Abstract
This paper develops the idea that valid arguments are equivalent to true conditionals by combining Kripke’s theory of truth with the evidential account of conditionals offered by Crupi and Iacona. As will be shown, in a first-order language that contains a naïve truth predicate and a suitable conditional, one can define a validity predicate in accordance with the thesis that the inference from a conjunction of premises to a conclusion is valid when the corresponding conditional is true. The validity predicate so defined significantly increases our expressive resources and provides a coherent formal treatment of paradoxical arguments.
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References
Beall, J. C., & Murzi, J. (2013). Two flavors of Curry’s paradox. The Journal of Philosophy, 110(3), 143–165.
Cobreros, P., Égré, P., Ripley, D., & van Rooij, R. (2012). Tolerant, classical, strict. Journal of Philosophical Logic, 41(2), 347–385.
Crupi, V., Dalmonte, T., & Iacona, A. (2022). Non-Monotonicity and Contraposition. manuscript.
Crupi, V., & Iacona, A. (2022). The Evidential Conditional. Erkenntnis, 87, 2897–2921.
Crupi, V., & Iacona, A. (2022). Three Ways of Being Non-Material. Studia Logica, 110, 47–93.
Crupi, V., & Iacona, A. (2024). Conditionals: Inferentialism Explicated. Erkenntnis, forthcoming.
Crupi, V., & Iacona, A. (2023). Outline of a Theory of Reasons. Philosophical Quarterly, 73, 117–142.
Feferman, S. (1991). Reflecting on incompleteness. The Journal of Symbolic Logic, 56(1), 1–49.
Field, H. (2003). A revenge-immune solution to the semantic paradoxes. Journal of Philosophical Logic, 32(2), 139–177.
Field, H. (2007). Solving the paradoxes, escaping revenge. In Jc. Beall (Ed.), Revenge of the Liar: new essays on the paradox (pp. 78–144). Oxford: Oxford University Press.
Field, H. (2008). Saving truth from paradox. Oxford: Oxford University Press.
Field, H. (2014). Naive truth and restricted quantification: Saving truth a whole lot better. The Review of Symbolic Logic, 7(1), 147–191.
Field, H. (2016). Indicative conditionals, restricted quantification, and naive truth. The Review of Symbolic Logic, 9(1), 181–208.
Field, H. (2020). Properties, propositions and conditionals. Australasian Philosophical Review, 4(2), 112–146.
Gabbay, D. M. (1985). Theoretical Foudation for Non-Monotonic Reasoning in Expert Systems. In: Logic and Models of Concurrent Systems. Springer.
Halbach, V. (2014). Axiomatic theories of truth. Second Edition. Cambridge University Press.
Halbach, V. (2020). Formal notes on the substitutional analysis of logical consequence. Notre Dame Journal of Formal Logic, 61(2), 317–339.
Halbach, V. (2020). The substitutional analysis of logical consequence. Noûs, 54(2), 431–450.
Halbach, V., Leitgeb, H., & Welch, P. (2003). Possible-worlds semantics for modal notions conceived as predicates. Journal of Philosophical Logic, 32(2), 179–223.
Halbach, V., & Welch, P. (2009). Necessities and necessary truths: A prolegomenon to the use of modal logic in the analysis of intensional notions. Mind, 118(469), 71–100.
Iacona, A. (2023). Valid Arguments as True Conditionals. Mind, 132, 428–451.
Jech, T. (2003). Set Theory. The Third Millennium Edition. Vol. 14. Berlin, Heidelberg, New York: Springer.
Kraus, S., Lehmann, D., & Magidor, M. (1990). Nonmonotonic reasoning, preferential models and cumulative logics. Journal of Artificial Intelligence, 44, 167–207.
Kripke, S. (1975). Outline of a theory of truth. The Journal of Philosophy, 72(19), 690–716.
Lewis, D. (1973). Counterfactuals. Blackwell.
McGee, V. (1991). Truth, vagueness, and paradox: An essay on the logic of truth. Hackett Publishing.
Moschovakis, Y. (1974). Elementary Induction on Abstract Structures. Amsterdam, London and New York: North-Holland / Elsevier.
Moschovakis, Y. (2010). Kleene’s amazing second recursion theorem. Bulletin of Symbolic Logic, 16(2), 189–239.
Murzi, J., & Rossi, L. (2021). Naïve validity. Synthese, 199(Suppl. 3), 819–841.
Nicolai, C., & Rossi, L. (2018). Principles for object-linguistic consequence: From logical to irreflexive. Journal of Philosophical Logic, 47(3), 549–577.
Nicolai, C., & Rossi, L. (2023). Systems for non-reflexive consequence. Studia Logica, 111, 947–977.
Raidl, E., Iacona, A., & Crupi, V. (2021). The Logic of the Evidential Conditional. The Review of Symbolic Logic, 1–13.
Rott, H. (1986). Ifs, though, and because. Erkenntnis, 25, 345–370.
Rott, H. (2019). Difference-making conditionals and the relevant Ramsey test. Review of Symbolic Logic.
Shapiro, L., & Beall, J. C. (2021). Curry’s Paradox. In N. Edward (Ed.), The Stanford Encyclopedia of Philosophy, Winter 2021. Zalta. Metaphysics Research Lab: Stanford University.
Stalnaker, R. (1991). A Theory of Conditionals. In: Conditionals, edited by F. Jackson, 28–45. Oxford University Press.
Stern, J. (2014). Modality and axiomatic theories of truth I: Friedman-Sheard. The Review of Symbolic Logic, 7(2), 273–298.
Stern, J. (2014). Modality and axiomatic theories of truth II: Kripke-Feferman. The Review of Symbolic Logic, 7(2), 299–318.
Stern, J. (2018). Supervaluation-style truth without supervaluations. Journal of Philosophical Logic, 47(5), 817–850.
Yablo, S. (2004). New grounds for naive truth theory. In: Liars and Heaps. New Essays on Paradox, edited by Beall, Jc, 312–330. Oxford: Oxford University Press.
Acknowledgements
We are grateful to Johannes Stern and to two anonymous referees for their valuable comments. We acknowledge the support of PLEXUS, a Marie Skłodowska-Curie action funded by the EU under the Horizon 2020 Research and Innovation Programme (Grant Agreement no 101086295).
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Open access funding provided by Università degli Studi di Torino within the CRUI-CARE Agreement.
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Iacona, A., Rossi, L. Naïve Truth and the Evidential Conditional. J Philos Logic 53, 559–584 (2024). https://doi.org/10.1007/s10992-024-09749-4
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DOI: https://doi.org/10.1007/s10992-024-09749-4