Abstract
The problem of future contingents is regarded as an important philosophical problem in connection with determinism and it should be treated by tense logic. Prior’s early work focused on the problem, and later Prior studied branching-time tense logic which was invented (i.e. first suggested) by Kripke. However, Prior’s idea to use three-valued logic for the problem seems to be still alive. In this paper, we consider partial and paraconsistent approaches to the problem of future contingents. These approaches theoretically meet Aristotle’s interpretation of future contingents.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Sometimes people give the incorrect axiomatization, which amounts to taking \(\mathrm{F}\) and \(\mathrm{P}\) as primitive and then giving axioms which are only suitable if \(\mathrm{G}\) and \(\mathrm{H}\) are primitive. We learned the fact from Lloyd Humberstone.
References
Akama, S., Murai, T., & Kudo, Y. (2010). Uncertainty in future: A paraconsistent approach. In V. H. Huynh (Ed.), Integrated management and applications (pp. 335–342). Advances in intelligent and soft computing Berlin: Springer.
Akama, S., Murai, T., & Miyamoto, S. (2011). A three-valued modal tense logic for the Master Argument. Logique et Analyse, 213, 19–30.
Akama, S. and Nagata, Y. 2005. On Prior’s three-valued modal logic Q. In Proceedings of ISMVL’2005 (pp. 14–19)
Akama, S., Nagata, Y., & Yamada, C. (2007). A three-valued temporal logic for future contingents. Logique et Analyse, 198, 99–111.
Akama, S., Nagata, Y., & Yamada, C. (2008). Three-valued temporal logic \(Q_t\) and future contingents. Studia Logica, 88, 215–231.
Aristotle. (1963). De Interpretatione (E.M. Edghill & W.D. Ross, Trans.) The works of Aristotle. Oxford: Oxford University Press
Beall, J. C. (2012). Future contradictions. Australasian Journal of Philosophy, 90, 547–557.
Blackburn, P., & Tzakova, M. (1999). Hybrid language and temporal logic. Logic Journal of the IGPL, 7, 27–54.
Craig, W. (2000). The tensed theory of time. Dordrecht: Kluwer.
da Costa, N. C. A. (1974). On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic, 15, 497–510.
Frede, D. (1985). The sea-battle reconsidered: A defense of the traditional interpretation. In J. Annas (Ed.), Oxford studies of ancient philosophy (Vol. 3, pp. 31–87). Oxford: Clarendon Press.
Gabbay, D., Hodkinson, I., & Reynolds, M. (1994). Temporal logic: Mathematical and computational aspects (Vol. 1). Oxford: Oxford University Press.
Hintikka, J. (1964). The once and future sea fight: Aristotle’s discussion of future contingents in de Interpretatione IX. Philosophical Review, 73, 461–492.
Humberstone, L. (2004). Yet another “choice of primitives” warning: normal modal logics. Logique et Analyse, 185–188, 395–407.
Jaskowski, S. (1948). Propositional calculus for contradictory deductive systems (in Polish). Studia Societatis Scientiarun Torunesis Sectio A, 1, 55–77.
Łukasiewicz, J. (1967). On 3-valued logic, 1920. In S. McCall (Ed.), Polish logic (pp. 16–18). Oxford: Oxford University Press.
McArthur, R. (1976). Tense logic. Dordrecht: Reidel.
Oaklander, L. (2004). The ontology of time. Buffalo, NY: Prometheus Books.
Øhrsrøm, P. & Hasle, P. 2011. Future contingents, The Stanford encyclopedia of philosophy. In Zalta E (ed.), http://plato.stanford.edu/archives/sum2011/entries/future-contingents
Ploug, T., & Øhrsrøm, P. (2012). Branching time, indeterminism and tense logic. Synthese, 188, 367–379.
Priest, G. (1982). To be and not to be: dialectical tense logic. Studia Logica, 41, 63–76.
Priest, G. (2006). In contradiction (2nd ed.). Oxford: Oxford University Press.
Prior, A. N. (1953). Three-valued logic and future contingents. Philosophical Quarterly, 3, 317–26.
Prior, A. N. (1957). Time and modality. Oxford: Oxford University Press.
Prior, A. N. (1967). Past, present and future. Oxford: Clarendon Press.
Smith, Q. (1993). Language and time. Oxford: Oxford University Press.
Thomason, R. H. (1970). Indeterminist time and truth-value gaps. Theoria, 36, 264–811.
Thomason, S. K. (1972). Semantic analysis of tense logic. Journal of Symbolic Logic, 37, 150–158.
van Fraassen, B. (1966). Singular terms, truth-value gaps, and free logic. Journal of Philosophy, 63, 481–495.
Varzi, A. (1999). An essay in universal semantics. Berlin: Springer.
Acknowledgments
We are grateful to the referee for this journal. The referees for ANP2014 gave important suggestions for this paper. We have also benefited from the discussions with Max Cresswell, Kit Fine and Peter Øhrstrøm at ANP2014. We also wish to thank Lloyd Humberstone for valuable comments.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Akama, S., Murai, T. & Kudo, Y. Partial and paraconsistent approaches to future contingents in tense logic. Synthese 193, 3639–3649 (2016). https://doi.org/10.1007/s11229-015-0905-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-015-0905-z