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Remarks on the foundations of mathematics

Oxford,: Blackwell. Edited by G. E. M. Anscombe, Rush Rhees & G. H. von Wright (1956)

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  1. On a semantic interpretation of Kant's concept of number.Wing-Chun Wong - 1999 - Synthese 121 (3):357-383.
    What is central to the progression of a sequence is the idea of succession, which is fundamentally a temporal notion. In Kant's ontology numbers are not objects but rules (schemata) for representing the magnitude of a quantum. The magnitude of a discrete quantum 11...11 is determined by a counting procedure, an operation which can be understood as a mapping from the ordinals to the cardinals. All empirical models for numbers isomorphic to 11...11 must conform to the transcendental determination of time-order. (...)
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  • Wittgenstein and spengler vis-à-vis Frazer.Aydan Turanli - 2005 - Philosophy and Social Criticism 31 (1):69-88.
    Perspicuous representation, Wittgenstein offers, is not another methodology, but it consists in seeing the connections. The Wittgensteinian perspicuous representation is therapeutic. The method he suggests for philosophy is the same method he suggests for social sciences. In both of these cases, he tries to get us to see the confusions we become entangled in when philosophizing and theorizing. In both of these disciplines he warns us not to advance explanatory, metaphysical theories. In this paper, I connect this concern with Wittgenstein’s (...)
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  • Book Review: On Interpretive Social Inquiry. [REVIEW]Theodore Schatzki - 2005 - Philosophy of the Social Sciences 35 (2):231-249.
    This essay addresses various issues about interpretive social investigation that arise in recent books by Berel Lerner and by Mark Risjord. The general topics considered are the relation between interpretation and explanation, the explanation of action, and alternative rationalities. Part 1 centers on Risjord’s attempt to draw interpretation into the explanatory enterprise, among other things pointing out the limiting assumptions of his account and asking whether social investigation has epistemologically significant practical ends. Part 2 addresses the roles of normativity and (...)
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  • On the Coherence of Wittgensteinian Constructivism.Amit Saad - 2016 - Acta Analytica 31 (4):455-462.
    Michael Dummett presents a modus tollens argument against a Wittgensteinian conception of meaning. In a series of papers, Dummett claims that Wittgensteinian considerations entail strict finitism. However, by a “sorites argument”, Dummett argues that strict finitism is incoherent and therefore questions these Wittgensteinian considerations.In this paper, I will argue that Dummett’s sorites argument fails to undermine strict finitism. I will claim that the argument is based on two questionable assumptions regarding some strict finitist sets of natural numbers. It will be (...)
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  • Wittgenstein's inversion of gödel's theorem.Victor Rodych - 1999 - Erkenntnis 51 (2-3):173-206.
  • The implications of an externalist theory of rule-following behavior for robot cognition.Diane Proudfoot - 2004 - Minds and Machines 14 (3):283-308.
    Given (1) Wittgensteins externalist analysis of the distinction between following a rule and behaving in accordance with a rule, (2) prima facie connections between rule-following and psychological capacities, and (3) pragmatic issues about training, it follows that most, even all, future artificially intelligent computers and robots will not use language, possess concepts, or reason. This argument suggests that AIs traditional aim of building machines with minds, exemplified in current work on cognitive robotics, is in need of substantial revision.
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  • Putnam, Peano, and the Malin Génie: could we possibly bewrong about elementary number-theory?Christopher Norris - 2002 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 33 (2):289-321.
    This article examines Hilary Putnam's work in the philosophy of mathematics and - more specifically - his arguments against mathematical realism or objectivism. These include a wide range of considerations, from Gödel's incompleteness-theorem and the limits of axiomatic set-theory as formalised in the Löwenheim-Skolem proof to Wittgenstein's sceptical thoughts about rule-following, Michael Dummett's anti-realist philosophy of mathematics, and certain problems – as Putnam sees them – with the conceptual foundations of Peano arithmetic. He also adopts a thought-experimental approach – a (...)
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  • Mathematical Alchemy.Penelope Maddy - 1986 - British Journal for the Philosophy of Science 37 (3):279-314.
  • Necessity, the a priori, and the standard meter.Eric Loomis - 1999 - Synthese 121 (3):291-307.
    This article critically examines Saul Kripke's (1972) argument for the separability of necessary truths from truths known a priori, focusing on his criticism of the standard meter case presented by Wittgenstein (1968). It attempts to show that Kripke's argument is unworkable on any of several readings. Wittgenstein's own broadly conventionalist account of necessary truth is then considered in the light of the standard meter example.
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  • Ludwig Wittgenstein’s Tractatus Logico-Philosophicus. [REVIEW]Daniel D. Hutto - 2016 - Topoi 35 (2):617-626.
    Readers beware! This book is other than it first seems. Ludwig Wittgenstein’s latest philosophical offering is unlike anything that we have had from him to date. Its preface warns that the Tractatus is no textbook. This is an extreme understatement; really it is a deep puzzle—one that must be handled with great care. As the first lines signal there has been a radical change in the author’s characteristic style. Gone are the ingenious, probing explorations of topics undertaken in his highly (...)
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  • Nietzsche on freedom.Robert Guay - 2002 - European Journal of Philosophy 10 (3):302–327.
    One of the very few matters of nearly universal agreement with respect to Nietzsche interpretation, one that bridges the great analytic/continental divide, is that Nietzsche was offering some sort of account of freedom, in contradistinction to the ‘ascetic’ or ‘slavish’ ways of the past. What remains in dispute is the character of this account. In this paper I present Nietzsche’s account of freedom and his arguments for the superior cogency of that account relative to other accounts of freedom, including irony (...)
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  • What Turing did after he invented the universal Turing machine.Diane Proudfoot & Jack Copeland - 2000 - Journal of Logic, Language and Information 9:491-509.
    Alan Turing anticipated many areas of current research incomputer and cognitive science. This article outlines his contributionsto Artificial Intelligence, connectionism, hypercomputation, andArtificial Life, and also describes Turing's pioneering role in thedevelopment of electronic stored-program digital computers. It locatesthe origins of Artificial Intelligence in postwar Britain. It examinesthe intellectual connections between the work of Turing and ofWittgenstein in respect of their views on cognition, on machineintelligence, and on the relation between provability and truth. Wecriticise widespread and influential misunderstandings of theChurch–Turing thesis (...)
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  • ‘Grasping the Difficulty in its Depth’: Wittgenstein and Globally Engaged Philosophy.Thomas D. Carroll - 2021 - Sophia 60 (1):1-18.
    In recent years, philosophers have used expressions of Wittgenstein’s (e.g. “language-games,” “form of life,” and “family resemblance”) in attempts to conceive of the discipline of philosophy in a broad, open, and perhaps global way. These Wittgenstein-inspired approaches indicate an awareness of the importance of cultural and historical diversity for approaching philosophical questions. While some philosophers have taken inspiration from Wittgenstein in embracing contextualism in philosophical hermeneutics, Wittgenstein himself was more instrumental than contextual in his treatment of other philosophers; his focus (...)
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  • Concept nativism and the rule following considerations.M. J. Cain - 2006 - Acta Analytica 21 (38):77-101.
    In this paper I argue that the most prominent and familiar features of Wittgenstein’s rule following considerations generate a powerful argument for the thesis that most of our concepts are innate, an argument that echoes a Chomskyan poverty of the stimulus argument. This argument has a significance over and above what it tells us about Wittgenstein’s implicit commitments. For, it puts considerable pressure on widely held contemporary views of concept learning, such as the view that we learn concepts by constructing (...)
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  • A Theory of Interpretation for Comparative and Chinese Philosophy.Jaap Brakel & Lin Ma - 2016 - Dao: A Journal of Comparative Philosophy 15 (4):575-589.
    Why should interpretation of conceptual schemes and practices across traditions work at all? In this paper we present the following necessary conditions of possibility for interpretation in comparative and Chinese philosophy: the interpreter must presuppose that there are mutually recognizable human practices; the interpreter must presuppose that “the other” is, on the whole, sincere, consistent, and right; the interpreter must be committed to certain epistemic virtues. Some of these necessary conditions are consistent with the fact that interpretation is not thwarted (...)
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  • Explanation and description: Wittgenstein on convention.Yemima Ben-Menahem - 1998 - Synthese 115 (1):99-130.
  • Confronting philosophical objections to Chomskyan linguistics.J. Mark - 2005 - European Journal of Analytic Philosophy 1 (2):5-24.
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