This paper follows Part I of our essay on case-intensional first-order logic (CIFOL; Belnap and Müller (2013)). We introduce a framework of branching histories to take account of indeterminism. Our system BH-CIFOL adds structure to the cases, which in Part I formed just a set: a case in BH-CIFOL is a moment/history pair, specifying both an element of a partial ordering of moments and one of the total courses of events (extending all the way into the future) that that moment (...) is part of. This framework allows us to define the familiar Ockhamist temporal/modal connectives, most notably for past, future, and settledness. The novelty of our framework becomes visible in our discussion of substances in branching histories, i.e., in its first-order part. That discussion shows how the basic idea of tracing an individual thing from case to case via an absolute property is applicable in a branching histories framework. We stress the importance of keeping apart extensionality and moment-definiteness, and give a formal account of how the specification of natural sortals and natural qualities turns out to be a coordination task in BH-CIFOL. We also provide a detailed answer to Lewis’s well-known argument against branching histories, exposing the fallacy in that argument. (shrink)

But Findlay's remark, like so much that has been written on the subject of time in the present century, was provoked in the first place by McTaggart's ...

As we navigate through life, we model time as flowing, the present as special, and the past as “dead.” This model of time—manifest time—develops in childhood and later thoroughly infiltrates our language, thought, and behavior. It is part of what makes a human life recognizably human. Yet if physics is correct, this model of the world is deeply mistaken. This book is about this conflict between manifest and physical time. The first half dives into the physics and philosophy to establish (...) the conflict’s existence; but it also argues that the claim that physics “spatializes” time is overstated. Rather, even relativity theory makes time special in deep and significant ways. The second half turns to psychology, biology, and more, seeking to understand why creatures like us develop manifest time. The novel picture that results is that manifest time is a natural reaction to the many cognitive and evolutionary challenges that we face. For subjects embedded in our circumstances, it makes sense to develop—even if fundamentally wrong. (shrink)

The open future view is the common-sense view that there is an ontological difference between the past, the present, and the future in the sense that the past and the present are real, whereas the future is not yet a part of reality. In this paper we develop a theory in which the open future view is consistently combined with special relativity. Technically, the heart of our contribution is a logical conservativity result showing that, although the open future view is (...) not definable inside the causal geometry of Minkowski space-time, it can be conservatively added to it. (shrink)

Branching space-time is a simple blend of relativity and indeterminism. Postulates and definitions rigorously describe the causal order relation between possible point events. The key postulate is a version of everything has a causal origin; key defined terms include history and choice point. Some elementary but helpful facts are proved. Application is made to the status of causal contemporaries of indeterministic events, to how splitting of histories happens, to indeterminism without choice, and to Einstein-Podolsky-Rosen distant correlations.

There is no EPR-like funny business if (contrary to apparent fact)our world is as indeterministic as you wish, but is free from theEPR-like quantum mechanical phenomena such as is sometimes described interms of superluminal causation or correlation between distant events.The theory of branching space-times can be used to sharpen thetheoretical dichotomy between EPR-like funny business and noEPR-like funny business. Belnap (2002) offered two analyses of thedichotomy, and proved them equivalent. This essay adds two more, bothconnected with Reichenbachs principle of the (...) common cause, theprinciple that sends us hunting for a common-causal explanation ofdistant correlations. The two previous ideas of funny business and thetwo ideas introduced in this essay are proved to be all equivalent,which increases ones confidence in the stability of (and helpfulnessof) the BST analysis of the dichotomy between EPR-like funny businessand its absence. (shrink)

A proof is given that there does not exist an event, that is not already in the past for some possible distant observer at the (our) moment that the latter is "now" for us. Such event is as "legally" past for that distant observer as is the moment five minutes ago on the sun for us (irrespective of the circumstance that the light of the sun cannot reach us in a period of five minutes). Only an extreme positivism: "that which (...) cannot yet be observed does not yet exist", can possibly withstand the conclusion concerned. Therefore, there is determinism, also in micro-physics. (shrink)

N. Maxwell (1985) has claimed that special relativity and "probabilism" are incompatible; "probabilism" he defines as the doctrine that "the universe is such that, at any instant, there is only one past but many alternative possible futures". Thus defined, the doctrine is evidently prerelativistic as it depends on the notion of a universal instant of the universe. In this note I show, however, that there is a straightforward relativistic generalization, and that therefore Maxwell's conclusion that the special theory of relativity (...) should be amended is unwarranted. I leave open the question whether or not probabilism (or the related doctrine of the flow of time) is true, but argue that the special theory of relativity has no fundamental significance for this question. (shrink)

The theory of branching space-times is designed as a rigorous framework for modelling indeterminism in a relativistically sound way. In that framework there is room for "funny business", i.e., modal correlations such as occur through quantummechanical entanglement. This paper extends previous work by Belnap on notions of "funny business". We provide two generalized definitions of "funny business". Combinatorial funny business can be characterized as "absence of prima facie consistent scenarios", while explanatory funny business characterizes situations in which no localized explanation (...) of inconsistency can be given. These two definitions of funny business are proved to be equivalent, and we provide an example that shows them to be strictly more general than the previously available definitions of "funny business". (shrink)

A collection of 13 papers by David Lewis, written on a variety of topics including causation, counterfactuals and indicative conditionals, the direction of time, subjective and objective probability, explanation, perception, free will, and rational decision. The conclusions reached include the claim that time travel is possible, that counterfactual dependence is asymmetrical, that events are properties of spatiotemporal regions, that the Prisoners’ Dilemma is a Newcomb problem, and that causation can be analyzed in terms of counterfactual dependence between events. These papers (...) can be seen as a “prolonged campaign” for a philosophical position Lewis calls “Humean supervenience,” according to which “all there is to the world is a vast mosaic of local matters of particular fact,” with all global features of the world thus supervening on the spatiotemporal arrangement of local qualities. (shrink)

The subject of Time has a wide intellectual appeal across different dis ciplines. This has shown in the variety of reactions received from readers of the first edition of the present Book. Many have reacted to issues raised in its philosophical discussions, while some have even solved a number of the open technical questions raised in the logical elaboration of the latter. These results will be recorded below, at a more convenient place. In the seven years after the first publication, (...) there have been some noticeable newer developments in the logical study of Time and temporal expressions. As far as Temporal Logic proper is concerned, it seems fair to say that these amount to an increase in coverage and sophistication, rather than further break-through innovation. In fact, perhaps the most significant sources of new activity have been the applied areas of Linguistics and Computer Science (including Artificial Intelligence), where many intriguing new ideas have appeared presenting further challenges to temporal logic. Now, since this Book has a rather tight composition, it would have been difficult to interpolate this new material without endangering intelligibility. (shrink)

permits a sound and rigorously definable notion of ‘originating cause’ or causa causans—a type of transition event—of an outcome event. Mackie has famously suggested that causes form a family of ‘inus’ conditions, where an inus condition is ‘an insufficient but non-redundant part of an unnecessary but sufficient condition’. In this essay the needed concepts of BST theory are developed in detail, and it is then proved that the causae causantes of a given outcome event have exactly the structure of a (...) set of Mackie inus conditions. The proof requires the assumption that there is no EPR-like ‘funny business’. This seems enough to constitute a theory of ‘causation’ in at least one of its many senses. Introduction The cement of the universe Preliminaries 3.1 First definitions and postulates 3.2 Ontology: propositions 3.3 Ontology: initial events 3.4 Ontology: outcome events 3.5 Ontology: transition events 3.6 Propositional language applied to events Causae causantes 4.1 Causae causantes are basic primary transition events 4.2 Causae causantes of an outcome chain 4.3 No funny business Causae causantes and inns and inus conditions 5.1 Inns conditions of outcome chains: not quite 5.2 Inns conditions of outcome chains 5.3 Inns conditions of scattered outcome events 5.4 Inus conditions for disjunctive outcome events 5.5 Inns and inus conditions of transition events Counterfactual conditionals Appendix: Tense and modal connectives in BST. (shrink)

It has been repeatedly argued, most recently by Nicholas Maxwell, that the special theory of relativity is incompatible with the view that the future is in some degree undetermined; and Maxwell contends that this is a reason to reject that theory. In the present paper, an analysis is offered of the notion of indeterminateness (or "becoming") that is uniquely appropriate to the special theory of relativity, in the light of a set of natural conditions upon such a notion; and reasons (...) are given for regarding this conception as (not just formally consistent with relativity theory, but also) philosophically reasonable. The bearings upon Maxwell's program for quantum theory are briefly considered. (shrink)

The paper defends an Aristotelian notion of indeterminism, as rigorously formulated in the framework of branching space-times (BST) of Belnap (1992), against the model-theoretic characterization of indeterminism that Montague (1962) introduced into the philosophy of science. It delineates BST branching against the background provided by Earman's (2008) distinction between individual vs. ensemble branching. It describes a construction of physically-motivated BST models, in which histories are isomorphic to Minkowski spacetime. Finally it responds to criticism leveled against BST by addressing some semantical (...) questions, a topological issue, and the past/future asymmetry. (shrink)

1.: In this paper I discuss Putnam’s view on time and the special theory of relativity. I first locate Putnam’s philosophical approach within a more general framework, essentially making reference to Sellar’s distinction between the scientific image and the manifest image of the world. I then reconstruct Putnam’s argument in favour of the reality of the future and the determinateness of truth-value for future tense sentences by showing that it is based on three premises that generate a contradiction. In the (...) second part of the paper I discuss Putnam’s argument both by using later results belonging to the foundations of STR and quantum mechanics, and by invoking some conceptual analysis on the pseudo-predicate “is real”. Since I will show that the presentists/eternalists debate is ill-founded if regarded as ontological, I will conclude that it boils down to our different practical attitudes towards past, present and future. (shrink)

We investigate the concepts of past, present, and future that build upon a modal distinction between the settled past and the open future. The concepts are defined in terms of a pre-causal ordering and of qualitative differences between alternative histories. Finally, we look what an event's past, present, and future look like in the so-called Minkowskian Branching Structures, in which histories are isomorphic to Minkowski spacetime.

We introduce the notion of a Minkowskian Branching Structure ("MBS" for short). Then we prove some results concerning the phenomenon of funny business in its finitary and infinitary variants.

The paper gives a physicist's view on the framework of branching space-time, 385--434). Branching models are constructed from physical state assignments. The models are then employed to give a formal semantics for the modal operators ``possibly'' and ``necessarily'' and for the counterfactual conditional. The resulting formal language can be used to analyze quantum correlation experiments. As an application sketch, Stapp's premises LOC1 and LOC2 from his purported proof of non-locality, 300--304) are analyzed.