This exploration of the global structure of spacetime within the context of general relativity examines the causal and singular structures of spacetime, revealing some of the curious possibilities that are compatible with the theory, such as `time travel' and `holes' of various types. Investigations into the epistemic and modal structures of spacetime highlight the difficulties in ruling out such possibilities, unlikely as they may seem at first. The upshot seems to be that what counts as a `physically reasonable' spacetime structure (...) in modern physics is far from clear. (shrink)

Here, we briefly review the notion of observational indistinguishability within the context of classical general relativity. We settle a conjecture given by Malament (1977) concerning the subject and then strengthen the result considerably. The upshot is this: There seems to be a robust sense in which the global structure of every cosmological model is underdetermined.

Cosmologists often use certain global properties to exclude "physically unreasonable" cosmological models from serious consideration. But, on what grounds should these properties be regarded as "physically unreasonable" if we cannot rule out, even with a robust type of inductive reasoning, the possibility of the properties obtaining in our own universe?

Here, we clarify the relationship among three space-time conditions of interest: geodesic completeness, hole-freeness, and inextendibility. In addition, we introduce a related fourth condition: effective completeness.

A number of models of general relativity seem to contain “holes” that are thought to be “physically unreasonable.” One seeks a condition to rule out these models. We examine a number of possibilities already in use. We then introduce a new condition: epistemic hole-freeness. Epistemic hole-freeness is not just a new condition—it is new in kind. In particular, it does not presuppose a distinction between space-times that are “physically reasonable” and those that are not.

In this note, we cast doubt on the requirement of spacetime inextendibility; it is not at all clear that our universe is “as large as it can be.”.

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.

There is a venerable position in the philosophy of space and time that holds that the geometry of spacetime is conventional, provided one is willing to postulate a “universal force field.” Here we ask a more focused question, inspired by this literature: in the context of our best classical theories of space and time, if one understands “force” in the standard way, can one accommodate different geometries by postulating a new force field? We argue that the answer depends on one’s (...) theory. In Newtonian gravitation the answer is yes; in relativity theory, it is no. (shrink)

It has been argued that spacetime must be inextendible – that it must be “as large as it can be” in some sense. Here, we register some skepticism with respect to this position.

Here we briefly review the concept of "prediction" within the context of classical relativity theory. We prove a theorem asserting that one may predict one's own future only in a closed universe. We then question whether prediction is possible at all (even in closed universes). We note that interest in prediction has stemmed from considering the epistemological predicament of the observer. We argue that the definitions of prediction found thus far in the literature do not fully appreciate this predicament. We (...) propose a more adequate alternative and show that, under this definition, prediction is essentially impossible in general relativity. (shrink)

Gödel's remarks concerning the ideality of time are examined. In the literature, some of these remarks have been somewhat neglected while others have been heavily criticized. In this note, we propose a clear and defensible sense in which Gödel's work bears on the question of whether there is an objective lapse of time in our world.

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.

Within the context of general relativity, we consider one definition of a “time machine” proposed by Earman, Smeenk, and Wüthrich. They conjecture that, under their definition, the class of time machine spacetimes is not empty. Here, we prove this conjecture. †To contact the author, please write to: Department of Philosophy, University of Washington, Box 353350, Seattle, WA 98195‐3350; e‐mail: manchak@uw.edu.

The hole argument purportedly shows that spacetime substantivalism implies a pernicious form of indeterminism. We show that the argument is seductive only because it mistakes a trivial claim (viz. there are isomorphic models) for a significant claim (viz. there are hole isomorphisms). We prove that the latter claim is false -- thereby closing the debate about whether substantivalism implies indeterminism.

It has been suggested by Clark Glymour that the spatio-temporal structure of the universe might be underdetermined by all observational data that could ever, theoretically, be gathered. It is possible for two spacetimes to be observationally indistinguishable (OI) yet topologically distinct. David Malament extended the argument for the underdetermination of spacetime structure by showing that under quite general conditions (such as the absence of any closed timelike curves) a spacetime will always have an OI counterpart (at least in weak sense). (...) Because the plight of the cosmologist seemed to be so discouraging in this regard, Malament considered the relationship between global properties and OI spacetimes. This information is helpful to the cosmologist. It allows, in principle, one to reject some spacetime models based on observational evidence. In this paper, I consider the relationship between variants of geodesic incompleteness and different senses (some old and some new) of OI. In light of the findings, it seems that (for the most part) the predicament of the cosmologist is not good. Quite generally, versions of geodesic incompleteness are not conserved even under the strongest formulations of OI. (shrink)

Non-collapse theories of quantum mechanics have the peculiar characteristic that, although their measurements produce definite results, their state vectors remain in a superposition of possible outcomes. David Albert has used this fact to show that the standard uncertainty relations can be violated if self-measurements are made. Bradley Monton, however, has held that Albert has not been careful enough in his treatment of self-measurement and that being more careful (considering mental state supervenience) implies no violation of the relations. In this paper, (...) I will outline both Albert's proposal and Monton's objections. Then, I will show how the uncertainty relations can be violated after all (even after being as careful as Monton). Finally, I will discuss how finding a way around the objections allows us to learn more about what is and what is not possible in non-collapse theories of quantum mechanics. (shrink)

There does not seem to be a consistent way to ground the concept of “force” in Cartesian first principles. In this article, I first review the literature on the subject. Then, I offer an alternative interpretation of force—one that seems to be coherent and consistent with Descartes’ project. Not only does the new position avoid the problems of previous interpretations, but it does so in such a way as to support and justify those previous interpretations. *Received June 2007; revised June (...) 2009. †To contact the author, please write to: Department of Philosophy, University of Washington, Box 353350, Seattle, WA 98195; e‐mail: manchak@uw.edu. (shrink)

Here, we show that one may "time travel" in Gödel spacetime with less total acceleration than was previously known. This answers a question posed by Malament.

Here, formal tools are used to pose and answer several philosophical questions concerning space and time. The questions involve the properties of possible worlds allowed by the general theory of relativity. In particular, attention is given to various causal properties such as “determinism” and “time travel”.

Here we provide a proof that there exist closed timelike curves in Gödel spacetime with total acceleration less than 2π(9 + 6√3)^1/2. This answers a question posed by David Malament.

Here, we hypothesize that a smooth nongeodesic closed timelike curve is never most efficient with respect to total acceleration if a kink is permitted at the initial point. We support our hypothesis in a variety of ways. Most notably, we show Malament's opposing conjecture concerning Gödel space-time to be false.

Focused correlation compares the degree of association within an evidence set to the degree of association in that evidence set given that some hypothesis is true. Wheeler and Scheines have shown that a difference in incremental confirmation of two evidence sets is robustly tracked by a difference in their focus correlation. In this essay, we generalize that tracking result by allowing for evidence having unequal relevance to the hypothesis. Our result is robust as well, and we retain conditions for bidirectional (...) tracking between incremental confirmation measures and focused correlation. (shrink)

The pragmatic inquiry process used in the Corporantes Pathfinder Notebook (CPN) enables students and others to discern their gifts, find purpose and direction in their lives, and seek a FIT between their values and various corporate cultures before making extensive commitments in their field of studies and their employment. Based on Peirce''s theory of Pragmatism the CPN fosters investigation, interpretation, and action resulting from reflected narratives written in response to a series of questions in the CPN. The CPN was used (...) successfully as a framework in a Business Ethics course for connecting career decisions to their personal lives. Other pedagogic activities were used such as case studies, role playing, service learning, team projects investigating ethical climates of corporations, as well as Socratic questioning and discussions of moral dilemmas to develop ethical sensitivity and understanding of ethical challenges and decisions. The CPN also has been used successfully by senior executives in over fifty applications. (shrink)

Here, we examine hole-freeness - a condition sometimes imposed to rule out seemingly artificial spacetimes. We show that under existing definitions (and contrary to claims made in the literature) there exist inextendible, globally hyperbolic spacetimes which fail to be hole-free. We then propose an updated formulation of the condition which enables us to show the intended result. We conclude with a few general remarks on the strength of the definition and then formulate a precise question which may be interpreted as: (...) Are all physically reasonable spacetimes hole-free? (shrink)

This document collects discussion and commentary on issues raised in the workshop by its participants. Contributors are: Greg Frost-Arnold, David Harker, P. D. Magnus, John Manchak, John D. Norton, J. Brian Pitts, Kyle Stanford, Dana Tulodziecki.

In 1897, Cambridge University created a professorship in Mental Philosophy and Logic; despite the double name it was filled by a “mental philosopher,” James Ward, who did no work in logic. The chief logician candidate, John Venn, then turned his attention elsewhere, leaving Cambridge without senior leadership in logic. Ward himself turned to other philosophical issues, doing little further original work in mental philosophy. Cambridge became a center for a fresh interpretation of logic in the early 20th century, but (...) with no help from Venn. Psychology split off from mental philosophy, and what remained, the “philosophy of mind,” was developed elsewhere until after Ward’s tenure. (shrink)

In 1866, the young John Venn published The Logic of Chance, motivated largely by the desire to correct what he saw as deep fallacies in the reasoning of historical determinists such as Henry Buckle and in the optimistic heralding of a true social science by Adolphe Quetelet. Venn accepted the inevitable determinism implied by the physical sciences, but denied that the stable social statistics cited by Buckle and Quetelet implied a similar determinism in human actions. Venn maintained that probability (...) statements were intelligible solely as projections of the ultimate frequency of an outcome in an unlimited series of trials and therefore led to no inferences about free will. An issue here was Venn's claim that although the aggregate probability may be stable, the individual events were completely irregular and, in fact, displayed randomness. Venn's concept of randomness was really apparent, or pseudo-, randomness, which could be totally determined. Ironically, Venn's frequentist position was very useful to the growing field of statistics, which could develop correlations and predictive models empirically without having to address implications for personal freedom or fatalism. (shrink)

Locke’s critique of enthusiastic religion is an attempt to undermine a form of supernaturalist belief. In this paper, I argue for a novel interpretation of that critique. By opening up a middle path between the views of John Passmore and Michael Ayers, I show that Locke is accusing the enthusiast of being a self-deceived believer. First, I demonstrate the manner in which a theory of self-deception squares with Locke’s intellectualist epistemology. Second, I argue that Locke thinks he can show (...) that the enthusiasts’ most cherished beliefs are in fact contrary to manifest evidence. In “matters of ultimate concern” to us---i.e., our religious beliefs---the critique is thus meant tobuttress Locke’s commitment to a naturalistic ethics of belief. (shrink)

This paper considers three accounts of the relationship between personal immortality and materialism. In particular, the pagan mortalism of the Epicureans is compared with the Christian mortalism of Thomas Hobbes and John Locke. It is argued 1) that there are significant similarities between these views, 2) that Locke and Hobbes were, to some extent, influenced by the Epicureans, and 3) that the relation between (im)mortality and (im)materialism is not as straightforward as is commonly supposed.

This paper considers three accounts of the relationship between personal immortality and materialism. In particular, the pagan mortalism of the Epicureans is compared with the Christian mortalism of Thomas Hobbes and John Locke. It is argued 1) that there are significant similarities between these views, 2) that Locke and Hobbes were, to some extent, influenced by the Epicureans, and 3) that the relation between mortality and materialism is not as straightforward as is commonly supposed.

John Venn is known as one of the clearest expounders of the interpretation of probability as the frequency of a particular outcome in a potentially unlimited series of possible events. This view he held to be incompatible with the alternate interpretation of probability as a measure of the degree of belief that would rationally be held about a certain outcome based upon the reliability of testimony and other prior information. This paper explores the reasons why Venn may have been (...) so opposed to the degree-of-belief interpretation and suggests that it may have been a way for him to resolve a conflict in his own mind between his ideas of proper scientific methods of inference and the religious beliefs that he held as a young man. (shrink)

The volume contains a collection of papers presented at the International Symposium, which took place in Hvar, Croatia, in 2006. In recent years there has been an upsurge of interest in the study of Plato, Platonism and Neoplatonism. Taking the position that it is of vital importance to establish an ongoing dialogue among scientists, artists, academics, theologians and philosophers concerning pressing issues of common interest to humankind, this collection of papers endeavours to bridge the gap between contemporary research in Platonist (...) philosophy and other fields where insights gained from the study of Plato and Platonist philosophy can be of consequence and benefit. Authors: Werner Beierwaltes, Luc Brisson, Amber Carpenter, John Dillon, Jonathan Doner, Franco Ferrari, Francesco Fronterotta, F.A.J. de Haas, Aaron Hughes, Byron Kaldis, Daniel Kolak, Thomas Leinkauf, Dionysis Mentzeniotis, Jean-Marc Narbonne, Giannis Stamatellos, Vladimir Stoupel, Patrick Quinn, Jure Zovko and Marie-Élize Zovko. (shrink)