Abstract
This paper has three aims: first, to present in a clear way Newton da Costa’s argument against the necessity of logical laws. In order to do so, we need to clearly advance his views on the idea that logic is context-relative, and not known a priori. Doing so, however, requires that we present his methodology for the development of counter-examples to logical laws: the use of hypothetical models in logic. Given that this method has been overlooked in most discussions on the epistemology of logic, our second goal is to present da Costa’s views on it carefully. The discussion of some tensions resulting from the relation of a system of logic and the context it governs, in da Costa’s approach, is our third goal. Basically, da Costa seems to swing between two incompatible views on such relation, requiring sometimes that a logic is dependent on a context, and in other cases, that the nature of the context is dependent on a logic. Bringing this to light may also benefit current discussions on logical relativism.
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Notes
Originally published in Portuguese; the title, in English could be translated as “Essay on the Foundations of Logic”.
Interestingly enough, Priest (2006, p.162), also uses a thought experiment to present a scenario where a version of inconsistent arithmetic holds as an applied theory, so that the consistent and the inconsistent arithmetics can be seen as legitimate rivals. The point is that, considered only as a pure formal system, inconsistent arithmetic could not rival classical arithmetic.
Again, it is interesting to compare with Priest’s (2006, p.162) use of thought experiment to apply inconsistent arithmetic. In Priest’s case, the thought experiment is called forth as positive evidence in favor of the possibility to apply inconsistent arithmetic; da Costa’s use of thought experiments, on the other hand, have the purpose of generating a more negative conclusion, of providing scenarios where it is emphasized that some laws and inferences do not hold. Of course, whether the use of thought experiments is seen as having a negative or a positive effect for some system depends on the emphasis given by who is advancing it, more than the nature of the nature of the thought experiment (see our discussion ahead of positive and negative aspects of uses of thought experiments).
Of course, it is implicitly assumed by da Costa that violation of LNC, violation of the rule of explosion, and paraconsistency, are all on a par. Recent literature on paraconsistency, however, separates more carefully these ingredients. (see the discussion in Barrio, Pailos and Szmuc 2018). For our purposes, however, that is not a problem, given that da Costa clearly aims only at an explicit violation of LNC.
Again, this depends on a specific view on the nature of scientific laws. Although this is an interesting topic, full of consequences for anti-exceptionalism, we shall not discuss it here.
Of course, da Costa does not put the issue in those terms; he does not seem to recognize the tension we are raising.
References
Arenhart JRB (2018) The price of true contradictions about the world. In: Carnielli W, Malinowski J (eds) Contradictions, from consistency to inconsistency. Springer, Cham, pp 11–31
Arenhart JRB (2019) Newton da Costa on non-reflexive logics and identity. Metatheoria 9:19–31
Barrio E, Pailos F, Szmuc D (2018) What is a paraconsistent logic? In: Carnielli W, Malinowski J (eds) Contradictions, from consistency to inconsistency. Springer, Cham, pp 89–108
Caret C (2019) Why logical pluralism? Forthcoming in Synthese. https://doi.org/10.1007/s11229-019-02132-w
da Costa NCA (1980) Ensaio sobre os fundamentos da lógica. Hucitec, São Paulo
French S, Krause D (2006) Identity in physics. A historical, philosophical and formal analysis. Oxford University Press, Oxford
Hjortland OT (2017) Anti-Exceptionalism about Logic. Philos Stud 174:631–658
Hjortland OT (2019) What counts as evidence for a logical theory? Australas J Log 16(7):250–282
Poincaré H (1952) [1905]. Science and hypothesis. New York, Dover
Priest G (2006) Doubt truth to be a liar. Oxford University Press, Oxford
Routley R (1980) The choice of logical foundations: Non-classical choices and the ultralogical choice. Stud Logica 39(1):77–98
Russell G (2018) Logical Nihilism: could there be no logic? Philos Issues 28:308–324
Schrödinger E (1996) Nature and the Greeks and Science and Humanism, with a foreword by Roger Penrose. Cambridge University Press, Cambridge
Shapiro S (2014) Varieties of Logic. Oxford University Press, Oxford
Tahko T (2011) A priori and a posteriori: a bootstrapping relationship. Metaphysica 12:151–164
Acknowledgements
The author is partially supported by CNPq. Work made possible by a Capes-Humboldt Experienced Research Fellowship at the Ruhr Universität Bochum, Bochum, Germany
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Arenhart, J.R.B. Newton da Costa on Hypothetical Models in Logic and on the Modal Status of Logical Laws. Axiomathes 32, 1191–1211 (2022). https://doi.org/10.1007/s10516-021-09577-0
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DOI: https://doi.org/10.1007/s10516-021-09577-0