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A Methodological Shift in Favor of (Some) Paraconsistency in the Sciences

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Abstract

Many have contended that non-classical logicians have failed at providing evidence of paraconsistent logics being applicable in cases of inconsistency toleration in the sciences. With this in mind, my main concern here is methodological. I aim at addressing the question of how should we study and explain cases of inconsistent science, using paraconsistent tools, without ruining into the most common methodological mistakes. My response is divided into two main parts: first, I provide some methodological guidance on how to approach cases of inconsistent science; and second, I focus on a peculiar type of formal methodologies for the scrutiny of inconsistent reasoning, the Paraconsistent Alternative Approach (henceforth, PAA) and argue that PAA can enhance a more accurate understanding of sensible reasoning in inconsistent contexts.

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Notes

  1. In the case of human reasoning, inconsistency toleration demands a previous identification of a contradiction in the reasoning reasoning, as well as the capability of the agent to reason sensibly with the inconsistent information.

  2. Some of the philosophical debates that have been significantly enriched by the discussions about applications of specific logical theories include the long lasting discussion on logical pluralism versus logical monism (Cf. [26, 36,37,38]), and the one between exceptionalism and anti-exceptionalism about logic (Cf. Hjortland 2017).

  3. This is a crucial point that is almost never made explicit in the corresponding literature but that is necessary for understanding the value of certain case studies in philosophical logic.

  4. A key problem with this presumption is that triviality is the most likely outcome only in the case in which the underlying logic would be classical, but for the high likelihood of this being the case, we have no evidence. And if there is not enough evidence in favor of triviality being the most likely outcome, one should weaken one’s expectations about how telling the absence of logical triviality might really be—either in favor or against any paraconsistent logic.

  5. As it was claimed for the case of the hegelian theory of motion by Boccardi and Macías-Bustos [6], and by Vickers ([35]: 186-90) for some other interesting cases of alleged inconsistency toleration.

  6. I am indebted to Moisés Macías-Bustos who helped to give a better phrasing of my ideas on this point.

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Acknowledgements

I am indebted to Moisés Macías-Bustos, Mary Gwin, Jonas Arenhart, Otavio Bueno, Gabrielle Ramos-Garcia and Itala Loffredo D’Ottaviano for fruitful discussions on these issues. I owe special thanks to the anonymous referees for their valuable comments and suggestions. Thanks to the audience at The Heterodox in Logic and Reason (WLD 2021).

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This research was supported by the Programa Nacional de Pós-Doutorado PNPD/CAPES (Brazil). This paper was awarded the ‘Mexican Academy of Logic (AML) Logic Prize 2021’. This prize is part of the project A Prize of Logic in Every Country (http://www.uni-log.org/logic-prize-world). As a result, the paper was presented at the ‘Logic Prizes Contest’, which took place at the 7th World Congress on Universal Logic, held in Crete, Greece, 2022.

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Martínez-Ordaz, M.d.R. A Methodological Shift in Favor of (Some) Paraconsistency in the Sciences. Log. Univers. 16, 335–354 (2022). https://doi.org/10.1007/s11787-022-00302-y

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