Faithfulness for naive validity
- 22 Downloads
Nontransitive responses to the validity Curry paradox face a dilemma that was recently formulated by Barrio, Rosenblatt and Tajer. It seems that, in the nontransitive logic ST enriched with a validity predicate, either you cannot prove that all derivable metarules preserve validity, or you can prove that instances of Cut that are not admissible in the logic preserve validity. I respond on behalf of the nontransitive approach. The paper argues, first, that we should reject the detachment principle for naive validity. Secondly, I show how to add a validity predicate to ST while avoiding the dilemma.
KeywordsNaive validity Nontransitive logic V-Curry paradox Substructural approaches to paradox
I am very grateful for invaluable conversations with and/or comments from Jaroslav Peregrin, Robert Brandom, Daniel Kaplan, Shawn Standefer, Ori Beck, David Ripley, Katharina Nieswandt, Stephen Mackereth, Shuhei Shimamura and two anonymous referees.
- Barrio, E., Rosenblatt, L., & Tajer, D. (2016). Capturing naive validity in the cut-free approach. Synthese. https://doi.org/10.1007/s11229-016-1199-5.
- Hlobil, U. (2018). The cut-free approach and the admissibility-Curry. Thought: A Journal of Philosophy (forthcoming).Google Scholar
- Ripley, D. (2017). Bilateralism, coherence, warrant. In F. Moltmann & M. Textor (Eds.), Act-Based Conceptions of Propositional Content (pp. 307–324). Oxford University Press.Google Scholar
- Rosenblatt, L. (2017). Naive validity, internalization and substructural approaches to paradox. Ergo, 4(4), 93–120.Google Scholar
- Shapiro, L. (2013). Validity Curry strengthened. Thought: A Journal of Philosophy, 2(2), 100–107.Google Scholar