Over the last forty years, philosophers have argued back and forth about backward causation. It requires a certain structure of time for something as backward causation to be not only possible but also to take place in the real world. In case temporal becoming is an objective feature of the world in the sense that the future is unreal, or at least ontologically indeterminate, it is impossible to see how backward causation can arise. Th e same difficulty does not hold with respect to forward causation. For even though it is assumed according to one dynamic view of time, the instant view or presentism, that merely present events exist—and past events therefore are no longer real or have become ontologically indeterminate—such a view can still maintain that past events once were there to cause present events. Future events, however, are still to come, and being indeterminate or nothing at all, they cannot cause any events in the present. In other words, causation backwards in time can occur only if we think of time as static; that is, no objective becoming exists, and the world consists of tenselessly occurring future events that exist in the same sense as past and present events. Backward causation requires the so-called full view, or possibly the half-full view, of time.

Does not the theory of a general tendency of entropy to diminish [sic] take too much for granted? To a certain extent it is supported by experimental evidence. We must accept such evidence as far as it goes and no further. We have no right to supplement it by a large draft of the scientific imagination. (Burbury 1904, 49)

Perhaps the real paradox of Zeno's Arrow is that, although entirely stationary, it has, against all odds, successfully traversed over two millennia of human thought to trouble successive generations of philosophers. The prospects were not good: few original Zenonian fragments survive, and our access to the paradoxes has been for the most part through unsympathetic commentaries. Moreover, like its sister paradoxes of motion, the Arrow has repeatedly been dismissed as specious and easily dissolved. Even those commentators who have taken it seriously have propounded solutions with which they profess themselves to be perfectly satisfied. So my question is: will Zeno's Arrow survive into the millennium just begun?

In a recent article, ‘Tensed Time and Our Differential Experience of the Past and Future,’ William Lane Craig (1999a) attempts to resuscitate A. N. Prior's (1959) ‘Thank Goodness’ argument against the B-theory by combining it with Plantinga's (1983) views about basic beliefs. In essence Craig's view is that since there is a universal experience and belief in the objectivity of tense and the reality of becoming, (that he identifies with ‘the presentist metaphysic’) ‘this belief constitutes an intrinsic defeater-defeater which overwhelms the objections brought against it.’ (1999a, 519) An intrinsic defeater-defeater is a belief that enjoys such warrant for us that it simply overwhelms the defeaters brought against it without specifically rebutting or undercutting them. Thus, Craig claims that an effete philosophical argument like McTaggart's paradox is nothing more than ‘an engaging and recalcitrant brain teaser whose conclusion nobody really takes seriously.’ (1999a, 532) It is difficult to reconcile this statement with Craig's own writings elsewhere. For Craig has vigorously argued in at least two other articles that 'hybrid A-B theorists like McCall, Schlesinger, and Smith [who give ontological status to both A-properties and B-relations] are in deep trouble’ (1998, 127) since they are all effectively refuted by McTaggart's Paradox (cf. Craig 1997). It is not Craig's inconsistency regarding the significance of McTaggart conundrum that I want to draw attention to, however. Rather I wish to raise a different issue.

For twenty years, D. H. Mellor has promoted an influential defence of a view of time he first called the ‘tenseless’ view, but now associates with what he calls the ‘B-theory.’ It is his defence of this view, not the view itself, which is generally taken to be novel. It is organized around a forcefully presented attack on rival views which he claims to be a development of McTaggart's celebrated argument that the ‘A-series’ is contradictory. I will call this attack ‘Mellor's McTaggart.’ Although it has received much critical attention, it has not been well understood. For one thing, it has changed over the years in a way that is little appreciated. Whereas Mellor's (1981) original version amounts to a dilemma each horn of which contains a single strand of argument, later statements (1986, 1998) of the first horn contain a second strand of argument unannounced. I shall be concerned to disentangle these strands. I shall also show them to have been largely anticipated by Gareth Evans (1979). However, my main aim is not the clarification of Mellor's McTaggart, but its refutation. I shall show that there is a rival to Mellor's view of time against which the first horn of the dilemma begs the question both as originally presented, and as supplemented. This rival is a ‘Priorean’ version of the ‘presentist’ doctrine that only what is present exists. Although Prior himself gave McTaggart's own argument short shrift, in refuting Mellor's development of it I do not merely resurrect Prior's moves. Mellor's McTaggart introduces specifically semantic considerations. It focuses not as McTaggart did on presentness and futurity etc., but on the truth-values of tokens of propositions in which presentness and futurity etc. are (said to be) ascribed. Consequently, its refutation requires an answer, from the perspective of a presentist metaphysics, to a question which came to the fore only after Prior's death. The question is this: How should semantic theory be developed in the light of the need for a theory of linguistic understanding? Though Evans (1979) flirted with the issue of how this question should be answered from a presentist perspective, the answer he articulates is wrong. I shall do no more than sketch the correct answer. That is all a refutation of Mellor's McTaggart requires.

It seems intuitively obvious that what I am doing right now is more real than what I did just one second ago, and it seems intuitively obvious that what I did just one second ago is more real than what I did forty years ago. And yet, remarkably, every philosopher of time today, except for the author, denies this obvious fact about reality. What went wrong? How could philosophers get so far away from what is the most experientially evident fact about reality?

McTaggart famously argued that time is unreal. Today, almost no one agrees with his conclusion.1 But his argument remains the locus classicus for both the A–theory and the B-theory of time. I want to show how McTaggart's argument provided the impetus for both of these opposing views of the nature of time. I will also present and defend what I take to be the correct view of the nature of time.

In the literature on time in the twentieth century stemming from J. M. E. McTaggart's famous argument for the unreality of time, two gems stand out. The first is C. D. Broad's patient dissection of McTaggart's argument in the chapter ‘Ostensible Temporality’ in his Examination of McTaggart's Philosophy. Broad carefully, and to my mind persuasively, uncovers the root errors in McTaggart's argument. In addition he tentatively proposes that the features of time that he calls its transitory aspect can be explained in terms of a dynamic aspect of time that he calls Absolute Becoming.

Time travel has been a staple of science fiction. With the advent of general relativity it has been entertained by serious physicists. But, especially in the philosophy literature, there have been arguments that time travel is inherently paradoxical. The most famous paradox is the grandfather paradox: you travel back in time and kill your grandfather, thereby preventing your own existence. To avoid inconsistency some circumstance will have to occur which makes you fail in this attempt to kill your grandfather. Doesn't this require some implausible constraint on otherwise unrelated circumstances? We examine such worries in the context of modern physics.

Since the death of strong reductionism, philosophers of science have expanded the horizons of their understandings of the physical, mental, and social worlds, and the complex relations among them. To give one interesting example, John Dupre has endorsed a notion of downward causation: ‘higher-level’ events causing events at a ‘lower’ ontological level. For example, my intention to type the letter ‘t’ causes the particular motions experienced by all the atoms in my left forefinger as I type it. The proper explanation of the motions of an atom at the tip of my forefinger primarily involves my intentions, rather than (for example) the immediately preceding motions of other nearby atoms, or any other such particle–level events.

Four–dimensionalism, or perdurantism, the view that temporally extended objects persist through time by having (spatio-)temporal parts or stages, includes two varieties, the worm theory and the stage theory. According to the worm theory, perduring objects are four–dimensional wholes occupying determinate regions of space–time and having temporal parts, or stages, each of them confined to a particular time. The stage theorist, however, claims, not that perduring objects have stages, but that the fundamental entities of the perdurantist ontology are stages. I argue that considerations of special relativity favor the worm theory over the stage theory.

In the literature on the compatibility between the time of our experience and the time of physics, the special theory of relativity has enjoyed central stage. By bringing into the discussion the general theory of relativity, I suggest a new analysis of the misunderstood notion of becoming, developed from hints in Gödel's published and unpublished arguments for the ideality of time. I claim that recent endorsements of such arguments, based on Gödel's own ‘rotating’ solution to Einstein's field equation, fail: once understood in the right way, becoming can be shown to be both mind-independent and compatible with spacetime physics. Being a needed tertium quid between views of time traditionally regarded as in conflict, such a new approach to becoming should also help to dissolve a crucial aspect of the century-old debate between the so-called A and B theories of time.

But this picture of a ‘block universe’, composed of a timeless web of ‘world-lines’ in a four-dimensional space, however strongly suggested by the theory of relativity, is a piece of gratuitous metaphysics. Since the concept of change, of something happening, is an inseparable component of the common-sense concept of time and a necessary component of the scientist's view of reality, it is quite out of the question that theoretical physics should require us to hold the Eleatic view that nothing happens in ‘the objective world’. Here, as so often in the philosophy of science, a useful limitation in the form of representation is mistaken for a deficiency of the universe (Black, 1962).

The conceptual and technical difficulties involved in creating quantum theory of gravity have led some physicists to question, and even in some cases to deny, the reality of time. More surprisingly, this denial has found a sympathetic audience among certain philosophers of physics. What should we make of these wild ideas? Does it even make sense to deny the reality of time? In fact physical science has been chipping away at common sense aspects of time ever since its inception. Section 1 offers a brief survey of the demolition process. Section 2 distinguishes a tempered from an extreme-y l radical form that a denial of time might take, and argues that extreme radicalism is empirically self-refuting. Section 3 begins an investigation of the prospects for tempered radicalism in a timeless theory of quantum gravity.

I want to consider some features of the position put forward by Julian Barbour in The End of Time that seem to me of particular philosophical interest. At the level of generality at which I'll be concerned with it, the view is relatively easy to describe. It can be arrived at by thinking of time as decomposing in some natural way linearly ordered atomic parts, ‘moments’, and combining an observation about the internal structure of moments with an epistemological doctrine about our access to the past. The epistemological doctrine, which I'll call ‘Presentism’, following Butterfield, is the view that our access to the past is mediated by records, or local representations, of it. The observation is that the state of the world at any moment has the structure of what Barbour calls a ‘time capsule’, which is to say that it constitutes a partial record of its past, it is pregnant with interrelated mutually consistent representations of its own history.