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 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.”.

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?

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.

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.

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)

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.

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.

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.

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.

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)

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.

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)

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 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)

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”.

Though the revised edition of A Theory of Justice, published in 1999, is the definitive statement of Rawls's view, so much of the extensive literature on Rawls's theory refers to the first edition.

Reissued here in its corrected second edition of 1864, this essay by John Stuart Mill argues for a utilitarian theory of morality. Originally printed as a series of three articles in Fraser's Magazine in 1861, the work sought to refine the 'greatest happiness' principle that had been championed by Jeremy Bentham, defending it from common criticisms, and offering a justification of its validity. Following Bentham, Mill holds that actions can be judged as right or wrong depending on whether they (...) promote happiness or 'the reverse of happiness'. Although attracted by Bentham's consequentialist framework based on empirical evidence rather than intuition, Mill separates happiness into 'higher' and 'lower' pleasures, arguing for a weighted system of measurement when making and judging decisions. Dissected and debated since its first appearance, the essay is Mill's key discussion on the topic and remains a fundamental text in the study of ethics. (shrink)

Wilhelm (Forthcom Synth 199:6357–6369, 2021) has recently defended a criterion for comparing structure of mathematical objects, which he calls Subgroup. He argues that Subgroup is better than SYM \(^*\), another widely adopted criterion. We argue that this is mistaken; Subgroup is strictly worse than SYM \(^*\). We then formulate a new criterion that improves on both SYM \(^*\) and Subgroup, answering Wilhelm’s criticisms of SYM \(^*\) along the way. We conclude by arguing that no criterion that looks only to the (...) automorphisms of mathematical objects to compare their structure can be fully satisfactory. (shrink)

J.L. Mackie insists that ordinary evaluative thought presents itself as a matter of sensitivity to aspects of the world. And this phenomenological thesis seems correct. When one or another variety of philosophical non-cognitivism claims to capture the truth about what the experience of value is like, or (in a familiar surrogate for phenomenology) about what we mean by our evaluative language, the claim is never based on careful attention to the lived character of evaluative thought or discourse. The idea is, (...) rather, that the very concept of the cognitive or factual rules out the possibility of an undiluted representation of how things are, enjoying, nevertheless, the internal relation to 'attitudes' or the will that would be needed to count as evaluative. On this view the phenomenology of value would involve a mere incoherence, if it were as Mackie says--a possibility that then tends (naturally enough) not to be so much as entertained. But, as Mackie sees, there is no satisfactory justification for supposing that the factual is, by definition, attitudinatively and motivationally neutral. This clears away the only obstacle to accepting his phenomenological claim; and the upshot is that non-cognitivism must offer to correct the phenomenology of value, rather than give an account of it. -/- In Machie's view the correction is called for. In this paper I want to suggest that he attributes an unmerited plausibility to this thesis, by giving a false picture of what one is committed to if one resists it. (shrink)

We consider various curious features of general relativity, and relativistic field theory, in two spacetime dimensions. In particular, we discuss: the vanishing of the Einstein tensor; the failure of an initial-value formulation for vacuum spacetimes; the status of singularity theorems; the non-existence of a Newtonian limit; the status of the cosmological constant; and the character of matter fields, including perfect fluids and electromagnetic fields. We conclude with a discussion of what constrains our understanding of physics in different dimensions.

In his preface Mr Wilson writes 'I feel that a great many adults … would do better to spend less time in simply accepting the concepts of others uncritically, and more time in learning how to analyse concepts in general'. Mr Wilson starts by describing the techniques of conceptual analysis. He then gives examples of them in action by composing answers to specific questions and by criticism of quoted passages of argument. Chapter 3 sums up the importance of this kind (...) of mental activity. Chapter 4 presents selections for the reader to analyse, followed by questions of university entrance/scholarship type. This is a book to be worked through, in a sense a text-book. (shrink)

A supertask is a task that consists in infinitely many component steps, but which in some sense is completed in a finite amount of time. Supertasks were studied by the pre-Socratics and continue to be objects of interest to modern philosophers, logicians and physicists. The term “super-task” itself was coined by J.F. Thomson (1954). Here we begin with an overview of the analysis of supertasks and their mechanics. We then discuss the possibility of supertasks from the perspective of general relativity.

In this philosophically sophisticated and historically significant work, John H. Zammito reconstructs Kant's composition of The Critique of Judgment and reveals that it underwent three major transformations before publication. He shows that Kant not only made his "cognitive" turn, expanding the project from a "Critique of Taste" to a Critique of Judgment but he also made an "ethical" turn. This "ethical" turn was provoked by controversies in German philosophical and religious culture, in particular the writings of Johann Herder and (...) the Sturm und Drang movement in art and science, as well as the related pantheism controversy. Such topicality made the Third Critique pivotal in creating a "Kantian" movement in the 1790s, leading directly to German Idealism and Romanticism. The austerity and grandeur of Kant's philosophical writings sometimes make it hard to recognize them as the products of a historical individual situated in the particular constellation of his time and society. Here Kant emerges as a concrete historical figure struggling to preserve the achievements of cosmopolitan Aufkl-rung against challenges in natural science, religion, and politics in the late 1780s. More specifically Zammito suggests that Kant's Third Critique was animated throughout by a fierce personal rivalry with Herder and by a strong commitment to traditional Christian ideas of God and human moral freedom. "A work of extraordinary erudition. Zammito's study is both comprehensive and novel, connecting Kant's work with the aesthetic and religious controversies of the late eighteenth century. He seems to have read everything. I know of no comparable historical study of Kant's Third Critique."-Arnulf Zweig, translator and editor of Kant's ;IPhilosophical Correspondence, 1759-1799;X "An intricate, subtle, and exciting explanation of how Kant's thinking developed and adjusted to new challenges over the decade from the first edition of the Critique of Pure Reason to the appearance of the Critique of Judgment. "--John W. Burbidge, Review of Metaphysics "There has been for a long time a serious gap in English commentary on Kant's Critique of Judgment Zammito's book finally fills it. All students and scholars of Kant will want to consult it."--Frederick Beiser, Times Literary Supplement. (shrink)

One usually identifies a particular collection of geometric objects with the models of general relativity. But within this standard collection lurk ‘physically unreasonable’ models of spacetime. If such models are ruled out, attention can be restricted to some sub-collection of ‘physically reasonable’ models which can be considered a variant theory of general relativity. Since we have yet to identify a privileged sub-collection of ‘physically reasonable’ models, it is helpful to think of ‘general relativity’ in a pluralistic way; we can study (...) a collection of such ‘physically reasonable’ collections of models. (shrink)

This article shows a clear sense in which general relativity allows for a type of ‘machine’ that can bring about a spacetime structure suitable for the implementation of ‘supertasks’. 1Introduction2Preliminaries3Malament–Hogarth Spacetimes4Machines5Malament–Hogarth Machines6Conclusion.

Though the revised edition of A Theory of Justice, published in 1999, is the definitive statement of Rawls's view, so much of the extensive literature on Rawls's theory refers to the first edition.

Knowledge and Lotteries is organized around an epistemological puzzle: in many cases, we seem consistently inclined to deny that we know a certain class of propositions, while crediting ourselves with knowledge of propositions that imply them. In its starkest form, the puzzle is this: we do not think we know that a given lottery ticket will be a loser, yet we normally count ourselves as knowing all sorts of ordinary things that entail that its holder will not suddenly acquire a (...) large fortune. After providing a number of specific and general characterizations of the puzzle, Hawthorne carefully examines the competing merits of candidate solutions. In so doing, he explores a number of central questions concerning the nature and importance of knowledge, including the relationship of knowledge to assertion and practical reasoning, the status of epistemic closure principles, the merits of various brands of scepticism, the prospects for a contextualist account of knowledge, and the potential for other sorts of salience-sensitive accounts. Along the way, he offers a careful treatment of pertinent issues at the foundations of semantics. His book will be of interest to anyone working in the field of epistemology, as well as to philosophers of language. (shrink)

Foreword I. Critical rationalism is a genuinely new philosophical perspective. It is not, however, one systematic view. The development of it by Popper and ...

What does reality encompass? Is it exclusively physical, or does it include mental and 'abstract' aspects? What are the elements of being, reality's raw materials? John Heil offers stimulating answers to these questions framed in terms of a comprehensive metaphysics of substances and properties inspired by Descartes, Locke, and their successors.

Everyone loves something or somebody, and most people are concerned with loving another person like themselves, all equal. This book is based on the belief that getting clear about the concept and meaning of love between equals is essential for success in our practical lives. For how can we love properly unless we have a fairly clear idea of what love is? The book is written in ordinary language and for the ordinary person, without jargon or philosophical technicalities. It aims (...) to show that love between equals involves a single basic disposition, though that disposition expresses itself in various ways. Thus, after an introduction explaining the need for analysis and clarification, the author then deals in order with love as desire or need; with intrinsic friendship and sharing the self; with basic difficulties concerning power, dependence, altruism and paranoia; with sex and erotic love; and finally with the value in human life of love between equals. The work as a whole gives clear, coherent and practical guidance for all who wish to grasp what such love is really like. (shrink)

I argue that incomprehensibility (what the ancient skeptics called acatalepsia) plays a central role in the skepticism of both Bayle and Hume. I challenge a commonly held view (recently argued by Todd Ryan) that Hume, unlike Bayle, does not present oppositions of reason--what Kant called antimonies.

We present several new studies focusing on “salience effects”—the decreased tendency to attribute knowledge to someone when an unrealized possibility of error has been made salient in a given conversational context. These studies suggest a complicated picture of epistemic universalism: there may be structural universals, universal epistemic parameters that influence epistemic intuitions, but that these parameters vary in such a way that epistemic intuitions, in either their strength or propositional content, can display patterns of genuine cross-cultural diversity.