The thin red line (TRL) is a theory about the semantics of future-contingents. The central idea is that there is such a thing as the 'actual future', even in the presence of indeterminism. It is inspired by a famous solution to the problem of divine foreknowledge associated with William of Ockham, in which the freedom of agents is argued to be compatible with God's omniscience. In the modern branching time setting, the theory of the TRL is widely regarded to suffer from several fundamental problems. In this paper we propose several new TRL semantics, each with differing degrees of success. This leads up to our final semantics, which is a cross between the TRL and supervaluationism. We discuss the notions of truth, validity and semantic consequence which result from our final semantics, and demonstrate some of its pleasing results. This account, we believe, answers the main objection in the literature, and thus places the TRL on the same level as any other competing semantics for future contingents.

The purpose of the paper is to rethink the role of actuality in the branching model of possibilities. We investigate the idea that the model should be enriched with an additional factor-the so-called Thin Red Line-which is supposed to represent the single possible course of events that gets actualized in time. We believe that this idea was often misconceived which prompted some unfortunate reactions. On the one hand, it suggested problematic semantic models of future tense and and on the other, it provoked questionable lines of criticism. We reassess the debate and point to potential pitfalls, focusing on the semantic dimension of the Thin Red Line theory. Our agenda transcends the semantics, however. We conclude that semantic considerations do not threaten the Thin Red Line theory and that the proper debate should be carried in the domain of metaphysics.Keywords Branching time · Thin Red Line · Future contingents · Actualism The paper is structured as follows: In the first section, we motivate introduction of the Thin Red Line (TRL) and explain how it may be applied for semantic purposes. In the second, we outline the semantic objection raised against TRL theory by BelnapThe research of Jacek Wawer was funded by the Polish National Science Center (funds granted by the Decision Number DEC-2013/11/N/HS1/04805). Green (1994) according to which TRL theory treats temporal and modal operators inadequately. We explain how the objection may be overturned by a simple postsemantic maneuver-to interpret a sentence used at the time and the history of the context. The postsemantic move, which we ultimately recommend, appeals to the notion of the history of the context (which we identify with the actual history). In the third section we focus on a particular line of criticism of the simple postsemantics-the postsemantic problem of Belnap et al. (2001). In the next three sections, we discuss two postsemantic responses to the problem-by MacFarlane (2003) and by Malpass and Wawer (2012)-and outline some of their weak points. In the last section, we reassess and undermine the postsemantic problem. We argue that it is underlined by metaphysical assumptions alien to the TRL theory. When TRL is stated in its proper setting of modal actualism, the postsemantic problem has no teeth and the simple theory introduced in the second section turns out to be free of both semantic and postsemantic difficulties. Why do we need the Thin Red Line?The reasons supporting the TRL are twofold-metaphysical and semantic. As we shall see, these two domains are closely connected and the theoretical choices made in one domain usually affect the decisions made in another.Let us explore metaphysics first. The branching model is meant to represent the possible ways in which the world may develop (for detailed discussion of the model and its significance see e.g., Belnap et al. 2001;Rumberg 2016;Wawer 2016). As Aristotle noticed, the notion of possibility is intelligible only if contrasted with the notion of actuality. Thus, the branching represent...

The focus of this paper is an argument presented by Fara (2010), which is against supervaluationism in the context of vagueness. I show how it applies equally to the branching-time (BT) supervaluationism (first presented in Thomason 1970), but not to the closely related 'STRL' semantics of Malpass & Wawer (2012).Keywords: supervaluationism; branching-time; the Thin Red Line; semantics; truth.RESUMEN: Este artículo se centra en un argumento presentado por Fara (2010) en contra del supervaluacionismo en el contexto de la vaguedad. Muestro cómo dicho argumento es igualmente aplicable al supervaluacionismo de tiempo ramificado (presentado por primera vez por Thomason 1970), pero no a la semántica 'STRL' de Malpass y Wawer (2012), que está estrechamente relacionada.Palabras clave: supervaluacionismo; tiempo ramificado; la Delgada Línea Roja; semántica; verdad. IntroductionIn her (2010) article, "Scope Confusions and Unsatisfiable Disjuncts: Two Problems for Supervaluationism", Delia Graff Fara presents various problems for 'canonical supervaluationism' (i.e. the supervaluationism of Fine 1975), the first of which I shall concentrate on in this paper. The problem consists in a troublesome formula, that I will call 'Fara's Formula' (FF), which she demonstrates is satisfiable in the supervaluationist semantics. I shall show that her problem affects the BT account of supervaluationism that most closely approaches Fine's canonical version (that of Thomason 1970Thomason , 2002. However, my main aim will be to demonstrate that there is a closely related theory in the BT context which avoids this problem; the Supervaluational Thin Red Line (STRL) semantics of Malpass & Wawer (2012). FF: true disjunctions with impossible disjunctsDelia Fara presents supervaluationism with a new complaint in her (2010) paper. Fara's complaint is a development of a well known difficulty with the theory. Put simply, the supervaluationist allows for (super-)true disjunctions with (super-)truthvalueless disjuncts. The idea is that it is unacceptable that, for example, it is (super-)true that 'either Juan or Carlos is the shortest person in the room', even though there is no (super-true) answer to 'which one is it?' (see Fara 2010, 376). In general the problem is as follows:* I would like to give thanks for their comments and contributions to Delia Graff Fara, Peter Øhrstrøm, Jacek Wawer, audiences in both Bristol and Cambridge and two anonymous referees.

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It is often said that time must have a beginning because otherwise the series of past events would have the paradoxical features of an actual infinite. In the present paper, we show that, even given a dynamic theory of time, the cardinality of an endless series of events, each of which will occur, is the same as that of a beginningless series of events, each of which has occurred. Both are denumerably infinite. So if (as we believe) an endless series of events is possible, then the possibility of a beginningless series of past events should not be rejected merely on the ground that it would be an actual infinite. What would be required to rebut our argument is a symmetry breaker – something that motivates treating the past relevantly differently to the future. We consider several attempts to provide a symmetry breaker and show that none of them is successful.