided into two parts. The purpose of Part One is to defend the claim that, despite numerous attempts, the so-called Kripkenstein’s sceptical challenge, and especially the problem of finitude, has not been offered a successful straight solution. The purpose of Part Two is to critically examine Robert Brandom’s philosophy, which can be treated (...)
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  • Neologicism and Conservativeness.Stephen Mackereth - forthcoming - Journal of Philosophy.
    Neologicists have claimed that Hume's Principle (HP) may be taken as a stipulative definition of cardinal number. This claim is threatened by the fact that HP is not conservative over pure second-order logic. I argue that the dominant neologicist response to the conservativeness objection is not satisfactory. Then I propose a novel version of neologicism, based on Heck's Two-sorted Hume's Principle (2HP), which does meet the conservativeness objection—provided that conservativeness is understood semantically and not deductively. I also argue that on (...)
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  • A General Schema for Bilateral Proof Rules.Ryan Simonelli - 2024 - Journal of Philosophical Logic (3):1-34.
    Bilateral proof systems, which provide rules for both affirming and denying sentences, have been prominent in the development of proof-theoretic semantics for classical logic in recent years. However, such systems provide a substantial amount of freedom in the formulation of the rules, and, as a result, a number of different sets of rules have been put forward as definitive of the meanings of the classical connectives. In this paper, I argue that a single general schema for bilateral proof rules has (...)
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  • Peter Schroeder-Heister on Proof-Theoretic Semantics.Thomas Piecha & Kai F. Wehmeier (eds.) - 2024 - Springer.
    This open access book is a superb collection of some fifteen chapters inspired by Schroeder-Heister's groundbreaking work, written by leading experts in the field, plus an extensive autobiography and comments on the various contributions by Schroeder-Heister himself. For several decades, Peter Schroeder-Heister has been a central figure in proof-theoretic semantics, a field of study situated at the interface of logic, theoretical computer science, natural-language semantics, and the philosophy of language. -/- The chapters of which this book is composed discuss the (...)
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  • Categorical Quantification.Constantin C. Brîncuș - forthcoming - Bulletin of Symbolic Logic:1-27.
    Due to Gӧdel’s incompleteness results, the categoricity of a sufficiently rich mathematical theory and the semantic completeness of its underlying logic are two mutually exclusive ideals. For first- and second-order logics we obtain one of them with the cost of losing the other. In addition, in both these logics the rules of deduction for their quantifiers are non-categorical. In this paper I examine two recent arguments –Warren (2020), Murzi and Topey (2021)– for the idea that the natural deduction rules for (...)
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  • Logical Multilateralism.Heinrich Wansing & Sara Ayhan - 2023 - Journal of Philosophical Logic 52 (6):1603-1636.
    In this paper we will consider the existing notions of bilateralism in the context of proof-theoretic semantics and propose, based on our understanding of bilateralism, an extension to logical multilateralism. This approach differs from what has been proposed under this name before in that we do not consider multiple speech acts as the core of such a theory but rather multiple consequence relations. We will argue that for this aim the most beneficial proof-theoretical realization is to use sequent calculi with (...)
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  • On the Provable Contradictions of the Connexive Logics C and C3.Satoru Niki & Heinrich Wansing - 2023 - Journal of Philosophical Logic 52 (5):1355-1383.
    Despite the tendency to be otherwise, some non-classical logics are known to validate formulas that are invalid in classical logic. A subclass of such systems even possesses pairs of a formula and its negation as theorems, without becoming trivial. How should these provable contradictions be understood? The present paper aims to shed light on aspects of this phenomenon by taking as samples the constructive connexive logic C, which is obtained by a simple modification of a system of constructible falsity, namely (...)
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  • ‘Conspiracy Theory’ as a Tonkish Term: Some Runabout Inference-Tickets from Truth to Falsehood.Charles Pigden - 2023 - Social Epistemology 37 (4):423-437.
    I argue that ‘conspiracy theory’ and ‘conspiracy theorist’ as commonly employed are ‘tonkish’ terms (as defined by Arthur Prior and Michael Dummett), licensing inferences from truths to falsehoods; indeed, that they are mega-tonkish terms, since their use is governed by different and competing sets of introduction and elimination rules, delivering different and inconsistent results. Thus ‘conspiracy theory’ and ‘conspiracy theorist’ do not have determinate extensions, which means that generalizations about conspiracy theories or conspiracy theorists do not have determinate truth-values. Hence (...)
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  • The New Collapse Argument against Quantifier Variance.Theodore Sider - 2023 - The Monist 106 (3):342-361.
    Quantifier variantists accept multiple alternative ontological languages in which quantifiers obey the usual inference rules despite having different meanings. But collapse arguments seem to show that these quantifiers would be provably equivalent to one another. Cian Dorr has pushed this discussion forward by formulating the collapse argument in terms of an algebra of meanings that are common amongst the languages. I attempt to show that quantifier variantists can respond. But an important distinction between types of quantifier variance emerges, between those (...)
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  • (1 other version)Shadows of Syntax: Revitalizing Logical and Mathematical Conventionalism.M. Rescorla - 2023 - History and Philosophy of Logic 45 (3):380-384.
    Volume 45, Issue 3, August 2024, Page 380-384.
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  • What is a Relevant Connective?Shawn Standefer - 2022 - Journal of Philosophical Logic 51 (4):919-950.
    There appears to be few, if any, limits on what sorts of logical connectives can be added to a given logic. One source of potential limitations is the motivating ideology associated with a logic. While extraneous to the logic, the motivating ideology is often important for the development of formal and philosophical work on that logic, as is the case with intuitionistic logic. One family of logics for which the philosophical ideology is important is the family of relevant logics. In (...)
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  • Need anything follow from a contradiction?Simon Thomas Hewitt - 2022 - Inquiry: An Interdisciplinary Journal of Philosophy 65 (3):278-297.
    ABSTRACT Classical and intuitionistic logic both validate Ex Contradictione Quodlibet, according to which any proposition whatsoever follows from a contradiction. Many philosophers have found ECQ counter-intuitive, but criticisms of the principle have almost universally been directed from a position of support for relevance or other orthodox paraconsistent logics, according to which some, but not necessarily all, propositions follow from a contradiction. This paper draws attention to the historically significant view that nothing whatsoever follows from a contradiction – Ex Contradictione Nihil. (...)
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  • Believing is said of groups in many ways (and so it should be said of them in none).Richard Pettigrew -
    In the first half of this paper, I argue that group belief ascriptions are highly ambiguous. What's more, in many cases, neither the available contextual factors nor known pragmatic considerations are sufficient to allow the audience to identify which of the many possible meanings is intended. In the second half, I argue that this ambiguity often has bad consequences when a group belief ascription is heard and taken as testimony. And indeed it has these consequences even when the ascription is (...)
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  • A forgotten logical expressivist: Strawson’s philosophy of logic and its challenges.Sybren Heyndels - 2022 - Synthese 200 (3):1-23.
    P.F. Strawson contributed to many philosophical domains, including the philosophy of language, the history of philosophy, metaphysics, moral philosophy and philosophical methodology. Most of his contributions in these areas have influenced contemporary debates, either because his views are still defended or because they are still considered worthy of detailed responses. His views on the philosophy of logic have been only rarely discussed, however. My aim in this paper is threefold. First, I provide a systematic account of Strawson’s philosophy of logic. (...)
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  • Logical Form and the Limits of Thought.Manish Oza - 2020 - Dissertation, University of Toronto
    What is the relation of logic to thinking? My dissertation offers a new argument for the claim that logic is constitutive of thinking in the following sense: representational activity counts as thinking only if it manifests sensitivity to logical rules. In short, thinking has to be minimally logical. An account of thinking has to allow for our freedom to question or revise our commitments – even seemingly obvious conceptual connections – without loss of understanding. This freedom, I argue, requires that (...)
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  • (3 other versions)Inferentialism: Why Rules Matter.Jaroslav Peregrin - 2014 - London and New York: Palgrave-Macmillan.
    In this study two strands of inferentialism are brought together: the philosophical doctrine of Brandom, according to which meanings are generally inferential roles, and the logical doctrine prioritizing proof-theory over model theory and approaching meaning in logical, especially proof-theoretical terms.
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  • Against Schmought.Matthew Vermaire - 2021 - Journal of Philosophy 118 (9):465-485.
    Matti Eklund has argued that a new problem in metanormative theory arises when we consider the possibility of "normative counterparts"—normative concepts with the same normative roles as OUGHT and RIGHT, but with different extensions. I distinguish two versions of the problem, and propose a solution: when we attend to the attitudinal commitments involved in the possession and application of some normative concepts, we find that tolerance for the possibility of normative counterparts is rationally ruled out.
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  • Inferentialism, Context-Shifting and Background Assumptions.Bartosz Kaluziński - 2022 - Erkenntnis 87 (6):2973-2992.
    In this paper I present how the normative inferentialist can make the distinction between sentence meaning and content of the utterance. The inferentialist can understand sentence meaning as a role conferred to that sentence by the rules governing inferential transitions and content of the utterance as just a part of sentence meaning. I attempt to show how such a framework can account for prominent scenarios presented by contextualists as a challenge to semantic minimalism/literalism. I argue that inferentialism can address contextualist (...)
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  • The Metaphysical Commitments of Logic.Thomas Brouwer - 2013 - Dissertation, University of Leeds
    This thesis is about the metaphysics of logic. I argue against a view I refer to as ‘logical realism’. This is the view that the logical constants represent a particular kind of metaphysical structure, which I dub ‘logico-metaphysical structure’. I argue instead for a more metaphysically lightweight view of logic which I dub ‘logical expressivism’. -/- In the first part of this thesis (Chapters I and II) I argue against a number of arguments that Theodore Sider has given for logical (...)
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  • Shadows of Syntax: Revitalizing Logical and Mathematical Conventionalism.Jared Warren - 2020 - New York, USA: Oxford University Press.
    What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...)
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  • Contingent a priori truths and performatives.Marco Ruffino - 2020 - Synthese 198 (S22):5593-5613.
    My primary goal in this paper is to defend the plausibility of Kripke’s thesis that there are contingent a priori truths, and to fill out some gaps in Kripke’s own account of these truths. But the strategy here adopted is, to the best of my knowledge, still unexplored and different from the one adopted both by Kripke himself and by his critics. I first argue that Kripke’s examples of such truths can only be legitimate if seen as introduced by performative (...)
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  • Meaning and Rules.Eva Picardi - 1988 - In J. C. Nyíri & Barry Smith (eds.), Practical Knowledge: Outlines of a Theory of Traditions and Skills. Croom Helm. pp. 90-121.
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  • Peano's Counterexample to Harmony.Leonardo Ceragioli - 2019 - Theoria 85 (6):459-484.
    Harmony and conservative extension are two criteria proposed to discern between acceptable and unacceptable rules. Despite some interesting works in this field, the exact relation between them is still not clear. In this article, some standard counterexamples to the equivalence between them are summarized, and a recent formulation of the notion of stability is used to express a more refined conjecture about their relation. Then Prawitz's proposal of a counterexample based on the truth predicate to this refined conjecture is shown (...)
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  • Knot is not that nasty.Elisángela Ramírez-Cámara & Luis Estrada-González - 2019 - Synthese 198 (S22):5533-5554.
    In this paper, we evaluate Button’s claim that knot is a nasty connective. Knot’s nastiness is due to the fact that, when one extends the set \ with knot, the connective provides counterexamples to a number of classically valid operational rules in a sequent calculus proof system. We show that just as going non-transitive diminishes tonk’s nastiness, knot’s nastiness can also be reduced by dropping Reflexivity, a different structural rule. Since doing so restores all other rules in the system as (...)
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  • Intensity of Experience: Maher’s Theory of Schizophrenic Delusion Revisited.Eisuke Sakakibara - 2018 - Neuroethics 12 (2):171-182.
    Maher proposed in 1974 that schizophrenic delusions are hypotheses formed to explain anomalous experiences. He stated that they are “rational, given the intensity of the experiences that they are developed to explain.” Two-factor theorists of delusion criticized Maher’s theory because 1) it does not explain why some patients with anomalous experiences do not develop delusions, and 2) adopting and adhering to delusional hypotheses is irrational, considering the totality of experiences and patients’ other beliefs. In this paper, the notion of the (...)
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  • Inferentialism and Structuralism: A Tale of Two Theories.Ryan Mark Nefdt - 2018 - Logique Et Analyse 61 (244):489-512.
    This paper aims to unite two seemingly disparate themes in the philosophy of mathematics and language respectively, namely ante rem structuralism and inferentialism. My analysis begins with describing both frameworks in accordance with their genesis in the work of Hilbert. I then draw comparisons between these philosophical views in terms of their similar motivations and similar objections to the referential orthodoxy. I specifically home in on two points of comparison, namely the role of norms and the relation of ontological dependence (...)
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  • Enciclopédia de Termos Lógico-Filosóficos.João Miguel Biscaia Branquinho, Desidério Murcho & Nelson Gonçalves Gomes (eds.) - 2006 - São Paulo, SP, Brasil: Martins Fontes.
    Esta enciclopédia abrange, de uma forma introdutória mas desejavelmente rigorosa, uma diversidade de conceitos, temas, problemas, argumentos e teorias localizados numa área relativamente recente de estudos, os quais tem sido habitual qualificar como «estudos lógico-filosóficos». De uma forma apropriadamente genérica, e apesar de o território teórico abrangido ser extenso e de contornos por vezes difusos, podemos dizer que na área se investiga um conjunto de questões fundamentais acerca da natureza da linguagem, da mente, da cognição e do raciocínio humanos, bem (...)
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  • Is inferentialism circular?Jaroslav Peregrin - 2018 - Analysis 78 (3):450-454.
    Variations on the argument “Inferences are moves from meaningful statements to meaningful statements; hence the meanings cannot be inferential roles” are often used as knock-down argument against inferentialism. In this short paper I indicate that the argument is simply a non sequitur.
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  • Categorical harmony and path induction.Patrick Walsh - 2017 - Review of Symbolic Logic 10 (2):301-321.
    This paper responds to recent work in the philosophy of Homotopy Type Theory by James Ladyman and Stuart Presnell. They consider one of the rules for identity, path induction, and justify it along ‘pre-mathematical’ lines. I give an alternate justification based on the philosophical framework of inferentialism. Accordingly, I construct a notion of harmony that allows the inferentialist to say when a connective or concept is meaning-bearing and this conception unifies most of the prominent conceptions of harmony through category theory. (...)
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  • The Tripartite Role of Belief: Evidence, Truth, and Action.Kenny Easwaran - 2017 - Res Philosophica 94 (2):1-18.
    Belief and credence are often characterized in three different ways—they ought to govern our actions, they ought to be governed by our evidence, and they ought to aim at the truth. If one of these roles is to be central, we need to explain why the others should be features of the same mental state rather than separate ones. If multiple roles are equally central, then this may cause problems for some traditional arguments about what belief and credence must be (...)
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  • (1 other version)Speaking with Shadows: A Study of Neo‐Logicism.Fraser MacBride - 2003 - British Journal for the Philosophy of Science 54 (1):103-163.
    According to the species of neo‐logicism advanced by Hale and Wright, mathematical knowledge is essentially logical knowledge. Their view is found to be best understood as a set of related though independent theses: (1) neo‐fregeanism—a general conception of the relation between language and reality; (2) the method of abstraction—a particular method for introducing concepts into language; (3) the scope of logic—second‐order logic is logic. The criticisms of Boolos, Dummett, Field and Quine (amongst others) of these theses are explicated and assessed. (...)
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  • Dialogical Harmony: tonk, constructive type theory and rules for anonymous players.Juan Redmond & Shahid Rahman - unknown
    Recent literature on dialogical logic discusses the case of tonk and the notion harmony in the context of a rule-based theory of meaning. Now, since the publications of those papers, a dialogical version of constructive type theory has been developed. The aim of the present paper is to show that, from the dialogical point of view, the harmony of the CTT-rules is the consequence of a more fundamental level of meaning characterized by the independence of players. We hope that the (...)
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  • (1 other version)Against Harmony.Ian Rumfitt - 1995 - In B. Hale & Crispin Wright (eds.), Blackwell Companion to the Philosophy of Language. Blackwell.
    Many prominent writers on the philosophy of logic, including Michael Dummett, Dag Prawitz, Neil Tennant, have held that the introduction and elimination rules of a logical connective must be ‘in harmony ’ if the connective is to possess a sense. This Harmony Thesis has been used to justify the choice of logic: in particular, supposed violations of it by the classical rules for negation have been the basis for arguments for switching from classical to intuitionistic logic. The Thesis has also (...)
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  • (1 other version)What is wrong with classical negation?Nils Kürbis - 2015 - Grazer Philosophische Studien 92 (1):51-86.
    The focus of this paper are Dummett's meaning-theoretical arguments against classical logic based on consideration about the meaning of negation. Using Dummettian principles, I shall outline three such arguments, of increasing strength, and show that they are unsuccessful by giving responses to each argument on behalf of the classical logician. What is crucial is that in responding to these arguments a classicist need not challenge any of the basic assumptions of Dummett's outlook on the theory of meaning. In particular, I (...)
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  • Inferentialism without Verificationism: Reply to Prawitz.Julien Murzi - 2011 - In Emiliano Ippoliti, Carlo Cellucci & Emily Grosholz (eds.), Logic and Knowledge. Newcastle upon Tyne: Cambridge Scholar Publishing. pp. 285-90.
    I discuss Prawitz’s claim that a non-reliabilist answer to the question “What is a proof?” compels us to reject the standard Bolzano-Tarski account of validity, andto account for the meaning of a sentence in broadly verificationist terms. I sketch what I take to be a possible way of resisting Prawitz’s claim---one that concedes the anti-reliabilist assumption from which Prawitz’s argument proceeds.
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  • Necessarily Maybe. Quantifiers, Modality and Vagueness.Alessandro Torza - 2015 - In Quantifiers, Quantifiers, and Quantifiers. Themes in Logic, Metaphysics, and Language. (Synthese Library vol. 373). Springer. pp. 367-387.
    Languages involving modalities and languages involving vagueness have each been thoroughly studied. On the other hand, virtually nothing has been said about the interaction of modality and vagueness. This paper aims to start filling that gap. Section 1 is a discussion of various possible sources of vague modality. Section 2 puts forward a model theory for a quantified language with operators for modality and vagueness. The model theory is followed by a discussion of the resulting logic. In Section 3, the (...)
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  • Devious Stipulations.John Horden - 2017 - Oxford Studies in Metaphysics 10.
    Recent attempts to answer ontological questions through conceptual analysis have been controversial. Still, it seems reasonable to assume that if the existence of certain things analytically follows from sentences we already accept, then there is no further ontological commitment involved in affirming the existence of those things. More generally, it is plausible that whenever a sentence analytically entails another, the conjunction of those sentences requires nothing more of the world for its truth than the former sentence alone. In his ‘Analyticity (...)
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  • Basic Logical Knowledge.Bob Hale - 2002 - Royal Institute of Philosophy Supplement 51:279-304.
    At least some of us, at least some of the time—when not in the grip of radical sceptical doubt—are inclined to believe that we know, for example, that if we infer a conclusion from two true premises, one a conditional whose consequent is that conclusion and the other the antecedent of that conditional, then our conclusion must be true, or that we know similar things about other simple patterns of inference. If we do indeed have knowledge of this sort, it (...)
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  • Lógica deóntica y verdad.Hugo R. Zuleta - 2006 - Análisis Filosófico 26 (1):115-133.
    El objeto principal de este trabajo consiste en discutir una propuesta de C. Alchourrón y A. Martino para hacer frente al problema de la fundamentación de la lógica deóntica, planteado por el dilema de Jørgensen. La propuesta criticada se basa en la idea de que no existe obstáculo alguno en compatibilizar la idea de que las normas carecen de valor de verdad con la idea de que poseen una lógica, una vez que se renuncia al "prejuicio filosófico" de que es (...)
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  • Practical Knowledge: Outlines of a Theory of Traditions and Skills.J. C. Nyíri & Barry Smith (eds.) - 1988 - Croom Helm.
    A series of papers on different aspects of practical knowledge by Roderick Chisholm, Rudolf Haller, J. C. Nyiri, Eva Picardi, Joachim Schulte Roger Scruton, Barry Smith and Johan Wrede.
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  • A letter on the present state of affairs: Prior, indeterminism and relativity 40 years later.Thomas Müller & Niko Strobach - 2012 - Synthese 188 (3):469-485.
    The paper re-evaluates Prior's tenets about indeterminism and relativity from the point of view of the current state of the debate. We first discuss Prior's claims about indeterministic tense logic and about relativity separately and confront them with new technical developments. Then we combine the two topics in a discussion of indeterministic approaches to space-time logics. Finally we show why Prior would not have to "dig his heels in" when it comes to relativity: We point out a way of combining (...)
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  • ‘Boghossian’s Blind Reasoning’, Conditionalization, and Thick Concepts. A Functional Model.Olga Ramírez - 2012 - Ethics in Progress Quarterly 3 (1):31-52.
    Boghossian’s (2003) proposal to conditionalize concepts as a way to secure their legitimacy in disputable cases applies well, not just to pejoratives – on whose account Boghossian first proposed it – but also to thick ethical concepts. It actually has important advantages when dealing with some worries raised by the application of thick ethical terms, and the truth and facticity of corresponding statements. In this paper, I will try to show, however, that thick ethical concepts present a specific case, whose (...)
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  • Could Evolution Explain Our Reliability about Logic.Joshua Schechter - 2005 - In Tamar Szabó Gendler & John Hawthorne (eds.), Oxford Studies in Epistemology. Oxford University Press. pp. 214.
    We are reliable about logic in the sense that we by-and-large believe logical truths and disbelieve logical falsehoods. Given that logic is an objective subject matter, it is difficult to provide a satisfying explanation of our reliability. This generates a significant epistemological challenge, analogous to the well-known Benacerraf-Field problem for mathematical Platonism. One initially plausible way to answer the challenge is to appeal to evolution by natural selection. The central idea is that being able to correctly deductively reason conferred a (...)
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  • What is inferentialism?Jaroslav Peregrin - unknown
    Inferentialism is the conviction that to be meaningful in the distinctively human way, or to have a 'conceptual content', is to be governed by a certain kind of inferential rules. The term was coined by Robert Brandom as a label for his theory of language; however, it is also naturally applicable (and is growing increasingly common) within the philosophy of logic.
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  • Weakly Classical Theories of Identity.Joshua Schechter - 2011 - Review of Symbolic Logic 4 (4):607-644.
    There are well-known quasi-formal arguments that identity is a "strict" relation in at least the following three senses: (1) There is a single identity relation and a single distinctness relation; (2) There are no contingent cases of identity or distinctness; and (3) There are no vague or indeterminate cases of identity or distinctness. However, the situation is less clear cut than it at first may appear. There is a natural formal theory of identity that is very close to the standard (...)
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  • Are Turing Machines Platonists? Inferentialism and the Computational Theory of Mind.Jon Cogburn & Jason Megil - 2010 - Minds and Machines 20 (3):423-439.
    We first discuss Michael Dummett’s philosophy of mathematics and Robert Brandom’s philosophy of language to demonstrate that inferentialism entails the falsity of Church’s Thesis and, as a consequence, the Computational Theory of Mind. This amounts to an entirely novel critique of mechanism in the philosophy of mind, one we show to have tremendous advantages over the traditional Lucas-Penrose argument.
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  • Consciousness, type physicalism, and inference to the best explanation.Brian P. McLaughlin - 2010 - Philosophical Issues 20 (1):266-304.
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  • Cut as Consequence.Curtis Franks - 2010 - History and Philosophy of Logic 31 (4):349-379.
    The papers where Gerhard Gentzen introduced natural deduction and sequent calculi suggest that his conception of logic differs substantially from the now dominant views introduced by Hilbert, Gödel, Tarski, and others. Specifically, (1) the definitive features of natural deduction calculi allowed Gentzen to assert that his classical system nk is complete based purely on the sort of evidence that Hilbert called ?experimental?, and (2) the structure of the sequent calculi li and lk allowed Gentzen to conceptualize completeness as a question (...)
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  • Wittgenstein and the Logic of Inference.Jan Zwicky - 1982 - Dialogue 21 (4):671-692.
    TheTractatusfirst appeared in 1921, the same year that Post's “Introduction to a General Theory of Elementary Propositions” appeared in theAmerican Journal of Mathematics. As the latter is the first piece clearly to present and exploit the distinction between a deductive system and a truth-functional interpretation of such a system, we may conclude that Wittgenstein's views had been arrived at somewhat before a variety of logical concepts had received the clarification and refinement incipient on the now taken-for-granted distinction between proof and (...)
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