This paper investigates the prospects of developing a branching modal framework while keeping with the spirit of Humean Supervenience. It is argued that such an approach is bound to face hard problems regarding haecceitism and the notion of recombination. Possible directions for future philosophical developments of branching frameworks are suggested.

This paper provides a short historical and systematic survey of parameters, problems, and proposals concerning the theoretical treatment of indivisible temporal boundaries throughout the ages. A very early trace of thinking about them is identified in Aristophanes’ comedy The Clouds. The approach of logicians in the late Middle Ages is placed in a broad context. Links of this topic to the issues of vagueness, modality, space and quantized time are discussed.

Open futurism is the indeterministic position according to which the future is ‘open’, i.e., there is now no fact of the matter as to what future contingent events will actually obtain. Many open futurists hold a branching conception of time, in which a variety of possible futures exist. This paper introduces two challenges to branching-time open futurism, which are similar in spirit to a challenge posed by Fine to tense realism. The paper argues that, to address the new challenges, open (...) futurists must adopt an objective, non-perspectival notion of actuality and subscribe to an A-theoretic, dynamic conception of reality. Moreover, given a natural understanding of “actual future”, it is perfectly sensible for open futurists to hold that a unique, objectively actual future exists, contrary to a common assumption in the current debate. The paper also contends that recognising the existence of a unique actual future helps open futurists to avoid potential misconceptions. (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)

The transition semantics presented in Rumberg (J Log Lang Inf 25(1):77–108, 2016a) constitutes a fine-grained framework for modeling the interrelation of modality and time in branching time structures. In that framework, sentences of the transition language L_t are evaluated on transition structures at pairs consisting of a moment and a set of transitions. In this paper, we provide a class of first-order definable Kripke structures that preserves L_t-validity w.r.t. transition structures. As a consequence, for a certain fragment of L_t, validity (...) w.r.t. transition structures turns out to be axiomatizable. The result is then extended to the entire language L_t by means of a quite natural ‘Henkin move’, i.e. by relaxing the notion of validity to bundled structures. (shrink)

The transition semantics presented in Rumberg :77–108, 2016a) constitutes a fine-grained framework for modeling the interrelation of modality and time in branching time structures. In that framework, sentences of the transition language \ are evaluated on transition structures at pairs consisting of a moment and a set of transitions. In this paper, we provide a class of first-order definable Kripke structures that preserves \-validity w.r.t. transition structures. As a consequence, for a certain fragment of \, validity w.r.t. transition structures turns (...) out to be axiomatizable. The result is then extended to the entire language \ by means of a quite natural ‘Henkin move’, i.e. by relaxing the notion of validity to bundled structures. (shrink)

This paper gives an overview of logico-philosophical issues of time and determinism. After a brief review of historical roots and 20th century developments, three current research areas are discussed: the definition of determinism, space-time indeterminism, and the temporality of individual things and their possibilities.

In this paper we describe a novel approach to defining an ontologically fundamental notion of co-presentness that does not go against the tenets of relativity theory. We survey the possible reactions to the problem of the present in relativity theory, introducing a terminological distinction between a static role of the present, which is served by the relation of simultaneity, and a dynamic role of the present, with the corresponding relation of co-presentness. We argue that both of these relations need to (...) be equivalence relations, but they need not coincide. Simultaneity, the sharing of a temporal coordinate, need not have fundamental ontological import, so that a relativizing strategy with respect to simultaneity seems promising. The notion of co-presentness, on the other hand, does have ontological import, and can therefore not be relativized to an observer or to an arbitrarily chosen frame. We argue that a formal representation of indeterminism can provide the structure needed to anchor the relation of co-presentness, and that this addition is in fact congenial to the notion of dynamic time as requiring real change. The resulting picture is one of an extended dynamic present, implying a formal distinction between static simultaneity and dynamic co-presentness. After working out the basics of our approach in the simpler framework of branching time, we provide our full analysis in the framework of branching space-times, which allows for a formal definition of modal correlations. The spatial extension of the dynamic present can reach as far as the modal correlations do. In the limit, the dynamic present could extend across a maximal space-like hypersurface. (shrink)

The theory of branching space-times, put forward by Belnap, considers indeterminism as local in space and time. In the axiomatic foundations of that theory, so-called choice points mark the points at which the possible future can turn out in different ways. Working under the assumption of choice points is suitable for many applications, but has an unwelcome topological consequence that makes it difficult to employ branching space-times to represent a range of possible physical space-times. Therefore it is interesting to develop (...) a branching space-times theory without choice points. This is what we set out to do in this paper, providing new foundations for branching space-times in terms of choice sets rather than choice points. After motivating and developing the resulting theory in formal detail, we show that it is possible to translate structures of one style into structures of the other style and vice versa. This result shows that the underlying idea of indeterminism as the branching of spatio-temporal histories is robust with respect to different implementations, making a choice between them a matter of expediency rather than of principle. (shrink)

This work aims to make tense logic a more robust tool for ontologists, philosophers, knowledge engineers and programmers by outlining a fusion of tense logic and ontology of time. In order to make tense logic better understandable, the central formal primitives of standard tense logic are derived as theorems from an informal and intuitive ontology of time. In order to make formulation of temporal propositions easier, temporal operators that were introduced by Georg Henrik von Wright are developed, and mapped to (...) the ontology of time. (shrink)