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  1. Intuitionistic Type Theory.Per Martin-Löf - 1980 - Bibliopolis.
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  • (1 other version)The formulae-as-types notion of construction.William Alvin Howard - 1980 - In Haskell Curry, Hindley B., Seldin J. Roger & P. Jonathan (eds.), To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus, and Formalism. Academic Press.
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  • The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History.Reviel Netz - 1999 - Cambridge and New York: Cambridge University Press.
    An examination of the emergence of the phenomenon of deductive argument in classical Greek mathematics.
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  • Sellars and the Space of Reasons [Sellars y el espacio de las razones].John McDowell - unknown
    In Empiricism and the Philosophy of Mind Sellars introduces the image of the space of reasons, and delineates a non-traditional empiricism, uncontaminated by the Myth of the Given. Brandom takes Sellars’s drift to be against empiricism as such, against the very idea that something deserving to be called “experience” could be relevant to the acquisition of empirical knowledge in any way except merely causally. In this paper I attack Brandom’s idea that we anyway need a concession to externalism for non-inferential (...)
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  • Dialectic, the Dictum de Omni and Ecthesis.Michel Crubellier, Mathieu Marion, Zoe Mcconaughey & Shahid Rahman - 2019 - History and Philosophy of Logic 40 (3):207-233.
    In this paper, we provide a detailed critical review of current approaches to ecthesis in Aristotle’s Prior Analytics, with a view to motivate a new approach, which builds upon previous work by Marion & Rückert (2016) on the dictum de omni. This approach sets Aristotle’s work within the context of dialectic and uses Lorenzen’s dialogical logic, hereby reframed with use of Martin-Löf's constructive type theory as ‘immanent reasoning’. We then provide rules of syllogistic for the latter, and provide proofs of (...)
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  • (1 other version)Other Minds.J. L. Austin - 2000 - In Sven Bernecker & Fred I. Dretske (eds.), Knowledge: readings in contemporary epistemology. New York: Oxford University Press.
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  • The Neglect of Epistemic Considerations in Logic: The Case of Epistemic Assumptions.Göran Sundholm - 2019 - Topoi 38 (3):551-559.
    The two different layers of logical theory—epistemological and ontological—are considered and explained. Special attention is given to epistemic assumptions of the kind that a judgement is granted as known, and their role in validating rules of inference, namely to aid the inferential preservation of epistemic matters from premise judgements to conclusion judgement, while ordinary Natural Deduction assumptions serve to establish the holding of consequence from antecedent propositions to succedent proposition.
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  • The Justification of Identity Elimination in Martin-Löf’s Type Theory.Ansten Klev - 2019 - Topoi 38 (3):577-590.
    On the basis of Martin-Löf’s meaning explanations for his type theory a detailed justification is offered of the rule of identity elimination. Brief discussions are thereafter offered of how the univalence axiom fares with respect to these meaning explanations and of some recent work on identity in type theory by Ladyman and Presnell.
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  • Foundations of Set Theory.Abraham Adolf Fraenkel & Yehoshua Bar-Hillel - 1973 - Atlantic Highlands, NJ, USA: Elsevier.
    Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there been such extensive, almost revolutionary, developments. This book tries to avoid a detailed discussion of those topics which would have required heavy technical machinery, while describing the major results obtained in their treatment if these results could be stated in relatively non-technical terms. This book comprises five chapters and begins with a discussion of (...)
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  • (1 other version)Logische Syntax der Sprache.R. Carnap - 1936 - Philosophy 11 (41):110-114.
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  • (3 other versions)Tractatus logico-philosophicus.Ludwig Wittgenstein - 1922 - Filosoficky Casopis 52:336-341.
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  • Ludic Proof: Greek Mathematics and the Alexandrian Aesthetic.Reviel Netz - 2009 - Cambridge University Press.
    This book represents a new departure in science studies: an analysis of a scientific style of writing, situating it within the context of the contemporary style of literature. Its philosophical significance is that it provides a novel way of making sense of the notion of a scientific style. For the first time, the Hellenistic mathematical corpus - one of the most substantial extant for the period - is placed centre-stage in the discussion of Hellenistic culture as a whole. Professor Netz (...)
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  • Type-theoretical Grammar.Aarne Ranta - 1994 - Oxford, England: Oxford University Press on Demand.
    It is the aim of INDICES to document recent explorations in the various fields of philosophical logic and formal linguistics and their applications in other disciplines. The main emphasis of this series is on self-contained monographs covering particular areas of recent research and surveys of methods, problems, and results in all fields of inquiry where recourse to logical analysis and logical methods has been fruitful. INDICES will contain monographs dealing with the central areas of philosophical logic (extensional and intensional systems, (...)
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  • On the meanings of the logical constants and the justifications of the logical laws.Per Martin-Löf - 1996 - Nordic Journal of Philosophical Logic 1 (1):11-60.
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  • Naturalizing Dialogic Pragmatics.Gerhard Heinzmann - 2006 - In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics: Assessing Philosophy of Logic and Mathematics Today. Dordrecht, Netherland: Springer. pp. 285--297.
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  • Aristotle's natural deduction system.John Corcoran - 1974 - In Ancient logic and its modern interpretations. Boston,: Reidel. pp. 85--131.
    This presentation of Aristotle's natural deduction system supplements earlier presentations and gives more historical evidence. Some fine-tunings resulted from conversations with Timothy Smiley, Charles Kahn, Josiah Gould, John Kearns,John Glanvillle, and William Parry.The criticism of Aristotle's theory of propositions found at the end of this 1974 presentation was retracted in Corcoran's 2009 HPL article "Aristotle's demonstrative logic".
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  • On the strength of dependent products in the type theory of Martin-Löf.Richard Garner - 2009 - Annals of Pure and Applied Logic 160 (1):1-12.
    One may formulate the dependent product types of Martin-Löf type theory either in terms of abstraction and application operators like those for the lambda-calculus; or in terms of introduction and elimination rules like those for the other constructors of type theory. It is known that the latter rules are at least as strong as the former: we show that they are in fact strictly stronger. We also show, in the presence of the identity types, that the elimination rule for dependent (...)
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  • La dialectique, entre logique et rhétorique.Laurent Keiff - 2010 - Revue de Métaphysique et de Morale 66 (2):149-178.
    Nous montrons dans cet article comment les approches dynamiques en logique contemporaine ont retrouvé, quoique sous d ’ autres attendus, une configuration théorique qu ’ on peut attribuer à Aristote au moment de la rédaction des Topiques. Dans cette configuration, la logique et la rhétorique – ou au moins la dialectique – se complètent dans le cadre conceptuel homogène offert par la dialectique, entendue comme une certaine forme relativement codifiée de débat critique. L ’ idée principale est qu ’ aujourd (...)
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  • (1 other version)Proofs of the Compactness Theorem.Alexander Paseau - 2010 - History and Philosophy of Logic 31 (1):73-98.
    In this study, several proofs of the compactness theorem for propositional logic with countably many atomic sentences are compared. Thereby some steps are taken towards a systematic philosophical study of the compactness theorem. In addition, some related data and morals for the theory of mathematical explanation are presented.
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  • Aristotle's Prior Analytics.Robin Smith - 1989 - Hackett Publishing Company.
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  • (5 other versions)Uber Sinn und Bedeutung.Gottlob Frege - 1892 - Zeitschrift für Philosophie Und Philosophische Kritik 100 (1):25-50.
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  • The collected papers of Gerhard Gentzen.Gerhard Gentzen - 1969 - Amsterdam,: North-Holland Pub. Co.. Edited by M. E. Szabo.
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  • Logic, language-games and information: Kantian themes in the philosophy of logic.Jaakko Hintikka - 1973 - Oxford,: Clarendon Press.
    I LOGIC IN PHILOSOPHY— PHILOSOPHY OF LOGIC i. On the relation of logic to philosophy I n this book, the consequences of certain logical insights for ...
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  • Truth and other enigmas.Michael Dummett - 1978 - Cambridge: Harvard University Press.
    A collection of all but two of the author's philosophical essays and lectures originally published or presented before August 1976.
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  • 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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  • Constructivism in Mathematics: An Introduction.A. S. Troelstra & Dirk Van Dalen - 1988 - Amsterdam: North Holland. Edited by D. van Dalen.
    The present volume is intended as an all-round introduction to constructivism. Here constructivism is to be understood in the wide sense, and covers in particular Brouwer's intuitionism, Bishop's constructivism and A.A. Markov's constructive recursive mathematics. The ending "-ism" has ideological overtones: "constructive mathematics is the (only) right mathematics"; we hasten, however, to declare that we do not subscribe to this ideology, and that we do not intend to present our material on such a basis.
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  • The axiom of choice.John L. Bell - 2008 - Stanford Encyclopedia of Philosophy.
    The principle of set theory known as the Axiom of Choice has been hailed as “probably the most interesting and, in spite of its late appearance, the most discussed axiom of mathematics, second only to Euclid's axiom of parallels which was introduced more than two thousand years ago” (Fraenkel, Bar-Hillel & Levy 1973, §II.4). The fulsomeness of this description might lead those unfamiliar with the axiom to expect it to be as startling as, say, the Principle of the Constancy of (...)
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  • (1 other version)Basic objectives of dialogue logic in historical perspective.Kuno Lorenz - 2001 - Synthese 127 (1-2):255 - 263.
    The extensive research in logic conducted by using concepts and methods of game theory as documented in this collection of papers, allows to see dialogue logic in a number of new perspectives. This situation may gain further clarity by looking back to the inception of dialogue logic in the late fifties and early sixties.
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  • Intuitionistic logic as epistemic logic.Jaakko Hintikka - 2001 - Synthese 127 (1-2):7 - 19.
    In the present day and age, it seems that every constructivist philosopher of mathematics and her brother wants to be known as an intuitionist. In this paper, It will be shown that such a self-identification is in most cases mistaken. For one thing, not any old (or new) constructivism is intuitionism because not any old relevant construction is carried out mentally in intuition, as Brouwer envisaged. (edited).
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  • Empiricism and the philosophy of mind.Wilfrid Sellars - 1956 - Minnesota Studies in the Philosophy of Science 1:253-329.
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  • Programming in Martin-Löf’s Type Theory: An Introduction.Bengt Nordström, Kent Petersson & Jan M. Smith - 1990 - Clarendon Press.
    In recent years, several formalisms for program construction have appeared. One such formalism is the type theory developed by Per Martin-L f. Well suited as a theory for program construction, it makes possible the expression of both specifications and programs within the same formalism. Furthermore, the proof rules can be used to derive a correct program from a specification as well as to verify that a given program has a certain property. This book contains a thorough introduction to type theory, (...)
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  • Neuer Beweis für die Möglichkeit einer Wohlordnung.Ernst Zermelo - 1907 - Mathematische Annalen 65 (1):107-128.
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  • Making it Explicit.Isaac Levi & Robert B. Brandom - 1996 - Journal of Philosophy 93 (3):145.
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  • Paraconsistent Logic: Consistency, Contradiction and Negation.Walter Carnielli & Marcelo Esteban Coniglio - 2016 - Basel, Switzerland: Springer International Publishing. Edited by Marcelo Esteban Coniglio.
    This book is the first in the field of paraconsistency to offer a comprehensive overview of the subject, including connections to other logics and applications in information processing, linguistics, reasoning and argumentation, and philosophy of science. It is recommended reading for anyone interested in the question of reasoning and argumentation in the presence of contradictions, in semantics, in the paradoxes of set theory and in the puzzling properties of negation in logic programming. Paraconsistent logic comprises a major logical theory and (...)
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  • (1 other version)The Runabout Inference-Ticket.A. N. Prior - 1960 - Analysis 21 (2):38-39.
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  • (1 other version)An Intuitionistic Theory of Types: Predicative Part.Per Martin-Löf - 1975 - In ¸ Iterose1975. North Holland.
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  • Ibn sīnā’s approach to equality and unity.Shahid Rahman, Johan Georg Granström & Zaynab Salloum - 2014 - Arabic Sciences and Philosophy 24 (2):297-307.
    RésuméAristote n'a pas développé une théorie de la quantification du prédicat, mais une étude récente de Hasnawi a montré qu'Ibn Sīnā a consacré à celle-ci une étude rigoureuse. Assumant la structure aristotélicienne sujet-prédicat, Ibn Sīnā qualifie les propositions qui comportent un prédicat quantifié, de propositions déviantes. Une conséquence de cette approche avicennienne est que la seconde quantification est absorbée par le prédicat. La distinction claire ainsi opérée entre un sujet quantifié, qui pose le domaine de la quantification, et une partie (...)
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  • On Hypothetical Judgements and Leibniz’s Notion of Conditional Right.Shahid Rahman - 2015 - In Matthias Armgardt, Patrice Canivez & Sandrine Chassagnard-Pinet (eds.), Past and Present Interactions in Legal Reasoning and Logic. Cham, Switzerland: Springer.
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  • Über Grenzzahlen und Mengenbereiche: Neue Untersuchungen über die Grundlagen der Mengenlehre.Ernst Zermelo - 1930 - Fundamenta Mathematicæ 16:29--47.
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  • Ein formales Modell der Syllogistik des Aristotles.Kurt Ebbinghaus & Aristotle - 1964 - Vandenhoeck & Reprecht.
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  • Dialogical logic.Laurent Keiff - 2010 - Stanford Encyclopedia of Philosophy.
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  • Outlines of a formalist philosophy of mathematics.Haskell Brooks Curry - 1951 - Amsterdam,: North-Holland Pub. Co..
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  • Realizability and intuitionistic logic.J. Diller & A. S. Troelstra - 1984 - Synthese 60 (2):253 - 282.
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  • (1 other version)Einführung in die operative Logik und Mathematik.Paul Lorenzen - 1955 - Berlin,: Springer.
    in die operative Logik und Mathematik Zweite Auflage Springer-Verlag Berlin Heidelberg New York 1969 Paul Lorenzen o. Prof. der Philosophie an der Universitat Erlangen Geschaftsfilhrende Herausgeber: Prof. Dr. B. Eckmann Eidgenossische Technische Hochschule Zurich Prof. Dr. B. L. van cler Waerclen Mathematisches Institut der Universitat ZUrich ISBN 978-3-642-86519-0 ISBN 978-3-642-86518-3 (eBook) DOl 10.1007/978-3-642-86518-3 Aile Rechte vorbehalten. Kein Teil dieses Buches darf ohne schriftliche Genehmigung des Springer-Verlages ubersetzt oder in irgendeiner Form vervielfaltigt werden © by Springer-Verlag Berlin· Heidelberg 1955 und 1969 (...)
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  • (1 other version)An Intuitionistic Theory of Types: Predicative Part.Per Martin-Löf - 1975 - In H. E. Rose & J. C. Shepherdson (eds.), Logic Colloquium ’73 Proceedings of the Logic Colloquium. Elsevier. pp. 73--118.
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  • Plato On Truth And Falsity In Names.J. V. Luce - 1969 - Classical Quarterly 19 (2):222-232.
    In Cratylus 385 b-c Plato argues that if statements () can be true or false, names (),2 as parts () of statements, are also capable of being true or false. From Aristotle onwards this view has often been challenged,3 and R. Robinson put the case against it trenchantly when he wrote:4This argument is bad; for names have no truth-value, and the reason given for saying that they do is a fallacy of division. No one in the dialogue points out that (...)
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  • Models for Modalities.Jaakko Hintikka - 1971 - Studia Logica 28:161-163.
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  • Ludwig Wittgenstein: Half-Truths and One-and-a-Half-Truths.Jaakko Hintikka - 1996 - Springer.
    IF WITI'GENSTEIN COULD TALK, COULD WE UNDERSTAND HIM? Perusing the secondary literature on Wittgenstein, I have frequently experienced a perfect Brechtean Entfremdungseffekt. This is interesting, I have felt like saying when reading books and papers on Wittgenstein, but who is the writer talking about? Certainly not Ludwig Wittgenstein the actual person who wrote his books and notebooks and whom I happened to meet. Why is there this strange gap between the ideas of the actual philosopher and the musings of his (...)
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  • Frege.Michael Dummett - 1975 - Teorema: International Journal of Philosophy 5 (2):149-188.
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  • Treatise on intuitionistic type theory.Johan Georg Granström - 2011 - New York: Springer.
    Prolegomena It is fitting to begin this book on intuitionistic type theory by putting the subject matter into perspective. The purpose of this chapter is to ...
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