Assertions and future tense semantics

Non-bivalent semantics of the future tense assert that propositions regarding future contingents are neither true nor false. One of the most relevant non-bivalent semantics is supervaluationism (Thomason in Theoria 36(3):264–281, 1970; Thomason, in: Gabbay, Guenthner (eds) Handbook of philosophical logic, Springer, Berlin, 1984), which preserves important logical principles. Recently, non-bivalent semantics are under attack from some pragmatics arguments: these semanticswould be incompatible with our practices of asserting future contingents and with the probability we ascribe to such assertions (Besson and Hattiangadi in Philosophical Studies 167(2):251–271, 2014; Cariani and Santorio in Mind 127(505):129–165, 2018). The aim of this paper is to defend supervaluationism against this kind of criticism.We argue that, if probability is interpreted as the subjective belief in a proposition and if a semantic contextualism is adopted, supervaluationism makes correct predictions concerning the norms that govern our practices of asserting future contingents. Obviously, other arguments can be proposed against supervaluationism, but they must be of a different kind, such as metaphysical arguments.