Abstract
Sören Halldén’s logic of nonsense is one of the most well-known many-valued logics available in the literature. In this paper, we discuss Peter Woodruff’s as yet rather unexplored attempt to advance a version of such a logic built on the top of a constructive logical basis. We start by recalling the basics of Woodruff’s system and by bringing to light some of its notable features. We then go on to elaborate on some of the difficulties attached to it; on our way to offer a possible solution to such difficulties, we discuss the relation between Woodruff’s system and two-dimensional semantics for many-valued logics, as developed by Hans Herzberger.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Åqvist, L., Reflections on the logic of nonsense, Theoria 28:138–157, 1962.
Beall, J.C., Off-topic: A new interpretation of weak-Kleene logic, The Australasian Journal of Logic 13(6), 2016.
Bonzio, S., T. Moraschini, and M. Pra Baldi, Logics of left variable inclusion and Płonka sums of matrices, Archive for Mathematical Logic 60(1):49–76, 2021.
Bonzio, S., and M. Pra Baldi, Containment logics: Algebraic completeness and axiomatization, Studia Logica 109(5):969–994, 2021.
Brouwer, L. E. J., Consciousness, philosophy, and mathematics, in P. Benacerraf and H. Putnam (eds.), Philosophy of Mathematics: Selected Readings, 2nd edn, Cambridge University Press, 1984, pp. 90–96.
Cobreros, P., P. Egré, D. Ripley, and R. van Rooij, Tolerant, classical, strict, Journal of Philosophical Logic 41(2):347–385, 2012.
Cobreros, P., P. Égré, D. Ripley, and R. Van Rooij, Reaching transparent truth, Mind 122(488):841–866, 2013.
De, M., Empirical negation, Acta Analytica, 28:49–69, 2013.
Dummett, M., The philosophical basis of intuitionistic logic, in P. Benacerraf and H. Putnam (eds.) Philosophy of Mathematics: Selected Readings, 2nd edn, Cambridge University Press, 1984, pp. 97–129.
Fitting, M., Strict/Tolerant Logics Built Using Generalized Weak Kleene Logics, The Australasian Journal of Logic, 18(2), 2021.
Frankowski, S., Formalization of a plausible inference, Bulletin of the Section of Logic 33(1):41–52, 2004.
Girard, J.-Y., Three-valued logic and cut-elimination: The actual meaning of Takeuti’s conjecture, vol. 136 of Dissertiones Mathematicae, Polish Scientific Publishers, 1976.
Haack, S., Philosophy of Logics, Cambridge University Press, 1978.
Halldén, S., The Logic of Nonsense, Uppsala Universitets Årsskrift, 1949.
Herzberger, H. G., Dimensions of truth, Journal of Philosophical Logic 2(4):535–556, 1973.
Kamide, N., and H. Wansing, Proof Theory of N4-related Paraconsistent Logics, vol. 54 of Studies in Logic, College Publications, London, 2015.
Omori, H., Halldén’s logic of nonsense and its expansions in view of logics of formal inconsistency, in Proceedings of DEXA 2016. IEEE Computer Society, 2016, pp. 129–133.
Omori, H., and J.R.B. Arenhart, Haack meets Herzberger and Priest, in 2022 IEEE 52nd International Symposium on Multiple-Valued Logic (ISMVL), 2022, pp. 137–144.
Omori, H., and J.R.B. Arenhart, Change of logic, without change of meaning, Theoria, 89(4):414–431, 2023.
Omori, H., and J.R.B. Arenhart, Is the de Finetti conditional a conditional? Argumenta, forthcoming.
Priest, G., Plurivalent logics, The Australasian Journal of Logic 11(1):1–13, 2014.
Segerberg, K., A contribution to nonsense-logics, Theoria 31(3):199–217, 1965.
Song, Y., Omori, H., and S. Tojo, A two-valued semantics for infectious logics, in 2021 IEEE 51st International Symposium on Multiple-Valued Logic (ISMVL), IEEE, 2021, pp. 50–55.
Woodruff, P., On constructive nonsense logic, in Modality, Morality, and Other Problems of Sense and Nonsense: Essays Dedicated to Sören Halldén, GWK Gleerup Bokforlag, Lund, 1973, pp. 192–205.
Acknowledgements
Earlier versions of this paper were presented by Hitoshi Omori at Logic Colloquium 2022 in July 2022, and Trends in Logic XXII also in July 2022. Many thanks goes to Paul Égré for very fruitful discussions, and the audience at both conferences for interesting questions and comments. The work of Jonas Rafael Becker Arenhart was partially supported by CNPq (Brazilian National Research Council). The work of Hitoshi Omori was supported by a Sofja Kovalevskaja Award of the Alexander von Humboldt-Foundation, funded by the German Ministry for Education and Research.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Special Issue: Strong and weak Kleene logics
Edited by Gavin St. John and Francesco Paoli.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Arenhart, J.R.B., Omori, H. On Woodruff’s Constructive Nonsense Logic. Stud Logica (2024). https://doi.org/10.1007/s11225-023-10092-z
Published:
DOI: https://doi.org/10.1007/s11225-023-10092-z