Counterpossibles in Science: The Case of Relative Computability

Noûs 52 (3):530-560 (2018)
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Abstract
I develop a theory of counterfactuals about relative computability, i.e. counterfactuals such as 'If the validity problem were algorithmically decidable, then the halting problem would also be algorithmically decidable,' which is true, and 'If the validity problem were algorithmically decidable, then arithmetical truth would also be algorithmically decidable,' which is false. These counterfactuals are counterpossibles, i.e. they have metaphysically impossible antecedents. They thus pose a challenge to the orthodoxy about counterfactuals, which would treat them as uniformly true. What’s more, I argue that these counterpossibles don’t just appear in the periphery of relative computability theory but instead they play an ineliminable role in the development of the theory. Finally, I present and discuss a model theory for these counterfactuals that is a straightforward extension of the familiar comparative similarity models.
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2016, 2017, 2018
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JENCIS-2
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First archival date: 2016-07-07
Latest version: 3 (2016-09-09)
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References found in this work BETA
Remarks on Counterpossibles.Brogaard, Berit & Salerno, Joe
Appendix.Yablo, Stephen

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Citations of this work BETA
The Necessity of Mathematics.Yli‐Vakkuri, Juhani & Hawthorne, John
Williamson on Counterpossibles.Francesco, Berto; Rohan, French; Graham, Priest & David, Ripley

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2016-07-07

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