A B S T R AC T: In this paper I consider an interpretation of future contingents which motivates a unification of a Łukasiewicz-style logic with the more classical supervaluational semantics. This in turn motivates a new non-classical logic modelling what is “made true by history up until now. ” I give a simple Hilbert-style proof theory, and a soundness and completeness argument for the proof theory with respect to the intended models.

In an earlier paper by the author, Åqvist , I presented an approach to the logic of historical necessity, or inevitability, in the sense of a “two-dimensional” combination of tense and modal logic for worlds, or histories, with the same time order, known as T × W logic. Distinctive features of that approach were, apart from its two-dimensionality, its being based on discrete and finite time, and its use of so-called systematic frame constants in order to enable us to indicate (...) longitudes and latitudes of any points in the co-ordinate systems under consideration. This led us to study and axiomatize an infinite hierarchy HTWxy of two-dimensional modal tense logics with the characteristic operators for historical necessity and possibility added to the original basic vocabulary. The main purpose of the present paper is then twofold: to extend the logics HTWxy to the interesting branch of philosophical logic constituted by deontic logic as combined with tense logic; and to deal with a curious puzzle known as the so-called epistemic obligation paradox – a well known stumbling-block in this area of research in philosophical logic. We argue for a solution to both these problems, which appeals to a new infinite hierarchy DHTWxym of extensions of the HTWxy in the sense of logics combining dyadic deontic modalities with temporal ones such as those for historical necessity and other two-dimensional modalities. (shrink)

A fairly simple theory of the semantics of tense is obtained by combining three claims: (i) for any time t, a present-tense sentence `p' is either true or false at t; (ii) for any time t0 earlier than t, the future-tense sentence `It will be the case that p at t' is true at t0 if `p' is true at t, false otherwise; (iii) for any time t0 later than t, the past-tense sentence `It was the case that p at (...) t' is true at t0 if `p' is true at t, false otherwise. This theory, which has been called the theory of timeless truth, is often dismissed on the basis of its alleged incapacity to comply with indeterminism. Here, instead, it will be suggested that there is no reason to be dismissive. Section 1 provides some elucidations about the theory. Sections 2 and 3 explain how a foregone objection to it can be resisted. Sections 4 and 5 show that there is a plausible sense in which (i)-(iii) are compatible with indeterminism. Sections 6 and 7 dispel some misunderstandings that may lead to think that indeterminism is not vindicated in some important sense other than that outlined. (shrink)

Ockhamism implies that future contingents may be true, their historical contingency notwithstanding. It is thus opposed to both the Peircean view according to which all future contingents are false, and Supervaluationist Indeterminism according to which all future contingents are neither true nor false. The paper seeks to defend Ockhamism against two charges: the charge that it cannot meet the requirement that truths be grounded in reality, and the charge that it proves incompatible with objective indeterminism about the future. In each (...) case, the defence draws on the idea that certain truths are truths only courtesy of others and of what makes the latter true. After introduction of the Ockhamist view, its competitors and implications, a suitable definition of grounded truth is being devised that both is faithful to the spirit of the grounding-requirement and allows the Ockhamist to heed that requirement quite comfortably. Then two senses in which the future might be open are being introduced, indeterminacy as failure of predetermination by past and present facts, and indeterminacy as failure of entailment by past and present truths. It is argued that while openness in the former sense, but not in the latter sense, coheres with the Ockhamist view, it is only openness in the former sense that matters for objective indeterminism. (shrink)

This paper suggests an epistemic interpretation of Belnap’s branching space-times theory based on Everett’s relative state formulation of the measurement operation in quantum mechanics. The informational branching models of the universe are evolving structures defined from a partial ordering relation on the set of memory states of the impersonal observer. The totally ordered set of their information contents defines a linear “time” scale to which the decoherent alternative histories of the informational universe can be referred—which is quite necessary for assigning (...) them a probability distribution. The “historical” state of a physical system is represented in an appropriate extended Hilbert space and an algebra of multi-branch operators is developed. An age operator computes the informational depth of historical states and its standard deviation can be used to provide a universal information/energy uncertainty relation. An information operator computes the encoding complexity of historical states, the rate of change of its average value accounting for the process of correlation destruction inherent to the branching dynamics. In the informational branching models of the universe, the asymmetry of phenomena in nature appears as a mere consequence of the subject’s activity of measuring, which defines the flow of time-information. (shrink)

In the tree-like representation of Time, two histories are undivided at a moment t whenever they share a common moment in the future of t. In the present paper, it will first be proved that Ockhamist and Peircean branching-time logics are unable to express some important sentences in which the notion of undividedness is involved. Then, a new semantics for branching-time logic will be presented. The new semantics is based on trees endowed with an indistinguishability function, a generalization of the (...) notion of undividedness. It will be shown that Ockhamist and Peircean semantics can be viewed as limit cases of the semantics developed in this paper. (shrink)

This essay uses a puzzle about assertion and time to explore the pragmatics, semantics, and epistemology of future discourse. The puzzle concerns cases in which a subject is in a position to say, at an initial time t, that it will be that ϕ, but is not in a position to say, at a later time t′, that it is or was that ϕ, despite not losing or gaining any relevant evidence between t and t′. We consider a number of (...) approaches to the puzzle and defend the view that subjects in these cases lose knowledge simply by moving through time. (shrink)

We care not only about what experiences we have, but when we have them too. However, on the B-theory of time, something’s timing isn’t an intrinsic way for that thing to be or become. Given B-theory, should we be rationally indifferent about the timing per se of an experience? In this paper, I argue that B-theorists can justify time-biased preferences for pains to be past rather than present and for pleasures to be present rather than past. In support of this (...) argument, I appeal to the doctrine of temporal parts or “four-dimensionalism” for short. When held in conjunction with a certain evaluative principle about whose experiences matter, four-dimensionalism reconciles B-theory with some time-biased preferences. (shrink)

In this paper we present BTC, which is a complete logic for branchingtime whose modal operator quantifies over histories and whose temporal operators involve a restricted quantification over histories in a given possible choice. This is a technical novelty, since the operators of the usual logics for branching-time such as CTL express an unrestricted quantification over histories and moments. The value of the apparatus we introduce is connected to those logics of agency that are interpreted on branching-time, as for instance (...) Stit Logics. (shrink)

Over the past few years, the tree model of time has been widely employed to deal with issues concerning the semantics of tensed discourse. The thought that has motivated its adoption is that the most plausible way to make sense of indeterminism is to conceive of future possibilities as branches that depart from a common trunk, constituted by the past and the present. However, the thought still needs to be further articulated and defended, and several important questions remain open, such (...) as the question of how actuality can be understood and formally represented in a branching framework. The present volume is intended to be a 360 degree reflection on the tree model. The contributions is gathers concern the model and its alternatives, both from a semantic and from a metaphysical point of view. ​. (shrink)

unified treatment of both (families of) interpretations is based on a revised notion of settledness. The main features of this approach are the following: (i) in branching structures, a world can be represented not by a single course of events, but by a node u in the tree, where u itself is seen as the cluster of courses of events passing through it; (ii) the utterance time is uniquely fixed; (iii) the utterance world is not uniquely fixed; (iv) because of (...) (iii), an utterance-event is associated not to a single context, but to a plurality of contexts, depending on which world we are considering as the utterance world. As a consequence, if a future-tensed sentence φ is uttered at u and its truth (falsehood) is already a settled issue at u itself, then the sentence is true (false) at u; otherwise the sentence is neither true nor false at u and, to get a definite truth value, we must wait until settledness is reached in a different context. Since what is crucial, in both cases, is the reference to a given state of information, such a treatment can be extended to other intriguing uses of the future tense, starting from the epistemic reading. These uses will be topic of a related paper. (shrink)

According to the actualist view, what is essential to the truth conditions of a future-tensed sentence ‘it will be the case that ϕ’ is reference to the unique course of events that will become actual. On the other hand, the modal view has it that the truth conditions of such a sentence require that the truth of ϕ be already “settled” at the time of utterance, where “being settled at time t” is defined by universal quantification over a domain of (...) courses of events, the futures compatible with what has happened up to time t. On the proposal we discuss in this paper, the actualist view and the modal view are seen as two related attitudes that speakers can have when they evaluate future-tensed sentences, and the corresponding interpretations undergo a unified semantic treatment based on a contextual notion of settledness. A central feature of our approach is a dynamic view of contexts of utterance, whereby the world of the utterance is not fixed once and for all, as different worlds, by the passing of time, can play this role in turn. Finally, one major goal of the paper is to show how the unified analysis we propose accounts for a particularly interesting interpretation of future-tensed sentences, often referred to as ‘epistemic reading’. (shrink)

The species of indeterminist tense logic called Peircean by A. N. Prior is proved to be recursively decidable.

Temporal logic is one of the many areas in which a possible world semantics is adopted. Prior's Ockhamist and Peircean semantics for branching-time, though, depart from the genuine Kripke semantics in that they involve a quantification over histories, which is a second-order quantification over sets of possible worlds. In the paper, variants of the original Prior's semantics will be considered and it will be shown that all of them can be viewed as first-order counterparts of the original semantics.

The basic notions in Prior's Ockhamist and Peircean logics of branching-time are the notion of moment and that of history. In the tree semantics, histories are defined as maximal linearly ordered sets of moments. In the geometrical approach, both moments and histories are primitive entities and there is no set theoretical dependency of the latter on the former. In the topological approach, moments can be defined as the elements of a rank 1 base of a non-Archimedean topology on the set (...) of histories. In this paper, it will be shown that the topological approach, and hence the other approaches, can be reconstructed in a framework in which the basic notions are those of history and of relative closeness relation among histories. (shrink)

Many philosophers take for granted that there is a strong pre‐theoretical intuition that the future is open and that it is worth trying to make sense of that intuition in theoretical terms. In this paper, I give a characterisation of the ordinary intuition in terms of three elements: our sense of agency, the difference in normativity between memories and expectations and naïve understanding of causality. Those intuitions allow us to pin down certain desiderata that an account of openness should respect. (...) Firstly, the fact that the future is open is not merely due to our epistemic situation (the fact that we do not know what the future will bring). Secondly, openness is not merely a matter of nomological indeterminism; even if indeterminism is part of what makes the future open, it cannot be the end of the story. Thirdly, openness requires more than ‘modal flexibility’ (i.e. the fact that the future could be different from what actually will be). I provide a minimal theory of openness, which respects those desiderata and which is based on the semantic notion of unsettledness and the metaphysical notion of indeterminacy. Roughly, the future is open if future‐tensed claims concerning contingent matters are such that their truth value is presently unsettled, and they are semantically unsettled because the future is metaphysically indeterminate. I then argue that this theory is compatible with what I call the closed future view. According to the latter, there is only one way in which things will go, although, given indeterminism, it is unsettled which way it is. I then consider an objection to my compatibility claim: if the open future claim is metaphysically substantive, there should be a way to differentiate it from the closed future scenario. I consider whether a friend of openness could rely on a dynamic metaphysics of time (such as presentism, or the growing block view) in order to differentiate their position from the closed future scenario. I argue that the appeal to a dynamic universe is ineffective. (shrink)

Indicative conditionals with present tense antecedents can have ‘shifted’ readings that are unexpected given the semantic behavior of the tenses outside of conditionals. In this paper, we compare two accounts of this phenomenon due to Kaufmann (J Semant 22(3):231–280, 2005) and Schulz (SALT XVIII, pp. 694–710, 2008), by reconstructing them in the framework of branching time. We then propose a novel account of indicative conditionals based on the branching time semantics suggested in Rumberg (J Logic Lang Inf 25(1):77–108, 2016), viz. (...) transition semantics. We show that not only is the account of ‘shifted’ readings with present tense antecedents within this semantics very natural, but it also is empirically superior to its rivals in some respects. (shrink)