Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-11T02:02:44.442Z Has data issue: false hasContentIssue false
  • English
  • Français

A RECOVERY OPERATOR FOR NONTRANSITIVE APPROACHES

Published online by Cambridge University Press:  06 November 2018

EDUARDO ALEJANDRO BARRIO ,
FEDERICO PAILOS  and
DAMIAN SZMUC
EDUARDO ALEJANDRO BARRIO*
Affiliation:
University of Buenos Aires and IIF-SADAF (CONICET)
FEDERICO PAILOS*
Affiliation:
University of Buenos Aires and IIF-SADAF (CONICET)
DAMIAN SZMUC*
Affiliation:
University of Buenos Aires and IIF-SADAF (CONICET)
*
*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF BUENOS AIRES PUAN 480, C1420 BUENOS AIRES ARGENTINA and IIF-SADAF (CONICET) BULNES 642, C1176ABL BUENOS AIRES ARGENTINA E-mail: eabarrio@gmail.com
†DEPARTMENT OF PHILOSOPHY UNIVERSITY OF BUENOS AIRES PUAN 480, C1420 BUENOS AIRES ARGENTINA and IIF-SADAF (CONICET) BULNES 642, C1176ABL BUENOS AIRES ARGENTINA E-mail: fpailos@hotmail.com
‡DEPARTMENT OF PHILOSOPHY UNIVERSITY OF BUENOS AIRES PUAN 480, C1420 BUENOS AIRES ARGENTINA and IIF-SADAF (CONICET) BULNES 642, C1176ABL BUENOS AIRES ARGENTINA E-mail: szmucdamian@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

In some recent articles, Cobreros, Egré, Ripley, & van Rooij have defended the idea that abandoning transitivity may lead to a solution to the trouble caused by semantic paradoxes. For that purpose, they develop the Strict-Tolerant approach, which leads them to entertain a nontransitive theory of truth, where the structural rule of Cut is not generally valid. However, that Cut fails in general in the target theory of truth does not mean that there are not certain safe instances of Cut involving semantic notions. In this article we intend to meet the challenge of answering how to regain all the safe instances of Cut, in the language of the theory, making essential use of a unary recovery operator. To fulfill this goal, we will work within the so-called Goodship Project, which suggests that in order to have nontrivial naïve theories it is sufficient to formulate the corresponding self-referential sentences with suitable biconditionals. Nevertheless, a secondary aim of this article is to propose a novel way to carry this project out, showing that the biconditionals in question can be totally classical. In the context of this article, these biconditionals will be essentially used in expressing the self-referential sentences and, thus, as a collateral result of our work we will prove that none of the recoveries expected of the target theory can be nontrivially achieved if self-reference is expressed through identities.

Keywords

03B0503B4703B53substructural logicscut rulerecovery operatorparadoxes
Type
Research Article
Information
The Review of Symbolic Logic , Volume 13 , Issue 1 , March 2020 , pp. 80 - 104
Copyright
Copyright © Association for Symbolic Logic 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

Barrio, E., Pailos, F., & Szmuc, D. (2017). A paraconsistent route to semantic closure. Logic Journal of the IGPL, 25 (4), 387–407.CrossRefGoogle Scholar
Barrio, E., Pailos, F., & Szmuc, D. (2018). What is a paraconsistent logic? In Carnielli, W. and Malinowski, J., editors. Between Consistency and Inconsistency. Trends in Logic. Dordrecht: Springer, pp. 89–108.CrossRefGoogle Scholar
Barrio, E., Rosenblatt, L., & Tajer, D. (2015). The logics of strict-tolerant logic. Journal of Philosophical Logic, 44(5), 551–571.CrossRefGoogle Scholar
Batens, D. (1989). Dynamic dialectical logics. In Priest, G., Sylvan, R., and Norman, J., editors. Paraconsistent Logic. Essays on the Inconsistent. München: Philosophia, pp. 187–217.Google Scholar
Beall, J. C. (2011). Multiple-conclusion LP and default classicality. Review of Symbolic Logic, 4(2), 326–336.CrossRefGoogle Scholar
Beall, J. C. (2013). Shrieking against gluts: The solution to the ‘just true’ problem. Analysis, 73(3), 438–445.CrossRefGoogle Scholar
Beall, J. C. (2014). Finding tolerance without gluts. Mind, 123(491), 791–811.CrossRefGoogle Scholar
Blasio, C., Marcos, J., & Wansing, H. (2018). An inferentially many-valued two-dimensional notion of entailment. Bulletin of the Section of Logic, 46, 233–262.Google Scholar
Carnielli, W. & Coniglio, M. (2016). Paraconsistent Logic: Consistency, Contradiction and Negation. Dordrecht: Springer.Google Scholar
Carnielli, W., Coniglio, M., & Marcos, J. (2007). Logics of formal inconsistency. In Gabbay, D. and Guenthner, F., editors. Handbook of Philosophical Logic, Vol. 14. Dordrecht: Springer, pp. 1–93.Google Scholar
Carnielli, W. & Marcos, J. (2002). A taxonomy of C-systems. In Carnielli, W., Coniglio, M., and D’Ottaviano, I., editors. Paraconsistency: The Logical Way to the Inconsistent. New York: Marcel Dekker, pp. 1–94.CrossRefGoogle Scholar
Carnielli, W., Marcos, J., & De Amo, S. (2004). Formal inconsistency and evolutionary databases. Logic and Logical Philosophy, 8, 115–152.CrossRefGoogle Scholar
Chemla, E., Egré, P., & Spector, B. (2017). Characterizing logical consequence in many-valued logics. Journal of Logic and Computation, 27(7), 2193–2226.Google Scholar
Cobreros, P., Egré, P., Ripley, D., & van Rooij, R. (2012). Tolerant, classical, strict. Journal of Philosophical Logic, 41(2), 347–385.CrossRefGoogle Scholar
Cobreros, P., Egré, P., Ripley, D., & van Rooij, R. (2013). Identity, Leibniz’s law and non-transitive reasoning. Metaphysica, 14(2), 253–264.CrossRefGoogle Scholar
Cobreros, P., Egré, P., Ripley, D., & van Rooij, R. (2014). Reaching transparent truth. Mind, 122(488), 841–866.CrossRefGoogle Scholar
Cook, R. T. (2004). Patterns of paradox. Journal of Symbolic Logic, 69(3), 767–774.CrossRefGoogle Scholar
Cook, R. T. (2005). What’s wrong with tonk (?). Journal of Philosophical Logic, 34(2), 217–226.CrossRefGoogle Scholar
Da Costa, N. (1974). On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic, 15(4), 497–510.CrossRefGoogle Scholar
Da Costa, N. (1993). Sistemas Formais Inconsistentes (Inconsistent Formal Systems, in Portuguese). Ph.D. Thesis, Universidade Federal do Paraná, Curitiba, Brazil, 1963.Google Scholar
Dicher, B. & Paoli, F. (forthcoming). ST, LP, and tolerant metainferences. In Başkent, C. and Ferguson, T. M., editors. Graham Priest on Dialetheism and Paraconsistency. Dordrecht: Springer.Google Scholar
Fjellstad, A. (2016). Omega-inconsistency without cuts and nonstandard models. The Australasian Journal of Logic, 13(5), 96–122.CrossRefGoogle Scholar
Frankowski, S. (2004). Formalization of a plausible inference. Bulletin of the Section of Logic, 33(1), 41–52.Google Scholar
Frankowski, S. (2004). p-Consequence versus q-Consequence operations. Bulletin of the Section of Logic, 33(4), 197–207.Google Scholar
Goodship, L. (1996). On dialethism. Australasian Journal of Philosophy, 74(1), 153–161.CrossRefGoogle Scholar
Hjortland, O. (2017). Theories of truth and the maxim of minimal mutilation. Synthese. Advance online publication, doi: 10.1007/s11229-017-1612-8.CrossRefGoogle Scholar
Horsten, L. (2009). Levity. Mind, 118(471), 555–581.CrossRefGoogle Scholar
Kripke, S. (1975). Outline of a theory of truth. Journal of Philosophy, 72(19), 690–716.CrossRefGoogle Scholar
Omori, H. (2015). Remarks on naive set theory based on LP. Review of Symbolic Logic, 8(2), 279–295.CrossRefGoogle Scholar
Paoli, F. (2013). Substructural Logics: A Primer. Dordrecht: Springer.Google Scholar
Picollo, L. (2018). Reference in arithmetic. Review of Symbolic Logic, 11(3), 573–603.CrossRefGoogle Scholar
Priest, G. (2006). In Contradiction: A Study of the Transconsistent. Oxford: Oxford University Press.CrossRefGoogle Scholar
Priest, G. (2014). One: Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness. Oxford: Oxford University Press.CrossRefGoogle Scholar
Priest, G. (2017). What if? The exploration of an idea. The Australasian Journal of Logic, 14(1), 54–127.CrossRefGoogle Scholar
Pynko, A. (2010). Gentzen’s cut-free calculus versus the logic of paradox. Bulletin of the Section of Logic, 39(1/2), 35–42.Google Scholar
Ripley, D. (2012). Conservatively extending classical logic with transparent truth. Review of Symbolic Logic, 5(2), 354–378.CrossRefGoogle Scholar
Ripley, D. (2013). Paradoxes and failures of cut. Australasian Journal of Philosophy, 91(1), 139–164.CrossRefGoogle Scholar
Scott, D. (1971). On engendering an illusion of understanding. Journal of Philosophy, 68(21), 787–807.CrossRefGoogle Scholar
Sharvit, Y. (2017). A note on (Strawson) entailment. Semantics and Pragmatics, 10(1), 1–38, 6.CrossRefGoogle Scholar
Tennant, N. (1982). Proof and paradox. Dialectica, 36(2–3), 265–296.CrossRefGoogle Scholar
Tennant, N. (2015). A new unified account of truth and paradox. Mind, 124(494), 571–605.CrossRefGoogle Scholar
van Rooij, R. (2017). Nonmonotonicity and knowability: As knowable as possible. In Başkent, C., Moss, L. S., and Ramanujam, R., editors. Rohit Parikh on Logic, Language and Society. Cham: Springer, pp. 53–65.CrossRefGoogle Scholar
von Fintel, K. (1999). NPI licensing, Strawson entailment, and context dependency. Journal of Semantics, 16(2), 97–148.CrossRefGoogle Scholar
Weir, A. (2005). Naive truth and sophisticated logic. In Beall, J. C. and Armour-Garb, B., editors. Deflationism and Paradox. Oxford: Oxford University Press, pp. 218–249.Google Scholar
Zardini, E. (2008). A model of tolerance. Studia Logica, 90(3), 337–368.CrossRefGoogle Scholar