Solutions to Paradox and the Theoretical Virtues
Location
PANEL: Philosophy Honors: Contemplating the Boundaries of Existence
CELA A019
Document Type
Presentation
Start Date
4-28-2023 10:00 AM
End Date
4-28-2023 11:00 AM
Abstract
Participants in recent debates over paradoxes of self-reference often turn to traditional theoretical virtues such as uniformity and non-ad hocness in order to evaluate competing solutions to paradox. A widely applied theoretical virtue unique to paradox solutions is that they avoid revenge, that is, that a solution to a traditional paradox not provide the materials for the formulation of a new paradox. I discuss the relationship between these desiderata for paradox solutions in relation to the paradoxes of denotation, such as Berry's paradox and the Hilbert-Bernays paradox. In particular, I attempt to show how a recent line of argument due to Graham Priest that a paracomplete solution to the paradox of the liar cannot extend uniformly to the Berry paradox conflicts with certain commitments about other paradoxes and theoretical virtues held by Priest himself, among others. I also explore similar questions in relation to normative paradoxes and paradoxes of validity, as well as the connection between these issues and debates outside of philosophical logic, for instance in metaphysics.
Keywords:
Paradox, Paracomplete logic, Theoretical virtues
Recommended Citation
Crampton-Hays, Henry, "Solutions to Paradox and the Theoretical Virtues" (2023). Research Symposium. 11.
https://digitalcommons.oberlin.edu/researchsymp/2023/presentations/11
Major
Philosophy; Mathematics
Project Mentor(s)
Amy Berg, Philosophy
Katherine Thomson-Jones, Philosophy
2023
Solutions to Paradox and the Theoretical Virtues
PANEL: Philosophy Honors: Contemplating the Boundaries of Existence
CELA A019
Participants in recent debates over paradoxes of self-reference often turn to traditional theoretical virtues such as uniformity and non-ad hocness in order to evaluate competing solutions to paradox. A widely applied theoretical virtue unique to paradox solutions is that they avoid revenge, that is, that a solution to a traditional paradox not provide the materials for the formulation of a new paradox. I discuss the relationship between these desiderata for paradox solutions in relation to the paradoxes of denotation, such as Berry's paradox and the Hilbert-Bernays paradox. In particular, I attempt to show how a recent line of argument due to Graham Priest that a paracomplete solution to the paradox of the liar cannot extend uniformly to the Berry paradox conflicts with certain commitments about other paradoxes and theoretical virtues held by Priest himself, among others. I also explore similar questions in relation to normative paradoxes and paradoxes of validity, as well as the connection between these issues and debates outside of philosophical logic, for instance in metaphysics.
