The Problem of Index-Initialisation in the Tempo-Modal Semantics


future contingents
semantics of modal languages
context dependence
modal metaphysics



In Kripke-semantics for modal logic, the truth value of a sentence depends on the choice of a semantic index (e.g. world, time, or place). It means that application of such semantics to natural language analysis requires indication of an index relevant for semantic analysis. It is commonly accepted that the relevant index is initialised by the context of an utterance. The idea has been rejected by the semanticists investigating tempo-modal languages in the framework of indeterminism, which generated the problem of initialization of the semantic index. I present the main argument of those semanticists and describe several responses to the initialisation problem. I finally argue that under certain metaphysical and semantic assumptions, one can respond to the initialisation failure in the classical way, even in indeterministic contexts.



Adams, R. M. (1974). Theories of Actuality. Noûs, 8(3), 211–231.

Belnap, N. (2002). Double Time References: Speech-Act Reports as Modal-ities in an Indeterminist Setting. In: D. Wolter, H. Wansing, M. de Rijke, M. Zakharyaschev (Eds.), Advances in Modal Logic (vol. 3, pp. 37–58). Singapore: World Scientific.

Belnap, N., Perloff, M., Xu, M. (2001). Facing the Future: Agents and Choices in Our Indeterministic World, New York: Oxford University Press.

van Fraassen, B. C. (1966). Singular Terms, Truth-Value Gaps, and Free Logic. Journal of Philosophy, 63(17), 481–495.

Kaplan, D. (1989). Afterthoughts. In: J. Almong, J. Perry, H. Wettstein (Eds.), Themes from Kaplan (pp. 565–614). New York: Oxford Univer-sity Press.

King, J. C. (2003). Tense, Modality, and Semantic Values. Philosophical Perspectives, 17(1), 195–246.

Kotarbiński, T. (1913). Zagadnienie istnienia przyszłości [„The Problem of the Existence of the Future]. Przegląd Filozoficzny, 16(1), 74–92.

Kripke, S. (1980). Naming and Necessity. Cambridge, Mass.: Harvard University Press.

Leśniewski, S. (1913). Czy prawda jest tylko wieczna czy też odwieczna [Is Truth Only Eternal or Both Eternal and Sempiternal?]. Nowe Tory, 10, 493–528.

Lewis, D. (1970). Anselm and Actuality. Noûs, 4(2), 175–188.

Lewis, D. (1986). On the Plurality of Worlds. Oxford: Blackwell Publish-ers.

Łukasiewicz, J. (1957). Aristotle’s Syllogistic from the Standpoint of Modern Formal Logic (2nd edition). Oxford: Oxford University Press.

Łukasiewicz, J. (1961). O determinizmie [On Determinism]. In: J. Słupecki (Ed.), Z zagadnień logiki i filozofii (pp. 114–126). Warszawa: PWN.

MacFarlane, J. (2003). Future Contingents and Relative Truth. The Phil-osophical Quarterly, 53(212), 321–336.

MacFarlane, J. (2008). Truth in the Garden of Forking Paths. In: M. Gar-cía-Carpintero, M. Kölbel (Eds.), Relative Truth (81–102). Oxford: Ox-ford University Press.

MacFarlane, J. (2014). Assessment Sensitivity: Relative Truth and Its Applications. Oxford: Clarendon Press.

Plantinga, A. (1974). The Nature of Necessity. New York: Oxford Univer-sity Press.

Ploug, T., Øhrstrøm, P. (2012). Branching Time, Indeterminism and Tense Logic. Synthese, 188(3), 367–379.

Prior, A. (1966). Postulates for Tense-Logic. American Philosophical Quarterly 3(2), 153–161.

Prior, A. (1967). Past, Present and Future. Oxford: Clarendon Press.

Stalnaker, R. (1976). Possible Worlds. Noûs, 10(1), 65–75.

Thomason, R. H. (1970). Indeterminist Time and Truth-Value Gaps. The-oria, 36(3), 264–281.

Thomason, R. H. (1984). Combinations of Tense and Modality. In:

D. Gabbay, F. Guenthner (Eds.), Handbook of Philosophical Logic (vol. 2, pp. 135–165). Dordrecht: D. Reidel Publishing Company.

Twardowski, K. (1900). O tzw. prawdach względnych [On the So-Called Relative Truths]. In: Księga Pamiątkowa Uniwersytetu Lwowskiego ku uczczeniu pięćsetnej rocznicy Fundacji Jagiellońskiej (pp. 64–93). Lviv: University of Lviv.

Wawer, J. (2014). The Truth about the Future. Erkenntnis, 79(3), 365–401.

Wawer, J. (2016). Branching Time and the Semantics of Future Contin-gents (doctoral dissertation). Kraków: Jagiellonian University.

Woleński, J. (1990). Kotarbiński, Many-Valued Logic, and Truth. In: J. Woleński (Ed.), Kotarbiński: Logic, Semantics and Ontology (191–198), Dordrecht: Kluwer Academic Publishers.