Counterpossibles in Science: The Case of Relative Computability

Noûs 52 (3):530-560 (2018)
  Copy   BIBTEX

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.

Similar books and articles

Computability and Recursion.Robert I. Soare - 1996 - Bulletin of Symbolic Logic 2 (3):284-321.
Counterpossibles and Similarity.David Vander Laan - 2004 - In Frank Jackson & Graham Priest (eds.), Lewisian Themes: The Philosophy of David K. Lewis. Oxford, UK: Clarendon Press. pp. 258-275.
Counterpossibles.Barak Krakauer - 2012 - Dissertation, University of Massachusetts
Alternative Frameworks and Counterpossibles.Maciej Sendłak - 2016 - Grazer Philosophische Studien 93 (1):24-41.
Computation and Hypercomputation.Mike Stannett - 2003 - Minds and Machines 13 (1):115-153.
Omission Impossible.Sara Bernstein - 2016 - Philosophical Studies 173 (10):2575-2589.
Remarks on Counterpossibles.Berit Brogaard & Joe Salerno - 2013 - Synthese 190 (4):639-660.
Church's Thesis and the Conceptual Analysis of Computability.Michael Rescorla - 2007 - Notre Dame Journal of Formal Logic 48 (2):253-280.
SAD Computers and Two Versions of the Church–Turing Thesis.Tim Button - 2009 - British Journal for the Philosophy of Science 60 (4):765-792.
Counterpossibles (Not Only) for Dispositionalists.Barbara Vetter - 2016 - Philosophical Studies 173 (10):2681-2700.

Analytics

Added to PP
2016-07-07

Downloads
910 (#8,040)

6 months
79 (#9,669)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Matthias Jenny
Massachusetts Institute of Technology

Citations of this work

Williamson on Counterpossibles.Berto Francesco, David Ripley, Graham Priest & Rohan French - 2018 - Journal of Philosophical Logic 47 (4):693-713.
Counterlogicals as Counterconventionals.Alexander W. Kocurek & Ethan J. Jerzak - 2021 - Journal of Philosophical Logic 50 (4):673-704.
If P, Then P!Matthew Mandelkern - 2021 - Journal of Philosophy 118 (12):645-679.
Impossible Worlds.Franz Berto & Mark Jago - 2013 - Oxford: Oxford University Press.
Sensitivity, Safety, and Impossible Worlds.Guido Melchior - 2021 - Philosophical Studies 178 (3):713-729.

View all 25 citations / Add more citations

References found in this work

Aboutness.Stephen Yablo - 2014 - Princeton University Press.
On Denoting.Bertrand Russell - 1905 - Mind 14 (56):479-493.

View all 111 references / Add more references