Removing the Oddity in First Degree Entailment

Kapsner, Andreas (23. August 2019): Removing the Oddity in First Degree Entailment. In: Thought: A Journal of Philosophy: pp. 1-10

Abstract

I discuss an old problem with first degree entailment (FDE), namely the unintuitive way disjunctions and conjunctions between statements with values B and N are defined. I supply a solution tothis problem that involves a modification of FDE that leaves the philosophical motivation for the logic unharmed. Furthermore, I argue that this modification allows us to incorporate the philosophical core idea of exactly true logic without leading to the unusual inferential behavior of that logic.

• Item Type: Journal article
• Keywords: first degree entailment; exactly true logic; conjunction; disjunction; many-valued logic
• Faculties: Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP) > Logic
• Subjects: 100 Philosophy and Psychology > 100 Philosophy; 100 Philosophy and Psychology > 160 Logic
• ISSN: 2161-2234
• Language: English

References

Anderson, Alan and Nuel Belnap. Entailment: The Logic of Necessity and Relevance. Princeton, NJ: Princeton University Press, 1975.

Belnap, Nuel. “How a Computer Should Think,” inContemporary Aspects of Philosophy, edited by G. Ryle. Dordrecht: Reidel Publishing Co., 1977a, 8–37.

Belnap, Nuel. “A Useful Four-Valued Logic,” in: Modern Uses of Multiple-Valued Logic, edited by J. M. Dunn and G. Epstein. Dordrecht: Reidel Publishing Co., 1977b, 8–37.

Correia, Fabrice. “Logical Grounding and First-Degree Entailments,” in: Themes from Ontology, Mind, and Logic: Present and Past. Essays in Honour of Peter Simons, Vol. 91. Leiden: Brill, 2015, 3–15.

Dunn, J. Michael. “Intuitive Semantics for First-Degree Entailment and ‘Coupled Trees’. ”Philo-sophical Studies 29 (1976): 149–168.

Font, Josep M. and Massoud Moussavi. “Note on a Six-Valued Extension of Three-Valued Logic. ”Journal of Applied Non-Classical Logics3.2 (1993): 173–187.

Joseph,L.Camp,Jr.Confusion: A Study in the Theory of Knowledge. first ed. Cambridge, MA: Harvard University Press, 2002.

Marcos, Joao. “The Value of the Two Values,” in: Logic without Frontiers: Festschrift for Alexandre Carnielli on the Occasion of his 60th Birthday, Tribute series, Vol.17, edited by J.-Y.Béziau and M. E. Coniglio. London: College Publications, 2011, 277–294.

Pietz, Andreas and Umberto Rivieccio. “Nothing but the Truth.” Journal of Philosophical Logic 42.1(2013): 125–135.

Priest, Graham. “The Logic of Paradox.” Journal of Philosophical Logic 8.1 (1979): 219–241.

Priest, Graham. “The Logic of the Catuskoti.” Comparative Philosophy 1.2 (2010): 51–51.

Priest, Graham. The Fifth Corner of Four: An Essay on Buddhist Metaphysics and the Catuskoti. NewYork: Oxford University Press, 2018.

Priest, Graham, Jeffrey C. Beall, and Bradley Armour-Garb. The Law of Non-contradiction: New Philosophical Essays. Oxford: Clarendon Press, 2006.

Restall, Greg. “First Degree Entailment, Symmetry and Paradox.” Logic and Logical Philosophy 26.1 (2017): 3–18.

Shramko, Yaroslav. “Dual-Belnap Logic and Anything but Falsehood.” Journal of Applied Logics IfCoLoG Journal of Logics and their Applications 6 (2019): 413–433.

Shramko, Yaroslav and Heinrich Wansing. “Some Useful 16-Valued Logics: How a ComputerNetwork Should Think.” Journal of Philosophical Logic 34.2 (2005): 121–153.

Wansing, Heinrich and Nuel Belnap. “Generalized Truth Values. A Reply to Dubois.” Logic. Journal of IGPL 18.6 (2009): 921–935.