I argue that David Lewis’s philosophically dominant conception of time travel cannot straightforwardly handle what we might call cases of relativistic time travel—that is, the sort of time travel which could only plausibly occur in a relativistic setting. I evaluate whether or not the Lewisian account can be successfully adapted such that it would able to analyse potential cases of relativistic time travel satisfactorily while still being employable in the analysis of those cases that make no mention of physics or (...) the structure of spacetime. This is primarily an analytical and explanatory exercise, rather than a polemical one. (shrink)

This article addresses the question whether supertasks are possible within the context of non-relativistic quantum mechanics. The supertask under consideration consists of performing an infinite number of quantum mechanical measurements in a finite amount of time. Recent arguments in the physics literature claim to show that continuous measurements, understood as N discrete measurements in the limit where N goes to infinity, are impossible. I show that there are certain kinds of measurements in quantum mechanics for which these arguments break down. (...) This suggests that there is a new context in which quantum mechanics, in principle, permits the performance of a supertask. (shrink)

This paper suggests that time travelling scenarios commonly depicted in science fiction introduce problems and dangers for the time traveller. If time travel takes time, then time travellers risk collision with past objects, relocation to distant parts of the universe, and time travel-specific injuries. I propose several models of time travel that avoid the dangers and risks of time travel taking time, and that introduce new questions about the relationship between time travel and spatial location.

The paper is an interpretation and defense of Kant's conception of things in themselves as noumena, along the following lines. Noumena are transempirical realities. As such they have several important roles in Kant's critical philosophy (Section 1). Our theoretical faculties cannot obtain enough content for a conception of noumena that would assure their real possibility as objects, but can establish their merely formal logical possibility (Sections 2-3). Our practical reason, however, grounds belief in the real possibility of some noumena, and (...) even knowledge of the noumenal reality of a free will (Section 4). Section 5 defends Kant's conception of noumena as a good piece of philosophy, particularly with respect to its distinction between logical and real possibility. Are noumena numerically identical with experienced (phenomenal) objects? Kantian principles yield the answers that human selves are, God isn't, and it's harder to say about bodies (Section 6). (shrink)

Malament-Hogarth spacetimes are the sort of models within general relativity that seem to allow for the possibility of supertasks. There are various ways in which these spacetimes might be considered physically problematic. Here, we examine these criticisms and investigate the prospect of escaping them.

There exists a growing literature on the so-called physical Church-Turing thesis in a relativistic spacetime setting. The physical Church-Turing thesis is the conjecture that no computing device that is physically realizable can exceed the computational barriers of a Turing machine. By suggesting a concrete implementation of a beyond-Turing computer in a spacetime setting, Istvan Nemeti and Gyula David have shown how an appreciation of the physical Church-Turing thesis necessitates the confluence of mathematical, computational, physical, and indeed cosmological ideas. In this (...) essay, I will honour Istvan's seventieth birthday, as well as his longstanding interest in, and his seminal contributions to, this field going back to as early as 1987 by modestly proposing how the concrete implementation in Nemeti and D\'avid might be complemented by a quantum-information-theoretic communication protocol between the computing device and the logician who sets the beyond-Turing computer a task such as determining the consistency of Zermelo-Fraenkel set theory. This suggests that even the foundations of quantum theory and, ultimately, quantum gravity may play an important role in determining the validity of the physical Church-Turing thesis. (shrink)

Lucretius argues that death does not harm the person who dies. Harm could occur only if a person’s future non-existence were harmful. But one’s future non-existence is no more harmful than one’s non-existence before birth. Since a person is not harmed by lacking existence before birth, one is not harmed by lacking existence after dying.

Lucretius argues that death does not harm the person who dies. Harm could occur only if a person’s future non-existence were harmful. But one’s future non-existence is no more harmful than one’s non-existence before birth. Since a person is not harmed by lacking existence before birth, one is not harmed by lacking existence after dying.

That quantum mechanical measurement processes are indeterministic is widely known. The time evolution governed by the differential Schrödinger equation can also be indeterministic under the extreme conditions of a quantum supertask, the quantum analogue of a classical supertask. Determinism can be restored by requiring normalizability of the supertask state vector, but it must be imposed as an additional constraint on the differential Schrödinger equation.

In this essay I consider the argument that Bernard Williams advances in ‘The Makropolus Case’ for the meaninglessness of immortality. I also consider various counter-arguments. I suggest that the more clearly these counter-arguments are targeted at the spirit of Williams's argument, rather than at its letter, the less clearly they pose a threat to it. I then turn to Nietzsche, whose views about the eternal recurrence might appear to make him an opponent of Williams. I argue that, properly interpreted, these (...) views in fact make him an ally. (shrink)

This article argues that the causal loops that occur in some time-travel scenarios and in certain solutions of the theory of relativity are no more mysterious than the infinitely descending causal chains familiar from Newtonian mechanics.

We present a counterexample to Krasnikov's much discussed time machine no-go result. In addition, we prove a positive statement: a time machine existence theorem under a modest "no holes" assumption.

Personal time, as opposed to external time, has a certain role to play in the correct account of death and immortality. But saying exactly what that role is, and what role remains for external time, is not straightforward. I formulate and defend accounts of death and immortality that specify these roles precisely.

The paper first tries to explain how the possibility of "time travel" arises in the Godel universe. It then goes on to discuss a technical problem conerning minimal acceleration requirements for time travel. A theorem is stated and a conjecture posed. If the latter is correct, time travel can be ruled out as a practical possibility in the Godel universe.

The paper is an interpretation and defense of Kant’s conception of things in themselves as noumena, along the following lines. Noumena are transempirical realities. As such they have several important roles in Kant’s critical philosophy (Section 1). Our theoretical faculties cannot obtain enough content for a conception of noumena that would assure their real possibility as objects, but can establish their merely formal logical possibility (Sections 2-3). Our practical reason, however, grounds belief in the real possibility of some noumena, and (...) even knowledge of the noumenal reality of a free will (Section 4). Section 5 defends Kant’s conception of noumena as a good piece of philosophy, particularly with respect to its distinction between logical and real possibility. Are noumena numerically identical with experienced (phenomenal) objects? Kantian principles yield the answers that human selves are, God isn’t, and it’s harder to say about bodies (Section 6). (shrink)

A true Turing machine requires an infinitely long paper tape. Thus a TM can be housed in the infinite world of Newtonian spacetime, but not necessarily in our world, because our world-at least according to our best spacetime theory, general relativity-may be finite. All the same, one can argue for the "existence" of a TM on the basis that there is no such housing problem in some other relativistic worlds that are similar to our world. But curiously enough-and this is (...) the main point of this paper-some of these close worlds have a special spacetime structure that allows TMs to perform certain Turing unsolvable tasks. For example, in one kind of spacetime a TM can be used to solve first-order predicate logic and the halting problem. And in a more complicated spacetime, TMs can be used to decide arithmetic. These new computers serve to show that Church's thesis is a thoroughly contingent claim. Moreover, since these new computers share the fundamental properties of a TM in ordinary operation, a computability theory based on these non-Turing computers is no less worthy of investigation than orthodox computability theory. Some ideas about this new mathematical theory are given. (shrink)

A true Turing machine (TM) requires an infinitely long paper tape. Thus a TM can be housed in the infinite world of Newtonian spacetime (the spacetime of common sense), but not necessarily in our world, because our world-at least according to our best spacetime theory, general relativity-may be finite. All the same, one can argue for the "existence" of a TM on the basis that there is no such housing problem in some other relativistic worlds that are similar ("close") to (...) our world. But curiously enough-and this is the main point of this paper-some of these close worlds have a special spacetime structure that allows TMs to perform certain Turing unsolvable tasks. For example, in one kind of spacetime a TM can be used to solve first-order predicate logic and the halting problem. And in a more complicated spacetime, TMs can be used to decide arithmetic. These new computers serve to show that Church's thesis is a thoroughly contingent claim. Moreover, since these new computers share the fundamental properties of a TM in ordinary operation (e.g. intuitive, finitely programmed, limited in computational capability), a computability theory based on these non-Turing computers is no less worthy of investigation than orthodox computability theory. Some ideas about this new mathematical theory are given. (shrink)