Abstract
Formal symptoms of relevance usually concern the propositional variables shared between the antecedent and the consequent of provable conditionals. Among the most famous results about such symptoms are Belnap’s early results showing that for sublogics of the strong relevant logic R, provable conditionals share a signed variable between antecedent and consequent. For logics weaker than R stronger variable sharing results are available. In 1984, Ross Brady gave one well-known example of such a result. As a corollary to the main result of the paper, we give a very simple proof of a related but strictly stronger result.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Change history
30 May 2023
A Correction to this paper has been published: https://doi.org/10.1007/s10992-023-09706-7
References
Belnap, N.D. (1960). Entailment and relevance. The Journal of Symbolic Logic, 25(2), 144–146.
Anderson, A.R., & Belnap, N.D. (1975). Entailment: The logic of relevance and necessity. Princeton: Princeton University Press.
Logan, S.A. (2021). Strong depth relevance. Australasian Journal of Logic, 18(6), 645–656.
Brady, R.T. (1984). Depth relevance of some paraconsistent logics. Studia Logica, 43(1-2), 63–73. https://doi.org/10.1007/BF00935740.
MacFarlane, J. (2000). What does it mean to say that logic is formal? Ph.D. Thesis, Dissertation, University of Pittsburgh.
Brady, R.T. (2006). Universal logic. CSLI Publications.
Acknowledgements
This paper benefited from the audiences of talks on various parts of this material at the Nonclassical Logic Webinar and at the Annual Meeting of the Australasian Association for Logic. In particular, I thank Graham Priest, Ross Brady, Dave Ripley, Ed Mares, Sara Ugolini, Shawn Standefer, and Guillermo Badia. Like much of my work of late, this paper also owes a great deal to the hive mind comprised of Andrew Tedder, Graham Leach-Krouse, Eileen Nutting, and Teresa Kouri. Finally, two referees for this journal were instrumental in my catching several crucial errors, for which I am quite grateful.
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.
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
Logan, S.A. Depth Relevance and Hyperformalism. J Philos Logic 51, 721–737 (2022). https://doi.org/10.1007/s10992-021-09648-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10992-021-09648-y