Abstract
The paper is concerned with a logical difficulty which Lionel Shapiro’s deflationist theory of logical consequence (as well as the author’s favoured, non-deflationist theory) gives rise to. It is argued that Shapiro’s non-contractive approach to solving the difficulty, although correct in its broad outlines, is nevertheless extremely problematic in some of its specifics, in particular in its failure to validate certain intuitive rules and laws associated with the principle of modus ponens. An alternative non-contractive theory is offered which does not suffer from the same problem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Beall, J. C. (2009). Spandrels of truth. Oxford: Oxford University Press.
Beall, J. C., & Murzi, J. (2012). Two flavors of Curry’s paradox. The Journal of Philosophy, forthcoming.
Brady, R. (2003). Prologue. In Brady, R. (Ed.), Relevant logics and their rivals (Vol. II, pp. 1–9). Aldershot: Ashgate.
Cobreros, P., Égré, P., Ripley, D., & van Rooij, R. (2012). Tolerant, classical, strict. Journal of Philosophical Logic, 41, 347–385.
Curry, H. (1942). The inconsistency of certain formal logics. The Journal of Symbolic Logic, 7, 115–117.
Field, H. (2006). Truth and the unprovability of consistency. Mind, 115, 567–605.
Field, H. (2008). Saving truth from paradox. Oxford: Oxford University Press.
Girard, J.-Y. (1987). Linear logic. Theoretical Computer Science, 50, 1–102.
McGee, V. (1985). A counterexample to modus ponens. The Journal of Philosophy, 82, 462–471.
Priest, G. (1979). The logic of paradox. Journal of Philosophical Logic, 8, 219–241.
Priest, G. (1980). Sense, entailment and modus ponens. Journal of Philosophical Logic, 9, 415–435.
Restall, G. (1994). On logics without contraction. PhD thesis, Department of Philosophy, University of Queensland.
Ripley, D. (2012). Conservatively extending classical logic with transparent truth. The Review of Symbolic Logic, 5, 354–378.
Shapiro, L. (2011). Deflating logical consequence. The Philosophical Quarterly, 61, 320–342.
Weir, A. (2005). Naive truth and sophisticated logic. In Armour-Garb, B., & Beall, J. C. (Eds.), Deflationism and paradox (pp. 218–249). Oxford: Oxford University Press.
Zardini, E. (2008). A model of tolerance. Studia Logica, 90, 337–368.
Zardini, E. (2008). Living on the slippery slope. The nature, sources and logic of vagueness. PhD thesis, Department of Logic and Metaphysics, University of St. Andrews.
Zardini, E. (2009). Towards first-order tolerant logics. In Prozorov, O. (Ed.), Philosophy, mathematics, linguistics: Aspects of interaction (pp. 35–38). St. Petersburg: Russian Academy of Science Press.
Zardini, E. (2011). Truth without contra(di)ction. The Review of Symbolic Logic, 4, 498–535.
Zardini, E. (2012a). First-order tolerant logics. The Review of Symbolic Logic, forthcoming.
Zardini, E. (2012). Getting one for two, or the contractors’ bad deal. Towards a unified solution to the semantic paradoxes. In Achourioti, T., Fujimoto, K., Galinon, H., & Martínez, J. (Eds.), volume on truth. Berlin: Springer.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zardini, E. Naive Modus Ponens . J Philos Logic 42, 575–593 (2013). https://doi.org/10.1007/s10992-012-9239-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10992-012-9239-1