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From McGee's puzzle to the Lottery Paradox

Lissia, Lina Maria (2019) From McGee's puzzle to the Lottery Paradox. [Preprint]

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Abstract

Vann McGee (1985) presents a putative counterexample to modus ponens. After clarifying that McGee actually targets an epistemic version of such a principle, I show that, contrary to a view commonly held in the literature, assuming the material conditional as an interpretation of the natural language conditional “if … then …” does not dissolve the puzzle. Indeed, I provide a slightly modified version of McGee’s famous election scenario in which (1) the relevant features of the scenario are preserved and (2) both (epistemic) modus ponens and modus tollens fail, even if we assume the material conditional. I go on to note that in the modified scenario (which I call “the restaurant scenario”) (epistemic) conjunction introduction does not hold. More specifically, I show that the restaurant scenario is actually a version of the lottery scenario Kyburg uses in his Lottery Paradox (Kyburg 1961). Two main conclusions ensue: first, we should expect a unified solution to both McGee’s puzzle and the Lottery Paradox. Second, under minimal assumptions, McGee shows that (epistemic) modus ponens fails, even for the material conditional. Both conclusions defy the existing accounts of McGee’s puzzle.


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Item Type: Preprint
Creators:
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Lissia, Lina Maria
Keywords: McGee's counterexample to modus ponens; Lottery Paradox; Belief Closure; Lockean Thesis; conditionals
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > Logic
Depositing User: Ms. Lina Maria Lissia
Date Deposited: 26 Feb 2020 17:53
Last Modified: 26 Feb 2020 17:53
Item ID: 16945
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > Logic
Date: 11 December 2019
URI: http://philsci-archive.pitt.edu/id/eprint/16945

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