Abstract
In this paper we re-assess the philosophical foundation of Exactly True Logic (\(\mathcal {ET\!L}\)), a competing variant of First Degree Entailment (\(\mathcal {FDE}\)). In order to do this, we first rebut an argument against it. As the argument appears in an interview with Nuel Belnap himself, one of the fathers of \(\mathcal {FDE}\), we believe its provenance to be such that it needs to be taken seriously. We submit, however, that the argument ultimately fails, and that \(\mathcal {ET\!L}\) cannot easily be dismissed. We then proceed to give an overview of the research that was inspired by this logic over the last decade, thus providing further motivation for the study of \(\mathcal {ET\!L}\) and, more generally, of \(\mathcal {FDE}\)-related logics that result from semantical analyses alternative to Belnap’s canonical one. We focus, in particular, on philosophical questions that these developments raise.
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Funding
Andreas Kapsner’s research has been supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Project 436508789. Umberto Rivieccio was supported by the I+D+i research project PID2019- 110843GA-I00 La geometría de las lógicas no-clásicas funded by the Ministry of Science and Innovation of Spain Open Access funding enabled and organized by Projekt DEAL.
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Kapsner, A., Rivieccio, U. The Value of the One Value: Exactly True Logic revisited. J Philos Logic 52, 1417–1444 (2023). https://doi.org/10.1007/s10992-023-09711-w
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DOI: https://doi.org/10.1007/s10992-023-09711-w