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What Achilles should have said to the Tortoise

In Steven Cahn (ed.), Thinking about Logic: Classic Essays. Taylor & Francis (2010)

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  1. Semantic theory and necessary truth.Ian Rumfitt - 2001 - Synthese 126 (1-2):283 - 324.
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  • Knowing a rule.Carlotta Pavese - 2015 - Philosophical Issues 25 (1):165-188.
    In this essay, I provide a new argument for Intellectualism about knowing how, one that does not rest on controversial assumptions about how knowing how is ascribed in English. In particular, I argue that the distinctive intentionality of the manifestations of knowing how ought to be explained in terms of a propositional attitude of belief about how to perform an action.
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  • Wittgensteinian instrumentalism.Alan Musgrave - 1980 - Theoria 46 (2-3):65-105.
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  • Reasoning and representing.Mark Eli Kalderon - 2001 - Philosophical Studies 105 (2):129-160.
    I argue that logical understanding is not propositional knowledgebut is rather a species of practical knowledge. I further arguethat given the best explanation of logical understanding someversion or another of inferential role semantics must be the correct account of the determinants of logical content.
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  • A Pragmatic-Semiotic Defence of Bivalence.Marc Champagne - 2021 - History and Philosophy of Logic 43 (2):143-157.
    Since Peirce defined the first operators for three-valued logic, it is usually assumed that he rejected the principle of bivalence. However, I argue that, because bivalence is a principle, the strategy used by Peirce to defend logical principles can be used to defend bivalence. Construing logic as the study of substitutions of equivalent representations, Peirce showed that some patterns of substitution get realized in the very act of questioning them. While I recognize that we can devise non-classical notations, I argue (...)
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  • Instrumental Rationality and Carroll's Tortoise.John Brunero - 2005 - Ethical Theory and Moral Practice 8 (5):557-569.
    Some philosophers have tried to establish a connection between the normativity of instrumental rationality and the paradox presented by Lewis Carroll in his 1895 paper “What the Tortoise Said to Achilles.” I here examine and argue against accounts of this connection presented by Peter Railton and James Dreier before presenting my own account and discussing its implications for instrumentalism (the view that all there is to practical rationality is instrumental rationality). In my view, the potential for a Carroll-style regress just (...)
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  • The Logical Evaluation of Arguments.David Botting - 2016 - Argumentation 30 (2):167-180.
    In this paper I will defend the controversial thesis that all argumentation in natural language can be reconstructed, for the purposes of assessment, as a deductively valid argument. Evaluation of the argumentation amounts to evaluation of the logical coherence of the premises. I will be taking the pragma-linguistic theory of Bermejo-Luque as an initial starting point.
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  • Logic, Reasoning, and Rationality.Erik Weber, Joke Meheus & Dietlinde Wouters (eds.) - 2014 - Dordrecht, Netherland: Springer.
    This book contains a selection of the papers presented at the Logic, Reasoning and Rationality 2010 conference in Ghent. The conference aimed at stimulating the use of formal frameworks to explicate concrete cases of human reasoning, and conversely, to challenge scholars in formal studies by presenting them with interesting new cases of actual reasoning. According to the members of the Wiener Kreis, there was a strong connection between logic, reasoning, and rationality and that human reasoning is rational in so far (...)
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  • What The Tortoise Has To Say About Diachronic Rationality.Markos Valaris - 2016 - Pacific Philosophical Quarterly 98 (S1):293-307.
    Even if you believe just what you rationally ought to believe, you may be open to rational criticism if you do so ‘for the wrong reasons’, as we say. Some have thought that this familiar observation supports the idea that there are diachronic norms of epistemic rationality – namely, norms of good reasoning. Partly drawing upon Carroll's story of Achilles and the Tortoise, this article criticises this line of thought on the grounds that it rests on a mistaken conception of (...)
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  • Dummett, Achilles and the tortoise.Pascal Engel - unknown
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  • Revisiting Quine on Truth by Convention.Jared Warren - 2017 - Journal of Philosophical Logic 46 (2):119-139.
    In “Truth by Convention” W.V. Quine gave an influential argument against logical conventionalism. Even today his argument is often taken to decisively refute logical conventionalism. Here I break Quine’s arguments into two— the super-task argument and the regress argument—and argue that while these arguments together refute implausible explicit versions of conventionalism, they cannot be successfully mounted against a more plausible implicit version of conventionalism. Unlike some of his modern followers, Quine himself recognized this, but argued that implicit conventionalism was explanatorily (...)
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  • Infinite Regress Arguments.Jan Willem Wieland - 2013 - Cham: Springer.
    This book on infinite regress arguments provides (i) an up-to-date overview of the literature on the topic, (ii) ready-to-use insights for all domains of philosophy, and (iii) two case studies to illustrate these insights in some detail. Infinite regress arguments play an important role in all domains of philosophy. There are infinite regresses of reasons, obligations, rules, and disputes, and all are supposed to have their own moral. Yet most of them are involved in controversy. Hence the question is: what (...)
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  • What Carroll’s Tortoise Actually Proves.Jan Willem Wieland - 2013 - Ethical Theory and Moral Practice 16 (5):983-997.
    Rationality requires us to have certain propositional attitudes (beliefs, intentions, etc.) given certain other attitudes that we have. Carroll’s Tortoise repeatedly shows up in this discussion. Following up on Brunero (Ethical Theory Moral Pract 8:557–569, 2005), I ask what Carroll-style considerations actually prove. This paper rejects two existing suggestions, and defends a third.
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  • And So On. Two Theories of Regress Arguments in Philosophy.Jan Willem Wieland - 2012 - Dissertation,
    This dissertation is on infinite regress arguments in philosophy. Its main goals are to explain what such arguments from many distinct philosophical debates have in common, and to provide guidelines for using and evaluating them. Two theories are reviewed: the Paradox Theory and the Failure Theory. According to the Paradox Theory, infinite regress arguments can be used to refute an existentially or universally quantified statement (e.g. to refute the statement that at least one discussion is settled, or the statement that (...)
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  • Norms, reasons and reasoning: a guide through Lewis Carroll’s regress argument.Corine Besson - 2018 - In Daniel Star (ed.), The Oxford Handbook of Reasons and Normativity. New York, NY, United States of America: Oxford University Press.
    This paper concerns connection between knowing or accepting a logical principle such as Modus Ponens and actions of reasoning involving it. Discussions of this connection typically mention the so-called ‘Lewis Carroll Regress’ and there is near consensus that the regress shows something important about it. Also, although the regress explicitly concerns logic, many philosophers think that it establishes a more general truth, about the structurally similar connection between epistemic or practical principles and actions involving them. This paper’s first aim is (...)
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  • Infinte Regress Arguments.Claude Gratton - 2009 - Dordrecht, Netherland: Springer.
    Infinite regress arguments are part of a philosopher's tool kit of argumentation. But how sharp or strong is this tool? How effectively is it used? The typical presentation of infinite regress arguments throughout history is so succinct and has so many gaps that it is often unclear how an infinite regress is derived, and why an infinite regress is logically problematic, and as a result, it is often difficult to evaluate infinite regress arguments. These consequences of our customary way of (...)
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  • Logical compulsion and necessity.Robert Wachbroit - 1987 - Erkenntnis 26 (1):45 - 56.
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