Counterpossibles in Science: The Case of Relative Computability

Noûs 52 (3):530-560 (2018)

Authors
Matthias Jenny
Massachusetts Institute of Technology
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.
Keywords counterpossibles  counterfactuals  computability  relative computability  recursion theory  Post-Turing thesis  relativized Church-Turing thesis
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Reprint years 2016, 2017, 2018
DOI 10.1111/nous.12177
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References found in this work BETA

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Citations of this work BETA

Williamson on Counterpossibles.Berto Francesco, David Ripley, Graham Priest & Rohan French - 2018 - Journal of Philosophical Logic 47 (4):693-713.
Impossible Worlds.Franz Berto & Mark Jago - 2019 - Oxford: Oxford University Press.

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