Abstract
Seen from the point of view of evaluation conditions, a usual way to obtain a connexive logic is to take a well-known negation, for example, Boolean negation or de Morgan negation, and then assign special properties to the conditional to validate Aristotle’s and Boethius’ Theses. Nonetheless, another theoretical possibility is to have the extensional or the material conditional and then assign special properties to the negation to validate the theses. In this paper we examine that possibility, not sufficiently explored in the connexive literature yet.We offer a characterization of connexive negation disentangled from the cancellation account of negation, a previous attempt to define connexivity on top of a distinctive negation. We also discuss an ancient view on connexive logics, according to which a valid implication is one where the negation of the consequent is incompatible with the antecedent, and discuss the role of our idea of connexive negation for this kind of view.
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Acknowledgements
We thank Axel Arturo Barceló-Aspeitia, Fernando Cano-Jorge, Sandra D.Cuenca. Hitoshi Omori, Elisángela Ramírez-Cámara, Christian Andrés Romero-Rodríguez, Mateusz Klonowski, Favio Ezequiel Miranda-Perea, Miguel Ángel Trejo-Huerta, Heinrich Wansing, Marek Nasieniewski and two anonymous reviewers for comments on previous versions of this paper.
Funding
This work was supported by the PAPIIT project IG400422 “Propositional variables and propositional constants”. The first author also received support from a DGAPA-PASPA sabbatical Grant. The second author also received support from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 101007627.
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Special Issue: Frontiers of Connexive Logic Edited by: Hitoshi Omori and Heinrich Wansing.
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Estrada-González, L., Nicolás-Francisco, R.A. Connexive Negation. Stud Logica 112, 511–539 (2024). https://doi.org/10.1007/s11225-023-10078-x
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DOI: https://doi.org/10.1007/s11225-023-10078-x