Logical Pluralism and Interpretations of Logical Systems
Keywordsinterpretations of logical systems, logical pluralism, pure and applied logics, collapse argument
Logical pluralism is a general idea that there is more than one correct logic. Carnielli and Rodrigues [2019a] defend an epistemic interpretation of the paraconsistent logic N4, according to which an argument is valid in this logic just in case it necessarily preserves evidence. The authors appeal to this epistemic interpretation to briefly motivate a kind of logical pluralism: “different accounts of logical consequence may preserve different properties of propositions”. The aim of this paper is to study the prospect of a logical pluralism based on different interpretations of logical systems. First, we give our analysis of what it means to interpret a logic – and make some hopefully useful distinctions along the way. Second, we present what we call an interpretational logical pluralism: there is more than one correct logic and a logic is correct only if it has some adequate interpretation. We consider four variants of this idea, bring up some possible objections, and try to find plausible solutions on behalf of the pluralist. We will argue that interpretations of logical systems provide a promising – albeit not unproblematic – route to logical pluralism.
Arenhart, J. R. B., 2021, “The evidence approach to paraconsistency versus the paraconsistent approach to evidence”, Synthese 198: 11537–11559. DOI: https://doi.org/10.1007/s11229-020-02813-x
Barrio, E., and B. Da Ré, 2018, “Paraconsistency and its philosophical interpretations”, The Australasian Journal of Logic 15 (2): 151–170. DOI: https://doi.org/10.26686/ajl.v15i2.4860
Beall, JC, 2019, “FDE as the One True Logic”, pages 115–125 in H. Omori and H. Wansing (eds.), New Essays on Belnap-Dunn Logic. Springer, Cham.
Beall, JC, 2016, “Off-topic: A new interpretation of weak Kleene logic”, Australasian Journal of Logic 13(6): 136–142. DOI: https://doi.org/10.26686/ajl.v13i6.3976
Beall, JC, and D. Ripley, 2004, “Analetheism and dialetheism”, Analysis 64 (1): 30–35. DOI: https://doi.org/10.1093/analys/64.1.30
Beall, JC, and G. Restall, 2006, Logical Pluralism, Oxford: Oxford University Press.
Belnap, N., 1977, “How a computer should think”, pages 30–56 in G. Ryle (ed.), Contemporary Aspects of Philosophy, Oriel Press.
Blake-Turner, C., and G. Russell, 2021, “Logical pluralism without the normativity”, Synthese 198: 4859–4877. DOI: https://doi.org/10.1007/s11229-018-01939-3
Bochvar, D., 1938, “On a three-valued logical calculus and its application to the analysis of contradictions”, Matematicheskii Sbornik 46 (4): 287-–308.
Brouwer, L. E. J., 1908, “The unreliability of logical principles”, pages 107–111 in A. Heyting (ed.), L.E.J. Brouwer: Collected Works, Vol. 1, North Holland Publisher,1975.
Caret, C. R., 2021, “Why logical pluralism?”, Synthese 198: 4947–4968. DOI: https://doi.org/10.1007/s11229-019-02132-w
Caret, C. R., 2017, “The collapse of logical pluralism has been greatly exaggerated”, Erkenntnis 82 (4): 739–760. DOI: https://doi.org/s10670-016-9841-7
Carnielli, W., and A. Rodrigues, 2019a, “An epistemic approach to paraconsistency: A logic of evidence and truth”, Synthese 196 (9): 3789–3813. DOI: https://doi.org/10.1007/s11229-017-1621-7
Carnielli, W. and A. Rodrigues, 2019b, “Inferential semantics, paraconsistency, and preservation of evidence”, pages 165–187 in C. Başkent and T. M. Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency, Springer International Publishing.
Ciuni, R., and M. Carrara, 2019, “Semantical analysis of weak Kleene logics”, Journal of Applied Non-Classical Logics 29 (1): 1–36. DOI: https://doi.org/10.1080/11663081.2018.1547514
Cook, R. T., 2010, “Let a thousand flowers bloom: A tour of logical pluralism”, Philosophy Compass 5 (6): 492–504. DOI: https://doi.org/10.1111/j.1747-9991.2010.00286.x
Correia, F., 2014, “Logical grounds”, The Review of Symbolic Logic 7 (1): 31–59. DOI: https://doi.org/10.1017/S1755020313000300
Dummett, M., 1975, “The philosophical basis of intuitionistic logic”, pages 215–244 in Truth and Other Enigmas, London: Duckworth.
Eklund, M., 2020, “Making sense of logical pluralism”, Inquiry 63 (3–4): 433–454. DOI: https://doi.org/10.1080/0020174X.2017.1321499
Field, H., 2015, “What is logical validity?”, in O. Hjortland and C. Caret (eds.), Foundations of Logical Consequence, Oxford: Oxford University Press.
Heyting, A., 1956, “La conception intuitionniste de la logique”, Les Etudes philosophiques. Nouvelle serie 11 (2): 226–233.
Hjortland O. T., 2017, “Anti-exceptionalism about logic”, Philosophical Studies 174 (3): 631–658. DOI: https://doi.org/10.1007/s11098-016-0701-8
Kouri Kissel, T., 2018, “Logical pluralism from a pragmatic perspective”, Australasian Journal of Philosophy 96 (3): 578–591. DOI: https://doi.org/10.1080/00048402.2017.1399151
Lo Guercio, N., and D. Szmuc, 2018, “Remarks on the epistemic interpretation of paraconsistent logic”, Principia: An international Journal of Epistemology, 22 (1): 153–170. DOI: https://doi.org/10.5007/1808-1711.2018v22n1p153
MacFarlane, J., 2004, “In what sense (if any) is logic normative for thought?”. Paper presented at the Central Division APA symposium on the normativity of logic.
MacFarlane, J., 2000, “What does it mean to say that logic is formal?”, PhD thesis, University of Pittsburgh.
Martin, B., and O. Hjortland, 2021, “Logical predictivism”, Journal of Philosophical Logic 50: 285-–318. DOI: https://doi.org/10.1007/s10992-020-09566-5
Priest, G., 1997, “Sylvan’s box: A short story and ten morals”, Notre Dame Journal of Formal Logic 38 (4): 573–582. DOI: https://doi.org/10.1305/ndjfl/1039540770
Priest, G., 2006a, Doubt Truth to be a Liar, Oxford: Oxford University Press. DOI: https://doi.org/10.1093/0199263280.003.0005
Priest, G., 2006b, In Contradiction: A Study of the Transconsistent, 2nd edition, Oxford: Oxford University Press. DOI: https://doi.org/10.1093/acprof:oso/9780199263301.001.0001
Russell, G., 2008, “One true logic?”, Journal of Philosophical Logic 37 (6): 593–611. DOI: https://doi.org/10.1007/s10992-008-9082-6
Russell, G., 2020, “Logic isn’t normative”, Inquiry 63 (3–4): 371–388. DOI: https://doi.org/10.1080/0020174x.2017.1372305
Stalnaker, R., 1984, Inquiry, The MIT Press.
Steinberger, F., 2019, “Logical pluralism and logical normativity”, Philosopher’s Imprint 19 (12): 1–19.
Tajer, D., 2020, “The normative autonomy of logic”, Erkenntnis 1–24. DOI: https://doi.org/10.1007/s10670-020-00321-5
Varzi, A. C., 2002, “On logical relativity”, Philosophical Issues 12: 197–219. DOI: https://doi.org/10.1111/j.1758-2237.2002.tb00067.x
Wansing, H., 2020, “Connexive logic”, Stanford Encyclopedia of Philosophy. https://plato.stanford.edu/entries/logic-connexive/
How to Cite
Copyright (c) 2022 Diego Tajer, Camillo Fiore
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.
Number of views and downloads: 1022
Number of citations: 0