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  1. 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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  • Alexander of Aphrodisias and the Heterodox dictum de omni et de nullo.Luca Gili - 2015 - History and Philosophy of Logic 36 (2):114-128.
    Aristotle's explanation of what is said ‘of every’ and ‘of none’ has been interpreted either as involving individuals, or as regarding exclusively universal terms. I claim that Alexander of Aphrodisias endorsed this latter interpretation of the dictum de omni et de nullo. This interpretation affects our understanding of Alexander's syllogistic: as a matter of fact, Alexander maintained that the dictum de omni et de nullo is one of the core principles of syllogistic.
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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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  • 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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  • Ibn Taymiyya Against the Greek Logicians.Wael B. Hallaq (ed.) - 1993 - Oxford, England: Clarendon Press.
    The introduction of Greek philosophy into the Muslim world left an indelible mark on Islamic intellectual history. Philosophical discourse became a constant element in even traditionalist Islamic sciences. However, Aristotelian metaphysics gave rise to doctrines about God and the universe that were found highly objectionable by a number of Muslim theologians, among whom the fourteenth-century scholar Ibn Taymiyya stood foremost. Ibn Taymiyya, one of the greatest and most prolific thinkers in medieval Islam, held Greek logic responsible for the `heretical' metaphysical (...)
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  • Frege: Philosophy of Language.Michael Dummett - 1973 - London: Duckworth.
    This highly acclaimed book is a major contribution to the philosophy of language as well as a systematic interpretation of Frege, indisputably the father of ...
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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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  • 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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  • 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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  • (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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  • Intuitionistic Type Theory.Per Martin-Löf - 1980 - Bibliopolis.
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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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  • 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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  • The Dialectical Forge: Juridical Disputation and the Evolution of Islamic Law.Walter Edward Young - 2016 - Cham, Switzerland: Springer Verlag.
    The Dialectical Forge identifies dialectical disputation as a primary formative dynamic in the evolution of pre-modern Islamic legal systems, promoting dialectic from relative obscurity to a more appropriate position at the forefront of Islamic legal studies. The author introduces and develops a dialectics-based analytical method for the study of pre-modern Islamic legal argumentation, examines parallels and divergences between Aristotelian dialectic and early juridical jadal-theory, and proposes a multi-component paradigm—the Dialectical Forge Model—to account for the power of jadal in shaping Islamic (...)
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  • Making it Explicit.Isaac Levi & Robert B. Brandom - 1996 - Journal of Philosophy 93 (3):145.
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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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  • (2 other versions)Languages of Art.Nelson Goodman - 1970 - Philosophy and Rhetoric 3 (1):62-63.
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  • (1 other version)The Runabout Inference-Ticket.A. N. Prior - 1960 - Analysis 21 (2):38-39.
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  • (3 other versions)Tractatus logico-philosophicus.Ludwig Wittgenstein - 1922 - Filosoficky Casopis 52:336-341.
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  • Dialogischer Konstruktivismus.Kuno Lorenz (ed.) - 2008 - Walter de Gruyter.
    In these seven essays published from 1986 to 2008, philosophy is portrayed as an activity in which one gives an account of the experiences that one has and transmits through acting and speaking. A dialogical principle is an essential element of this account: in the I-role," one acts and speaks, while in the you-role," one passively experiences and understands. Only through learning from one another can the mutually dependent qualities of individuality and sociality gradually develop. ".
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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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  • Mathematics and the Mind: An Introduction Into Ibn Sīnā’s Theory of Knowledge.Hassan Tahiri - 2015 - Cham: Springer Verlag.
    Few philosophers that have been studied as much as Ibn Sīnā have been as much misunderstood. His extraordinary ability to reflect upon and write in a variety of styles about seemingly every topic in every domain has steered his thought from philosophy and theology to mysticism and esoterism. Instead of helping us to learn and understand better Ibn Sīnā than he has previously been understood, the recent surge of Avicennan studies only adds more confusion to the already complex social context (...)
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  • Legal Reasoning.Martin Philip Golding - 1983 - Alfred a Knopf.
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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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  • Dialogical logic.Laurent Keiff - 2010 - Stanford Encyclopedia of Philosophy.
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  • The dialogical approach to paraconsistency.Sahid Rahman & Walter A. Carnielli - 2000 - Synthese 125 (1-2):201-232.
    Being a pragmatic and not a referential approach tosemantics, the dialogical formulation ofparaconsistency allows the following semantic idea tobe expressed within a semi-formal system: In anargumentation it sometimes makes sense to distinguishbetween the contradiction of one of the argumentationpartners with himself (internal contradiction) and thecontradiction between the partners (externalcontradiction). The idea is that externalcontradiction may involve different semantic contextsin which, say A and ¬A have been asserted.The dialogical approach suggests a way of studying thedynamic process of contradictions through which thetwo (...)
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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)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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  • (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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  • Immanent Reasoning or Equality in Action: A Plaidoyer for the Play Level.Nicolas Clerbout, Ansten Klev, Zoe McConaughey & Shahid Rahman - 2018 - Cham, Switzerland: Springer Verlag.
    This monograph proposes a new way of implementing interaction in logic. It also provides an elementary introduction to Constructive Type Theory. The authors equally emphasize basic ideas and finer technical details. In addition, many worked out exercises and examples will help readers to better understand the concepts under discussion. One of the chief ideas animating this study is that the dialogical understanding of definitional equality and its execution provide both a simple and a direct way of implementing the CTT approach (...)
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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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  • Articulating Medieval Logic.Terence Parsons - 2014 - Oxford, England: Oxford University Press.
    Terence Parsons presents a new study of the development and continuing value of medieval logic, which expanded Aristotle's basic principles of logic in important ways. Parsons argues that the resulting system is as rich as contemporary first-order symbolic logic.
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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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  • Logic and games.Wilfrid Hodges - 2008 - Stanford Encyclopedia of Philosophy.
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  • The Rise of Colleges. Institutions of Learning in Islam and the West.Norman Daniel & George Makdisi - 1984 - Journal of the American Oriental Society 104 (3):586.
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  • Logic as Calculus and Logic as Language.Jean Van Heijenoort - 1967 - Synthese 17 (1):324-330.
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  • The Type Theoretic Interpretation of Constructive Set Theory.Peter Aczel, Angus Macintyre, Leszek Pacholski & Jeff Paris - 1984 - Journal of Symbolic Logic 49 (1):313-314.
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  • Islamic Disputation Theory: A Study of the Development of Dialectic in Islam From the Tenth Through Fourteenth Centuries.Larry Benjamin Miller - 1984 - Dissertation, Princeton University
    This is a study of dialectic and systematic disputation as described in the theoretical writings of Islamic theologians, jurists, and philosophers. An attempt is made to reconstruct the contents of the earliest systematic treatment of the subject by b. al-Riwandi. The theological understanding of dialectic is then contrasted with the teachings of the Arab Aristotelians--al-Farabi, Avicenna, and Averroes, on dialectic. It is then shown how jurists took over the theological method of dialectic and applied it to problems peculiar to jurisprudence. (...)
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  • A century of judgement and inference,1837-1936 : Some strands in the development of logic.Göran Sundholm - 2009 - In Leila Haaparanta (ed.), The development of modern logic. New York: Oxford University Press.
    This chapter tells how, within a century, the notions of judgment and inference were driven out of logical theory and replaced by propositions and consequence. Systematic considerations guide the treatment. The history is unashamedly Whiggish: the current position is shown as the outcome, or even culmination, of a historical development.
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  • Dialogical connexive logic.Shahid Rahman & Helge Rückert - 2001 - Synthese 127 (1-2):105-139.
    Many of the discussions about conditionals can best be put as follows:can those conditionals that involve an entailment relation be formulatedwithin a formal system? The reasons for the failure of the classical approachto entailment have usually been that they ignore the meaning connectionbetween antecedent and consequent in a valid entailment. One of the firsttheories in the history of logic about meaning connection resulted from thestoic discussions on tightening the relation between the If- and the Then-parts of conditionals, which in this (...)
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  • (1 other version)Formal systems of dialogue rules.Erick C. W. Krabbe - 1984 - Synthese 58 (2):295 - 328.
    Section 1 contains a survey of options in constructing a formal system of dialogue rules. The distinction between material and formal systems is discussed (section 1.1). It is stressed that the material systems are, in several senses, formal as well. In section 1.2 variants as to language form (choices of logical constants and logical rules) are pointed out. Section 1.3 is concerned with options as to initial positions and the permissibility of attacks on elementary statements. The problem of ending a (...)
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  • A natural extension of natural deduction.Peter Schroeder-Heister - 1984 - Journal of Symbolic Logic 49 (4):1284-1300.
    The framework of natural deduction is extended by permitting rules as assumptions which may be discharged in the course of a derivation. this leads to the concept of rules of higher levels and to a general schema for introduction and elimination rules for arbitrary n-ary sentential operators. with respect to this schema, (functional) completeness "or", "if..then" and absurdity is proved.
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  • (1 other version)Al Kindi and the universilisation of Knowledge through mathematics.Hassan Tahiri - 2014 - Revista de Humanidades de Valparaíso 4:81-90.
    The Arabic-Islamic tradition is founded on the following new epistemic attitude that reinvents knowledge: to learn from the contributions of previous civilisations through the systematic survey of all extant scientific works; to contribute to the further development of knowledge by linking it, through usefulness, to practice and the practical need of society; to facilitate its learning for younger generations and its transmission to future civilizations since it is conceived not as a finished product but as an ongoing process. The worldwide (...)
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  • Inconsistency-Adaptive Dialogical Logic.Mathieu Beirlaen & Matthieu Fontaine - 2016 - Logica Universalis 10 (1):99-134.
    Even when inconsistencies are present in our premise set, we can sensibly distinguish between good and bad arguments relying on these premises. In making this distinction, the inconsistency-adaptive approach of Batens strikes a particularly nice balance between inconsistency-tolerance and inferential strength. In this paper, we use the machinery of Batens’ approach to extend the paraconsistent approach to dialogical logic as developed by Rahman and Carnielli. In bringing these frameworks closer together, we obtain a dynamic mechanism for the systematic study of (...)
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  • Why Play Logical Games?Mathieu Marion - 2009 - In Ondrej Majer, Ahti-Veikko Pietarinen & Tero Tulenheimo (eds.), Games: Unifying Logic, Language, and Philosophy. Dordrecht, Netherland: Springer Verlag. pp. 3--26.
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  • First-order logic.Raymond Merrill Smullyan - 1968 - New York [etc.]: Springer Verlag.
    This completely self-contained study, widely considered the best book in the field, is intended to serve both as an introduction to quantification theory and as ...
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  • Having the world in view: essays on Kant, Hegel, and Sellars.John McDowell - 2009 - Cambridge: Harvard University Press.
    In this new book, John McDowell builds on his much discussed Mind and World—one of the most highly regarded books in contemporary philosophy.
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  • Propositions as games as types.Aarne Ranta - 1988 - Synthese 76 (3):377 - 395.
    Without violating the spirit of Game-Theoretical semantics, its results can be re-worked in Martin-Löf''s Constructive Type Theory by interpreting games as types of Myself''s winning strategies. The philosophical ideas behind Game-Theoretical Semantics in fact highly recommend restricting strategies to effective ones, which is the only controversial step in our interpretation. What is gained, then, is a direct connection between linguistic semantics and computer programming.
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