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  1. (4 other versions)Philosophical investigations.Ludwig Wittgenstein & G. E. M. Anscombe - 1953 - Revue Philosophique de la France Et de l'Etranger 161:124-124.
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  • Epistemic Angst: Radical Skepticism and the Groundlessness of Our Believing.Duncan Pritchard - 2015 - Princeton: Princeton University Press.
    Epistemic Angst offers a completely new solution to the ancient philosophical problem of radical skepticism—the challenge of explaining how it is possible to have knowledge of a world external to us. Duncan Pritchard argues that the key to resolving this puzzle is to realize that it is composed of two logically distinct problems, each requiring its own solution. He then puts forward solutions to both problems. To that end, he offers a new reading of Wittgenstein's account of the structure of (...)
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  • Warrant for nothing (and foundations for free)?Crispin Wright - 2004 - Aristotelian Society Supplementary Volume 78 (1):167–212.
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  • On Certainty.Ludwig Wittgenstein, G. E. M. Anscombe, G. H. Von Wright & Denis Paul - 1972 - Mind 81 (323):453-457.
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  • What is Deep Disagreement?Chris Ranalli - 2018 - Topoi 40 (5):983-998.
    What is the nature of deep disagreement? In this paper, I consider two similar albeit seemingly rival answers to this question: the Wittgensteinian theory, according to which deep disagreements are disagreements over hinge propositions, and the fundamental epistemic principle theory, according to which deep disagreements are disagreements over fundamental epistemic principles. I assess these theories against a set of desiderata for a satisfactory theory of deep disagreement, and argue that while the fundamental epistemic principle theory does better than the Wittgensteinian (...)
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  • (1 other version)Deep disagreement and hinge epistemology.Chris Ranalli - 2020 - Synthese 197 (11):4975-5007.
    This paper explores the application of hinge epistemology to deep disagreement. Hinge epistemology holds that there is a class of commitments—hinge commitments—which play a fundamental role in the structure of belief and rational evaluation: they are the most basic general ‘presuppositions’ of our world views which make it possible for us to evaluate certain beliefs or doubts as rational. Deep disagreements seem to crucially involve disagreements over such fundamental commitments. In this paper, I consider pessimism about deep disagreement, the thesis (...)
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  • (1 other version)Deep disagreement and hinge epistemology.Chris Ranalli - 2018 - Synthese:1-33.
    This paper explores the application of hinge epistemology to deep disagreement. Hinge epistemology holds that there is a class of commitments—hinge commitments—which play a fundamental role in the structure of belief and rational evaluation: they are the most basic general ‘presuppositions’ of our world views which make it possible for us to evaluate certain beliefs or doubts as rational. Deep disagreements seem to crucially involve disagreements over such fundamental commitments. In this paper, I consider pessimism about deep disagreement, the thesis (...)
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  • Deep Disagreement, Hinge Commitments, and Intellectual Humility.Drew Johnson - 2022 - Episteme 19 (3):353-372.
    Why is it that some instances of disagreement appear to be so intractable? And what is the appropriate way to handle such disagreements, especially concerning matters about which there are important practical and political needs for us to come to a consensus? In this paper, I consider an explanation of the apparent intractability of deep disagreement offered by hinge epistemology. According to this explanation, at least some deep disagreements are rationally unresolvable because they concern ‘hinge’ commitments that are unresponsive to (...)
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  • Disagreement, Certainties, Relativism.Martin Kusch - 2018 - Topoi 40 (5):1097-1105.
    This paper seeks to widen the dialogue between the “epistemology of peer disagreement” and the epistemology informed by Wittgenstein’s last notebooks, later edited as On Certainty. The paper defends the following theses: not all certainties are groundless; many of them are beliefs; and they do not have a common essence. An epistemic peer need not share all of my certainties. Which response to a disagreement over a certainty is called for, depends on the type of certainty in question. Sometimes a (...)
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  • Purifying applied mathematics and applying pure mathematics: how a late Wittgensteinian perspective sheds light onto the dichotomy.José Antonio Pérez-Escobar & Deniz Sarikaya - 2021 - European Journal for Philosophy of Science 12 (1):1-22.
    In this work we argue that there is no strong demarcation between pure and applied mathematics. We show this first by stressing non-deductive components within pure mathematics, like axiomatization and theory-building in general. We also stress the “purer” components of applied mathematics, like the theory of the models that are concerned with practical purposes. We further show that some mathematical theories can be viewed through either a pure or applied lens. These different lenses are tied to different communities, which endorse (...)
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  • Conceptual engineering for mathematical concepts.Fenner Stanley Tanswell - 2018 - Inquiry: An Interdisciplinary Journal of Philosophy 61 (8):881-913.
    ABSTRACTIn this paper I investigate how conceptual engineering applies to mathematical concepts in particular. I begin with a discussion of Waismann’s notion of open texture, and compare it to Shapiro’s modern usage of the term. Next I set out the position taken by Lakatos which sees mathematical concepts as dynamic and open to improvement and development, arguing that Waismann’s open texture applies to mathematical concepts too. With the perspective of mathematics as open-textured, I make the case that this allows us (...)
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  • Showing Mathematical Flies the Way Out of Foundational Bottles: The Later Wittgenstein as a Forerunner of Lakatos and the Philosophy of Mathematical Practice.José Antonio Pérez-Escobar - 2022 - Kriterion – Journal of Philosophy 36 (2):157-178.
    This work explores the later Wittgenstein’s philosophy of mathematics in relation to Lakatos’ philosophy of mathematics and the philosophy of mathematical practice. I argue that, while the philosophy of mathematical practice typically identifies Lakatos as its earliest of predecessors, the later Wittgenstein already developed key ideas for this community a few decades before. However, for a variety of reasons, most of this work on philosophy of mathematics has gone relatively unnoticed. Some of these ideas and their significance as precursors for (...)
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  • The fundamental model of deep disagreements.Victoria Lavorerio - 2021 - Metaphilosophy 52 (3-4):416-431.
    We call systematic disputes that are particularly hard to resolve deep disagreements. We can divide most theories of deep disagreements in analytic epistemology into two camps: the Wittgensteinian view and the fundamental epistemic principles view. This essay analyzes how both views deal with two of the most pressing issues a theory of deep disagreement must address: their source and their resolution. After concluding that the paradigmatic theory of each camp struggles on both fronts, the essay proceeds to show that, despite (...)
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  • Wittgenstein on Mathematics and Certainties.Martin Kusch - 2016 - International Journal for the Study of Skepticism 6 (2-3):120-142.
    _ Source: _Volume 6, Issue 2-3, pp 120 - 142 This paper aims to contribute to the debate over epistemic versus non-epistemic readings of the ‘hinges’ in Wittgenstein’s _On Certainty_. I follow Marie McGinn’s and Daniele Moyal-Sharrock’s lead in developing an analogy between mathematical sentences and certainties, and using the former as a model for the latter. However, I disagree with McGinn’s and Moyal-Sharrock’s interpretations concerning Wittgenstein’s views of both relata. I argue that mathematical sentences as well as certainties are (...)
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  • Which Hinge Epistemology?Annalisa Coliva - 2016 - International Journal for the Study of Skepticism 6 (2-3):79-96.
    _ Source: _Volume 6, Issue 2-3, pp 79 - 96 The paper explores the idea of a “hinge epistemology,” considered as a theory about justification which gives center-stage to Wittgenstein’s notion of _hinges_. First, some basic methodological considerations regarding the relationship between merely exegetical work on Wittgenstein’s texts and more theoretically committed work are put forward. Then, the main problems raised in _On Certainty_ and the most influential interpretative lines it has given rise to so far are presented and discussed. (...)
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  • (3 other versions)Proofs and Refutations: The Logic of Mathematical Discovery.Imre Lakatos, John Worrall & Elie Zahar - 1977 - Philosophy 52 (201):365-366.
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  • Sense and Certainty.Marie Mcginn - 1989 - Mind 98 (392):635-637.
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  • Mathematizing as a virtuous practice: different narratives and their consequences for mathematics education and society.Deborah Kant & Deniz Sarikaya - 2020 - Synthese 199 (1-2):3405-3429.
    There are different narratives on mathematics as part of our world, some of which are more appropriate than others. Such narratives might be of the form ‘Mathematics is useful’, ‘Mathematics is beautiful’, or ‘Mathematicians aim at theorem-credit’. These narratives play a crucial role in mathematics education and in society as they are influencing people’s willingness to engage with the subject or the way they interpret mathematical results in relation to real-world questions; the latter yielding important normative considerations. Our strategy is (...)
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  • Open texture, rigor, and proof.Benjamin Zayton - 2022 - Synthese 200 (4):1-20.
    Open texture is a kind of semantic indeterminacy first systematically studied by Waismann. In this paper, extant definitions of open texture will be compared and contrasted, with a view towards the consequences of open-textured concepts in mathematics. It has been suggested that these would threaten the traditional virtues of proof, primarily the certainty bestowed by proof-possession, and this suggestion will be critically investigated using recent work on informal proof. It will be argued that informal proofs have virtues that mitigate the (...)
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  • Three Roles of Empirical Information in Philosophy: Intuitions on Mathematics do Not Come for Free.Deniz Sarikaya, José Antonio Pérez-Escobar & Deborah Kant - 2021 - Kriterion – Journal of Philosophy 35 (3):247-278.
    This work gives a new argument for ‘Empirical Philosophy of Mathematical Practice’. It analyses different modalities on how empirical information can influence philosophical endeavours. We evoke the classical dichotomy between “armchair” philosophy and empirical/experimental philosophy, and claim that the latter should in turn be subdivided in three distinct styles: Apostate speculator, Informed analyst, and Freeway explorer. This is a shift of focus from the source of the information towards its use by philosophers. We present several examples from philosophy of mind/science (...)
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  • Mathematical consensus: a research program.Roy Wagner - 2022 - Axiomathes 32 (3):1185-1204.
    One of the distinguishing features of mathematics is the exceptional level of consensus among mathematicians. However, an analysis of what mathematicians agree on, how they achieve this agreement, and the relevant historical conditions is lacking. This paper is a programmatic intervention providing a preliminary analysis and outlining a research program in this direction.First, I review the process of ‘negotiation’ that yields agreement about the validity of proofs. This process most often does generate consensus, however, it may give rise to another (...)
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  • Not a difference of opinion: Wittgenstein and Turing on contradictions in mathematics.Wim Vanrie - 2024 - Philosophical Investigations 47 (4):584-602.
    In his 1939 Cambridge Lectures on the Foundations of Mathematics, Wittgenstein proclaims that he is not out to persuade anyone to change their opinions. I seek to further our understanding of this point by investigating an exchange between Wittgenstein and Turing on contradictions. In defending the claim that contradictory calculi are mathematically defective, Turing suggests that applying such a calculus would lead to disasters such as bridges falling down. In the ensuing discussion, it can seem as if Wittgenstein challenges Turing's (...)
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  • Contradictions and falling bridges: what was Wittgenstein’s reply to Turing?Ásgeir Berg Matthíasson - 2020 - British Journal for the History of Philosophy 29 (3).
    In this paper, I offer a close reading of Wittgenstein's remarks on inconsistency, mostly as they appear in the Lectures on the Foundations of Mathematics. I focus especially on an objection to Wittgenstein's view given by Alan Turing, who attended the lectures, the so-called ‘falling bridges’-objection. Wittgenstein's position is that if contradictions arise in some practice of language, they are not necessarily fatal to that practice nor necessitate a revision of that practice. If we then assume that we have adopted (...)
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  • Are There Mathematical Hinges?Annalisa Coliva - 2020 - International Journal for the Study of Skepticism 10 (3-4):346-366.
    In this paper I argue that, contrary to what several prominent scholars of On Certainty have claimed, Wittgenstein did not maintain that simple mathematical propositions like “2 × 2 = 4” or “12 × 12 = 144,” much like G. E. Moore’s truisms, could be examples of hinge propositions. In particular, given his overall conception of mathematics, it was impossible for him to single out these simpler mathematical propositions from the rest of mathematical statements, to reserve only to them a (...)
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  • Empirical regularities in Wittgenstein's philosophy of mathematics.Mark Steiner - 2009 - Philosophia Mathematica 17 (1):1-34.
    During the course of about ten years, Wittgenstein revised some of his most basic views in philosophy of mathematics, for example that a mathematical theorem can have only one proof. This essay argues that these changes are rooted in his growing belief that mathematical theorems are ‘internally’ connected to their canonical applications, i.e. , that mathematical theorems are ‘hardened’ empirical regularities, upon which the former are supervenient. The central role Wittgenstein increasingly assigns to empirical regularities had profound implications for all (...)
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  • On Certainty, Change, and “Mathematical Hinges”.James V. Martin - 2022 - Topoi 41 (5):987-1002.
    Annalisa Coliva (Int J Study Skept 10(3–4):346–366, 2020) asks, “Are there mathematical hinges?” I argue here, against Coliva’s own conclusion, that there are. I further claim that this affirmative answer allows a case to be made for taking the concept of a hinge to be a useful and general-purpose tool for studying mathematical practice in its real complexity. Seeing how Wittgenstein can, and why he would, countenance mathematical hinges additionally gives us a deeper understanding of some of his latest thoughts (...)
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  • On the Contemporary Practice of Philosophy of Mathematics.Colin Jakob Rittberg - 2019 - Acta Baltica Historiae Et Philosophiae Scientiarum 7 (1):5-26.
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  • Wittgenstein on Mathematical Meaningfulness, Decidability, and Application.Victor Rodych - 1997 - Notre Dame Journal of Formal Logic 38 (2):195-224.
    From 1929 through 1944, Wittgenstein endeavors to clarify mathematical meaningfulness by showing how (algorithmically decidable) mathematical propositions, which lack contingent "sense," have mathematical sense in contrast to all infinitistic "mathematical" expressions. In the middle period (1929-34), Wittgenstein adopts strong formalism and argues that mathematical calculi are formal inventions in which meaningfulness and "truth" are entirely intrasystemic and epistemological affairs. In his later period (1937-44), Wittgenstein resolves the conflict between his intermediate strong formalism and his criticism of set theory by requiring (...)
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  • Lakatos’ Quasi-Empiricism Revisited.Wei Zeng - 2022 - Kriterion – Journal of Philosophy 36 (2):227-246.
    The central idea of Lakatos’ quasi-empiricism view of the philosophy of mathematics is that truth values are transmitted bottom-up, but only falsity can be transmitted from basic statements. As it is falsity but not truth that flows bottom-up, Lakatos emphasizes that observation and induction play no role in both conjecturing and proving phases in mathematics. In this paper, I argue that Lakatos’ view that one cannot obtain primitive conjectures by induction contradicts the history of mathematics, and therefore undermines his quasi-empiricism (...)
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  • Wittgenstein and the unity of good.Oskari Kuusela - 2020 - European Journal of Philosophy 28 (2):428-444.
    This paper discusses the problem of the unity of moral good, concerning the kind of unity that moral good or the concept thereof constitutes. In particular, I am concerned with how Wittgenstein’s identification of various complex modes of conceptual unity, and his introduction of a methodology of clarification for dealing with such complex concepts, can help with the problem of unity, as it rises from the moral philosophical tradition. Relating to this I also address the disputed question, whether Wittgenstein regards (...)
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  • Wynn’s Experiments and the Later Wittgenstein’s Philosophy of Mathematics.Sorin Bangu - 2012 - Iyyun 61:219-240.
    This paper explores the connections between K. Wynn's well-known experiments in cognitive psychology and later Wittgenstein's views on the philosophy of mathematics.
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