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  1. Judgement and the Epistemic Foundation of Logic.Maria van der Schaar (ed.) - 2012 - Dordrecht, Netherland: Springer.
    This compelling reevaluation of the relationship between logic and knowledge affirms the key role that the notion of judgement must play in such a review. The commentary repatriates the concept of judgement in the discussion, banished in recent times by the logical positivism of Wittgenstein, Hilbert and Schlick, and the Platonism of Bolzano. The volume commences with the insights of Swedish philosopher Per Martin-Löf, the father of constructive type theory, for whom logic is a demonstrative science in which judgement is (...)
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  • Maddy On The Multiverse.Claudio Ternullo - 2019 - In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Verlag. pp. 43-78.
    Penelope Maddy has recently addressed the set-theoretic multiverse, and expressed reservations on its status and merits ([Maddy, 2017]). The purpose of the paper is to examine her concerns, by using the interpretative framework of set-theoretic naturalism. I first distinguish three main forms of 'multiversism', and then I proceed to analyse Maddy's concerns. Among other things, I take into account salient aspects of multiverse-related mathematics , in particular, research programmes in set theory for which the use of the multiverse seems to (...)
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  • (1 other version)Dag Prawitz on Proofs and Meaning.Heinrich Wansing (ed.) - 2014 - Cham, Switzerland: Springer.
    This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an (...)
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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 Fundamental Problem of General Proof Theory.Dag Prawitz - 2019 - Studia Logica 107 (1):11-29.
    I see the question what it is that makes an inference valid and thereby gives a proof its epistemic power as the most fundamental problem of general proof theory. It has been surprisingly neglected in logic and philosophy of mathematics with two exceptions: Gentzen’s remarks about what justifies the rules of his system of natural deduction and proposals in the intuitionistic tradition about what a proof is. They are reviewed in the paper and I discuss to what extent they succeed (...)
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  • Dalla psicologia del giudizio all'ontologia dello stato di cose.Barry Smith - 1997 - Discipline Filosofiche 7 (2):7--28.
    Logic is often conceived as a science of propositions, or of relations between propositions. There is an alternative view, however, defended by Meinong, Pfänder, Reinach and others, which sees logic as a science of “Sachverhalte” or states of affairs. A consideration of this view, which was defended especially by thinkers within the tradition of Brentano, throws new light on the problems of intentionality and of mental content. It throws light also on the development of logic in Poland. Here the influence (...)
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  • Une théorie unifiée de la vérité et de la référence.Barry Smith & Berit Brogaard - 2004 - In Jean-Maurice Monnoyer (ed.), La Structure Du Monde. Vrin, Paris. pp. 141-184.
    The truthmaker theory rests on the thesis that the link between a true judgment and that in the world to which it corresponds is not a one-to-one but rather a one-to-many relation. An analogous thesis in relation to the link between a singular term and that in the world to which it refers is already widely accepted. This is the thesis to the effect that singular reference is marked by vagueness of a sort that is best understood in supervaluationist terms. (...)
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  • The cognitive act and the first-person perspective: an epistemology for constructive type theory.Maria van der Schaar - 2011 - Synthese 180 (3):391 - 417.
    The notion of cognitive act is of importance for an epistemology that is apt for constructive type theory, and for epistemology in general. Instead of taking knowledge attributions as the primary use of the verb 'to know' that needs to be given an account of, and understanding a first-person knowledge claim as a special case of knowledge attribution, the account of knowledge that is given here understands first-person knowledge claims as the primary use of the verb 'to know'. This means (...)
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  • Assertion and grounding: a theory of assertion for constructive type theory.Maria Schaar - 2011 - Synthese 183 (2):187-210.
    Taking Per Martin-Löf’s constructive type theory as a starting-point a theory of assertion is developed, which is able to account for the epistemic aspects of the speech act of assertion, and in which it is shown that assertion is not a wide genus. From a constructivist point of view, one is entitled to assert, for example, that a proposition A is true, only if one has constructed a proof object a for A in an act of demonstration. One thereby has (...)
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  • A unified theory of truth and reference.Barry Smith & Berit Brogaard - 2000 - Logique Et Analyse 43 (169-170):49–93.
    The truthmaker theory rests on the thesis that the link between a true judgment and that in the world to which it corresponds is not a one-to-one but rather a one-to-many relation. An analogous thesis in relation to the link between a singular term and that in the world to which it refers is already widely accepted. This is the thesis to the effect that singular reference is marked by vagueness of a sort that is best understood in supervaluationist terms. (...)
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  • Aspects of a logical theory of assertion and inference.Ansten Klev - 2024 - Theoria 90 (5):534-555.
    The aim here is to investigate assertion and inference as notions of logic. Assertion will be explained in terms of its purpose, which is to give interlocutors the right to request the assertor to do a certain task. The assertion is correct if, and only if, the assertor knows how to do this task. Inference will be explained as an assertion equipped with what I shall call a justification profile, a strategy for making good on the assertion. The inference is (...)
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  • Constructive Type Theory, an appetizer.Laura Crosilla - 2024 - In Peter Fritz & Nicholas K. Jones (eds.), Higher-Order Metaphysics. Oxford University Press.
    Recent debates in metaphysics have highlighted the significance of type theories, such as Simple Type Theory (STT), for our philosophical analysis. In this chapter, I present the salient features of a constructive type theory in the style of Martin-Löf, termed CTT. My principal aim is to convey the flavour of this rich, flexible and sophisticated theory and compare it with STT. I especially focus on the forms of quantification which are available in CTT. A further aim is to argue that (...)
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  • Identity in Martin‐Löf type theory.Ansten Klev - 2021 - Philosophy Compass 17 (2):e12805.
    The logic of identity contains riches not seen through the coarse lens of predicate logic. This is one of several lessons to draw from the subtle treatment of identity in Martin‐Löf type theory, to which the reader will be introduced in this article. After a brief general introduction we shall mainly be concerned with the distinction between identity propositions and identity judgements. These differ from each other both in logical form and in logical strength. Along the way, connections to philosophical (...)
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  • Wittgenstein et la preuve mathématique comme vérifacteur.Mathieu Marion - 2011 - Philosophiques 38 (1):137-156.
    Dans ce texte, je pars de l’analyse intuitionniste de la vérité mathématique, « A est vrai si et seulement s’il existe une preuve de A » comme cas particulier de l’analyse de la vérité en termes de « vérifacteur », et je montre pourquoi Wittgenstein partageait celle-ci avec les intuitionnistes. Cependant, la notion de preuve à l’oeuvre dans cette analyse est, selon l’intuitionnisme, celle de la « preuve-comme-objet », et je montre par la suite, en interprétant son argument sur le (...)
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  • Facts.Kevin Mulligan - 2008 - Stanford Encyclopedia of Philosophy.
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  • Anti-realist semantics.Wolfram Hinzen - 2000 - Erkenntnis 52 (3):281-311.
    I argue that the implementation of theDummettian program of an ``anti-realist'' semanticsrequires quite different conceptions of the technicalmeaning-theoretic terms used than those presupposed byDummett. Starting from obvious incoherences in anattempt to conceive truth conditions as assertibilityconditions, I argue that for anti-realist purposesnon-epistemic semantic notions are more usefully kept apart from epistemic ones rather than beingreduced to them. Embedding an anti-realist theory ofmeaning in Martin-Löf's Intuitionistic Type Theory(ITT) takes care, however, of many notorious problemsthat have arisen in trying to specify suitableintuitionistic (...)
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  • Mathematics and phenomenology: The correspondence between O. Becker and H. Weyl.Paolo Mancosu & T. A. Ryckman - 2002 - Philosophia Mathematica 10 (2):130-202.
    Recently discovered correspondence from Oskar Becker to Hermann Weyl sheds new light on Weyl's engagement with Husserlian transcendental phenomenology in 1918-1927. Here the last two of these letters, dated July and August, 1926, dealing with issues in the philosophy of mathematics are presented, together with background and a detailed commentary. The letters provide an instructive context for re-assessing the connection between intuitionism and phenomenology in Weyl's foundational thought, and for understanding Weyl's term ‘symbolic construction’ as marking his own considered position (...)
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  • Assertion and grounding: a theory of assertion for constructive type theory.Maria van der Schaar - 2011 - Synthese 183 (2):187-210.
    Taking Per Martin-Löf’s constructive type theory as a starting-point a theory of assertion is developed, which is able to account for the epistemic aspects of the speech act of assertion, and in which it is shown that assertion is not a wide genus. From a constructivist point of view, one is entitled to assert, for example, that a proposition A is true, only if one has constructed a proof object a for A in an act of demonstration. One thereby has (...)
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  • The Seeming Interdependence Between the Concepts of Valid Inference and Proof.Dag Prawitz - 2019 - Topoi 38 (3):493-503.
    We may try to explain proofs as chains of valid inference, but the concept of validity needed in such an explanation cannot be the traditional one. For an inference to be legitimate in a proof it must have sufficient epistemic power, so that the proof really justifies its final conclusion. However, the epistemic concepts used to account for this power are in their turn usually explained in terms of the concept of proof. To get out of this circle we may (...)
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  • Proofs as Acts and Proofs as Objects: Some questions for Dag Prawitz.Goran Sundholm - 1998 - Theoria 64 (2-3):187-216.
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  • Antirealism and the Roles of Truth.B. G. Sundholm - unknown
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  • A Recommendation for Correspondence Theory of Truth.K. S. Sangeetha - 2016 - Journal of the Indian Council of Philosophical Research 33 (3):465-480.
    The purpose of this paper is to show that the correspondence theory as a truth-maker theory has certain advantages over some of the other theories of truth. The cost of this advantage is postulating extra entities—facts. However, the benefits outweigh the costs; facts facilitate our understanding of the nature of truth made by the world. Facts are required for understanding this world; therefore, one cannot claim that a separate cost is incurred for explaining truth. It is further argued that because (...)
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  • A Century of Inference: 1837-1936.B. G. Sundholm - unknown
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  • History and Philosophy of Constructive Type Theory.Giovanni Sommaruga - 2000 - Dordrecht, Netherland: Springer.
    A comprehensive survey of Martin-Löf's constructive type theory, considerable parts of which have only been presented by Martin-Löf in lecture form or as part of conference talks. Sommaruga surveys the prehistory of type theory and its highly complex development through eight different stages from 1970 to 1995. He also provides a systematic presentation of the latest version of the theory, as offered by Martin-Löf at Leiden University in Fall 1993. This presentation gives a fuller and updated account of the system. (...)
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  • Implicit epistemic aspects of constructive logic.Göran Sundholm - 1997 - Journal of Logic, Language and Information 6 (2):191-212.
    In the present paper I wish to regard constructivelogic as a self-contained system for the treatment ofepistemological issues; the explanations of theconstructivist logical notions are cast in anepistemological mold already from the outset. Thediscussion offered here intends to make explicit thisimplicit epistemic character of constructivism.Particular attention will be given to the intendedinterpretation laid down by Heyting. This interpretation, especially as refined in the type-theoretical work of Per Martin-Löf, puts thesystem on par with the early efforts of Frege andWhitehead-Russell. This quite (...)
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  • Fazedores-de-verdade.Azambuja Rodrigues Filho - 2009 - Doispontos 6 (2).
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  • Necessity of Thought.Cesare Cozzo - 2014 - In Heinrich Wansing (ed.), Dag Prawitz on Proofs and Meaning. Cham, Switzerland: Springer. pp. 101-20.
    The concept of “necessity of thought” plays a central role in Dag Prawitz’s essay “Logical Consequence from a Constructivist Point of View” (Prawitz 2005). The theme is later developed in various articles devoted to the notion of valid inference (Prawitz, 2009, forthcoming a, forthcoming b). In section 1 I explain how the notion of necessity of thought emerges from Prawitz’s analysis of logical consequence. I try to expound Prawitz’s views concerning the necessity of thought in sections 2, 3 and 4. (...)
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