Σ01 soundness isn’t enough: Number theoretic indeterminacy’s unsavory physical commitments

British Journal for the Philosophy of Science (forthcoming)
  Copy   BIBTEX

Abstract

It’s sometimes suggested that we can (in a sense) settle the truth-value of some statements in the language of number theory by stipulation, adopting either φ or ¬φ as an additional axiom. For example, in Clarke-Doane (2020b) and a series of recent APA presentations, Clarke-Doane suggests that any Σ01 sound expansion of our current arithmetical practice would express a truth. In this paper, I’ll argue that (given a certain popular assumption about the model-theoretic representability of languages like ours) we can’t know ourselves to have any such freedom.

Similar books and articles

Manipulation and Unsavory Seduction.Eric Cave - 2014 - In Manipulation. New York, NY, USA: pp. 176-200.
Can Mary's Qualia Be Epiphenomenal?Daniel Lim & Wang Hao - 2014 - Res Philosophica 91 (3):503-512.
Unsavory Seduction.Eric M. Cave - 2009 - Ethical Theory and Moral Practice 12 (3):235-245.
A defense of physical becoming.James A. McGilvray - 1979 - Erkenntnis 14 (3):275 - 299.
Validity and soundness.Author unknown - 2004 - Internet Encyclopedia of Philosophy.
The Soundness Paradox.Dale Jacquette - 2003 - Logic Journal of the IGPL 11 (5):547-556.
Unifying Functional Interpretations.Paulo Oliva - 2006 - Notre Dame Journal of Formal Logic 47 (2):263-290.
Ontological infidelity.Patrick Dieveney - 2008 - Synthese 165 (1):1 - 12.
An ontology for commitments in multiagent systems. [REVIEW]Munindar P. Singh - 1999 - Artificial Intelligence and Law 7 (1):97-113.

Analytics

Added to PP
2021-04-16

Downloads
97 (#129,099)

6 months
44 (#30,642)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Sharon Berry
Indiana University, Bloomington

Citations of this work

No citations found.

Add more citations

References found in this work

Mathematical truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
Truth and meaning.Donald Davidson - 1967 - Synthese 17 (1):304-323.
Truth and meaning.Donald Davidson - 1967 - Synthese 17 (1):304-323.
Morality and Mathematics.Justin Clarke-Doane - 2020 - Oxford, England: Oxford University Press.
Models and reality.Hilary Putnam - 1980 - Journal of Symbolic Logic 45 (3):464-482.

View all 13 references / Add more references