The title alone of McCall’s book reveals its ambitious enterprise. The book’s structure is a long inference to the best explanation: chapters present problems that are solved by a single, ontological model. Problems as diverse as time flow, quantum measurement, counterfactual semantics, and free will are discussed. McCall’s style of writing is lucid and pointed—in general, very pleasant to read.

J. M. E. McTaggart, in a famous argument, denied the reality of time because he thought that passage or temporal becoming was essential for the existence of time and that passage was a self-contradictory concept. This denial of passage has provoked a vast literature, two of the most important contributions being C. D. Broad’s painstaking defence of passage in his Examination of McTaggart’s Philosophy and D. C. Williams’ dazzling condemnation of it “The Myth of Passage.” -/- A careful reading of (...) these apparently opposed essays reveals that there is a common notion of passage that both philosophers endorse, the successive occurrence of sets of simultaneous events (assuming classical or Newtonian spacetime structure as background). This unexpected agreement provides a notion of the passage of time that, I claim, is lean enough to survive the criticisms of passage-deniers yet robust enough to satisfy the requirements of passage-affirmers. I undertake to describe and defend this notion. -/- . (shrink)

This essay is the first act of a two-act play. My ultimate aim is to defend a simple proposition: time passes. To be more precise, I want to defend the claim that the passage of time is an intrinsic asymmetry in the structure of space-time itself, an asymmetry that has no spatial counterpart and is metaphysically independent of the material contents of space-time. It is independent, for example, of the entropy gradient of the universe. This view is part of common-sense, (...) but has been widely attacked by philosophers. The passage of time, we are told, is a myth, an illusion, even an incoherent notion. Because the notion that time passes is common sense, it perhaps requires little positive defence; if there are no weighty objections to the view, it ought to be accepted. So the first, and more important, act of the play is defusing the arguments which have been used to cast doubt on the passage of time. I have positive arguments to give, but not having space for them here, I will confine myself to an examination of the common philosophical arguments that have been used to cast doubt on the passage of time. (shrink)

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.

Are probabilism and special relativity compatible? Dieks argues that they are. But the possible universe he specifies, designed to exemplify both probabilism and special relativity, either incorporates a universal “now”, or amounts to a many world universe, or fails to have any one definite overall Minkowskian-type space-time structure. Probabilism and special relativity appear to be incompatible after all. What is at issue is not whether “the flow of time” can be reconciled with special relativity, but rather whether explicitly probabilistic versions (...) of quantum theory should be rejected because of incompatibility with special relativity. (shrink)

This book is a defense of modal realism; the thesis that our world is but one of a plurality of worlds, and that the individuals that inhabit our world are only a few out of all the inhabitants of all the worlds. Lewis argues that the philosophical utility of modal realism is a good reason for believing that it is true.

I discuss three connections between Dummett's writings about time and philosophical aspects of physics. The first connection arises from remarks of Dummett's about the different relations of observation to time and to space. The main point is uncontroversial and applies equally to classical and quantum physics. It concerns the fact that perceptual processing is so rapid, compared with the typical time-scale on which macroscopic objects change their observable properties, that it engenders the idea of a `common now', spread across space. (...) The other two connections are specific to quantum theory, as interpreted along the lines of Everett. So for these two connections, the physics side is controversial, just as the philosophical side is. In Section 3, I connect the subjective uncertainty before an Everettian `splitting' of the multiverse to Dummett's suggestion, inspired by McTaggart, that a complete, i.e. indexical-free description of a temporal reality is impossible. And in Section 4, I connect Barbour's denial that time is real---a denial along the lines of Everett, rather than McTaggart---to Dummett's suggestion that statements about the past are not determinately true or false, because they are not effectively decidable. (shrink)

This is the text of The Lindley Lecture for 1962, given by Arthur N. Prior (1914-1969).

Growing-Block theorists hold that past and present things are real, while future things do not yet exist. This generates a puzzle: how can Growing-Block theorists explain the fact that some sentences about the future appear to be true? Briggs and Forbes develop a modal ersatzist framework, on which the concrete actual world is associated with a branching-time structure of ersatz possible worlds. They then show how this branching structure might be used to determine the truth values of future contingents. They (...) point out three different ways of interpreting the logical connectives, which give rise to three different logics of the open future: one supervaluationist, one corresponding to Lukasiewicz's strong Kleene logic, and one intuitionist. (shrink)

I offer an interpretation and a partial defense of Kit Fine's ‘Argument from Passage’, which is situated within his reconstruction of McTaggart's paradox. Fine argues that existing A-theoretic approaches to passage are no more dynamic, i.e. capture passage no better, than the B-theory. I argue that this comparative claim is correct. Our intuitive picture of passage, which inclines us towards A-theories, suggests more than coherent A-theories can deliver. In Finean terms, the picture requires not only Realism about tensed facts, but (...) also Neutrality, i.e. the tensed facts not being ‘oriented towards’ one privileged time. However unlike Fine, and unlike others who advance McTaggartian arguments, I take McTaggart's paradox to indicate neither the need for a more dynamic theory of passage nor that time does not pass. A more dynamic theory is not to be had: Fine's ‘non-standard realism’ amounts to no more than a conceptual gesture. But instead of concluding that time does not pass, we should conclude that theories of passage cannot deliver the dynamicity of our intuitive picture. For this reason, a B-theoretic account of passage that simply identifies passage with the succession of times is a serious contender. (shrink)

In this paper I assess the prospects for combining contemporary Everettian quantum mechanics (EQM) with branching-time semantics in the tradition of Kripke, Prior, Thomason and Belnap. I begin by outlining the salient features of ‘decoherence-based’ EQM, and of the ‘consistent histories’ formalism that is particularly apt for conceptual discussions in EQM. This formalism permits of both ‘branching worlds’ and ‘parallel worlds’ interpretations; the metaphysics of EQM is in this sense underdetermined by the physics. A prominent argument due to Lewis (On (...) the Plurality of Worlds, 1986 ) supports the non-branching interpretation. Belnap et al. (Facing the Future: Agents and Choices in Our Indeterministic World, 2001 ) refer to Lewis’ argument as the ‘Assertion problem’, and propose a pragmatic response to it. I argue that their response is unattractively ad hoc and complex, and that it prevents an Everettian who adopts branching-time semantics from making clear sense of objective probability. The upshot is that Everettians are better off without branching-time semantics. I conclude by discussing and rejecting an alternative possible motivation for branching time. (shrink)

A commonly held idea regarding the nature of time is that the future is open and the past is fixed or closed. This article investigates the notion that there is an asymmetry in openness between the past and the future. The following questions are considered: How exactly is this asymmetry in openness to be understood? What is the relation between an open future and various ontological views about the future? Is an open future a branching future? What is the relation (...) between an open future and the question of whether contingent statements about the future are true or false? Is an open future compatible with a single determinate future? (shrink)

The question I want to explore is whether experience supports an antireductionist ontology of time, that is, whether we should take it to support an ontology that includes a primitive, monadic property of nowness responsible for the special feel of events in the present, and a relation of passage that events instantiate in virtue of literally passing from the future, to the present, and then into the past.

A modest proposal concerning laws, counterfactuals, and explanations - - Why be Humean? -- Suggestions from physics for deep metaphysics -- On the passing of time -- Causation, counterfactuals, and the third factor -- The whole ball of wax -- Epilogue : a remark on the method of metaphysics.

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

From García-Carpintero and Kölbel, eds, Relative Truth.

There is a common form of problem, to be found in many areas of philosophy, concerning the relationship between our perspective on reality and reality itself. We make statements (or form judgements) about how things are from a given standpoint or perspective. We make the statement ‘it is raining’ from the standpoint of the present time, for example, or the statement‘it is here’ from the standpoint of where we are, or the statement ‘I am glad’ from the standpoint of a (...) subject. In each of these cases, the statement has a certain ‘aspect’ or perspectival character in virtue of which its truth is capable of varying from one standpoint to another. Thus the statement ‘it is raining’ is tensed, the statement ‘it is here’ is ‘spatiocentric’ and the statement ‘I am glad’ is first-personal. The problem we then face is to determine whether this aspect is a feature of the reality which is described or merely a feature of the statement by which it is described. Is reality itself somehow tensed or spatiocentric or firstpersonal or is it merely that we describe a tenseless or spatially uncentered or impersonal reality from a tensed or spatiocentric or first-personal point of view? (shrink)

The manifest image is teeming with activity. Objects are booming and buzzing by, changing their locations and properties, vivid perceptions are replaced, and we seem to be inexorably slipping into the future. Time—or at least our experience in time— seems a very turbulent sort of thing. By contrast, time in the scientist image seems very still. The fundamental laws of physics don’t differentiate between past and future, nor do they pick out a present moment that flows. Except for a minus (...) sign in the relativistic metric, there are few differences between the temporal and spatial coordinates in natural science. We seem to have, to echo another debate, an “explanatory gap” between time as we find it in experience and as we find it in science. Reconciling these two images of the world is the principal goal of philosophy of time. (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.

∗ Apologies to Mark Hinchliff for stealing the title of his dissertation. (See Hinchliff, A Defense of Presentism. As it turns out, however, the version of Presentism defended here is different from the version defended by Hinchliff. See Section 3.1 below.).

If it is not now determined whether there will be a sea battle tomorrow, can an assertion that there will be one be true? The problem has persisted because there are compelling arguments on both sides. If there are objectively possible futures which would make the prediction true and others which would make it false, symmetry considerations seem to forbid counting it either true or false. Yet if we think about how we would assess the prediction tomorrow, when a sea (...) battle is raging (or not), it seems we must assign the utterance a definite truth-value. I argue that both arguments must be given their due, and that this requires relativizing utterance-truth to a context of assessment. I show how this relativization can be handled in a rigorous formal semantics, and I argue that we can make coherent sense of assertion without assuming that utterances have their truth-values absolutely. (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.

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)

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)

A theory of temporal passage is put forward which is "objective" in the sense that time flow characterizes the universe independently of the existence of conscious beings. The theory differs from Grunbaum's "mind-dependence" theory, and is designed to avoid Grunbaum's criticisms of an earlier theory of Reichenbach's. The representation of temporal becoming is accomplished by the introduction of indeterministic universe-models; each model representing the universe at a time. The models depict the past as a single four-dimensional manifold, and the future (...) as a branched structure of such manifolds. Time flow is relativistic in that it manifests itself in a frame-dependent (but not observer-dependent) way. The indeterministic character of the universe-models is mirrored in a "temporal" theory of truth which rejects the principle of bivalence, and suitable semantics are provided for this theory. Finally, an account of physical law is given which defines it in terms of physical possibility, rather than vice versa. (shrink)

In this paper I expound an argument which seems to establish that probabilism and special relativity are incompatible. I examine the argument critically, and consider its implications for interpretative problems of quantum theory, and for theoretical physics as a whole.

It is common to dismiss the passage of time as illusory since its passage has not been captured within modern physical theories. I argue that this is a mistake. Other than the awkward fact that it does not appear in our physics, there is no indication that the passage of time is an illusion.

“Branching space-times” (BST) is intended as a representation of objective, event-based indeterminism. As such, BST exhibits both a spatio-temporal aspect and an indeterministic “modal” aspect of alternative possible historical courses of events. An essential feature of BST is that it can also represent spatial or space-like relationships as part of its (more or less) relativistic theory of spatio-temporal relations; this ability is essential for the representation of local (in contrast with “global”) indeterminism. This essay indicates how BST might be seen (...) to grow out of Newton’s deterministic and non-relativistic theory by two independent moves: (1) Taking account of indeterminism, and (2) attending to spatio-temporal relationships in a spirit derived from Einstein’s theory of special relativity. Since (1) and (2) are independent, one can see that there is room for four theories: Newtonian determinism, branching time indeterminism, relativistic determinism, and (finally) branching space-times indeterminism. (shrink)

This paper assesses branching spacetime theories in light of metaphysical considerations concerning time. I present the A, B, and C series in terms of the temporal structure they impose on sets of events, and raise problems for two elements of extant branching spacetime theories—McCall’s ‘branch attrition’, and the ‘no backward branching’ feature of Belnap’s ‘branching space-time’—in terms of their respective A- and B-theoretic nature. I argue that McCall’s presentation of branch attrition can only be coherently formulated on a model with (...) at least two temporal dimensions, and that this results in severing the link between branch attrition and the flow of time. I argue that ‘no backward branching’ prohibits Belnap’s theory from capturing the modal content of indeterministic physical theories, and results in it ascribing to the world a time-asymmetric modal structure that lacks physical justification. (shrink)

The literature on the compatibility between the time of our experience--characterized by passage or becoming--and time as is represented within spacetime theories has been affected by a persistent failure to get a clear grasp of the notion of becoming, both in its relation to an ontology of events tt"spreadtt" in a four-dimensional manifold, and in relation to temporally asymmetric physical processes.In the first part of my paper I try to remedy this situation by offering what I consider a clear and (...) faithful explication of becoming, valid independently of the particular spacetime setting in which we operate. Along the way, I will show why the metaphysical debate between the so-called tt"presentiststt" and tt"eternaliststt" is completely irrelevant to the question of becoming, as the debate itself is generated by a failure to distinguish between a tensed and a tenseless sense of tt"existencett". After a much needed distinction between absolute and relational becoming, I then show in what sense classical spacetime physics presupposes both types of becoming, for the simple reason that spacetime physics presupposes an ontology of events. As a consequence, not only does it turn out that using physics to try to provide empirical evidence for the existence of becoming amounts to putting the cart before the horses, but also that the order imposed by tt"the arrow of becomingtt" is more fundamental than any other physical arrow of time, despite the fact that becoming cannot be used to explain why entropy grows, or retarded electromagnetic radiation prevails versus advanced radiation. (shrink)

According to the B-theory, the passage of time is an illusion. The B-theory therefore requires an explanation of this illusion before it can be regarded as fullysatisfactory; yet very few B-theorists have taken up the challenge of trying to provide one. In this paper I take some first steps toward such an explanation by first making a methodological proposal, then a hypothesis about a key element in the phenomenology of temporal passage. The methodological proposal focuses onthe representational content of the (...) element of experience by virtue of which time seems to pass. The hypothesis involves the claim that the experience of changeinvolves the representation of something enduring, rather than perduring, through any change. (shrink)

Although C. D. Broad's notion of Becoming has received a fair amount of attention in the philosophy-of-time literature, there are no serious attempts to show how to replace the standard 'block' spacetime models by models that are more congenial to Broad's idea that the sum total of existence is continuously increased by Becoming or the coming into existence of events. In the Newtonian setting Broad-type models can be constructed in a cheating fashion by starting with a Newtonian block model, carving (...) chips off the block, and assembling the chips in an appropriately structured way. However, attempts to construct Broad-type models in a non-cheating fashion reveal a number of problematic aspects of Becoming that have not received adequate attention in the literature. The paper then turns to an assessment of the problem and prospects of adapting Becoming models to relativistic spacetimes. The results of the assessment differ in both minor and major ways from the ones in the extant literature. Finally, the paper describes how the causal set approach to quantum gravity promises to provide a mechanism for realizing Becoming, though the form of Becoming that emerges may not conform to any of the versions discussed in the philosophical literature. (shrink)