Leibnizian metaphysics underpins the universally held view that spacetime must be inextendible – that it must be “as large as it can be” in a sense. But here we demonstrate a surprising fact within the context of general relativity: the property of inextendibility turns out to be unstable when attention is restricted to certain collections of “physically reasonable”spacetimes.

We discuss some recent work by Tim Maudlin concerning Black Hole Information Loss. We argue, contra Maudlin, that there is a paradox, in the straightforward sense that there are propositions that appear true, but which are incompatible with one another. We discuss the significance of the paradox and Maudlin's response to it.

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.

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.

We show a sense in which the spacetime property of effective completeness—a type of “local hole-freeness” or “local inextendibility”—is not stable.

Within the context of general relativity, the Heraclitus asymmetry property requires that no distinct pair of spacetime events have the same local structure Manchak and Barrett (2023). Here, we explore Heraclitus-maximal worlds – those which are “as large as they can be” with respect to the Heraclitus property. Using Zorn’s lemma, we prove that such worlds exist and highlight a number of their properties. If attention is restricted to Heraclitus-maximal worlds, we show senses in which observers have the epistemic (...) resources to know which world they inhabit. (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)

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.

This paper examines two ways in which the ‘privileged coordinates’ of a geometric space might have significance. First, the structure of the space might be ‘determined by its privileged coordinates’. Second, the space might be presentable using ‘Kleinian methods’. We examine the geometric spaces for which these two conditions hold. Along the way, we investigate the relationship between these two conditions.

Il y a un conflit entre les normes surnaturelles qui ne tiennent pas compte des possibilités humaines et les normes naturelles qui conduisent à des règles d’action fondées sur la connaissance positive du milieu où nous vivons ; mais il est impossible que les secondes affranchissent l’homme des premières. La question de leur accord se trouve donc posée.

Using the same technique employed in The Tragic Finale, Desan now has written an admirable guide to Sartre's Critique de la Raison Dialectique. Desan begins by tracing Sartre's development from the time of L'Etre et le Néant with careful attention to the heated controversies that appeared in Les Temps Modernes. This provides the context for a lucid and fair explication of the main argument of the Critique. Throughout, Desan has maintained a judicious balance between exposition, explication, and criticism. The study (...) can not replace the reading of the original work, but there is no doubt that it serves as an excellent guide through the labyrinth of Sartre's intricate and turgid dialectic.—R. J. B. (shrink)

This book was originally written for the French series, Philosophes de tous les temps. It follows the format of this series with an introductory essay and series of brief selections from James. Although Reck states that he "sought to see James as the French see him," he does not limit himself to a single perspective but presents a judicious, balanced interpretation of James. There is little exploitation of the recent "discovery" of James by phenomenologically oriented philosophers. In his introductory essay, (...) Reck has attempted to be comprehensive. The essay succeeds admirably in presenting a fine introduction to James.—R. J. B. (shrink)

Ever since the publication of L'Etre et le Néant in 1942, the intellectual world has awaited the promised publication of Sartre's ethics and political philosophy. During this period Sartre became deeply involved in politics and has moved closer to the Communist line. Now we have this massive volume which is designed to pave the way toward a reconciliation of Existentialism and Marxism. In a manner reminiscent of Hegel, Sartre traces the dialectical passage from the individual through the series --"a plurality (...) of solitudes"---to the dynamic group. Throughout, Sartre's psychological insight is evident, but the attempted union of Existentialism and Marxism seems both desperate and forced.--R. J. B. (shrink)

L’article examine la reprise que le « prince des Averroïstes » Jean de Jandun fait de cette phrase délicate d’Averroès, tirée de son Grand Commentaire du De anima d’Aristote : « forte igitur philosophia invenitur in maiori parte subiecti in omni tempore ». On cherche à montrer par l’analyse des textes que l’interprétation du maître ès arts s’écarte radicalement de la pensée du Cordouan qu’il prétend suivre. Tandis qu’Averroès suppose l’existence continue d’au moins un philosophe dans le monde, Jean de (...) Jandun, rejetant comme irréaliste l’idée d’un homme parfait en qui s’incarnerait tout le savoir, et tributaire d’une erreur de traduction arabo-latine qui donne « sujet » pour « lieu », soutient qu’il n’y a chaque fois de perfection que si l’on totalise tous les savoirs particuliers des différents penseurs en activité sur la terre. Autrement dit, la philosophie est parfaite, certes, mais il n’y a pas de philosophe parfait. C’est coniunctim que la science est achevée, et non pas divisim. Un tel constat, qui rapproche l’analyse de Jean de celle menée par Dante au début de sa Monarchia, permet deux révisions : d’une part, l’idée d’un « averroïsme » latin réactionnaire, se contentant de répéter les paroles du maître, est à revoir ; d’autre part, cela signifie qu’il n’y a pas chez Jean les bases théoriques de l’idéal éthico-intellectualiste dont l’historiographie moderne assure qu’il en fut le champion parisien. (shrink)

This work contains three essays which were delivered at a Symposium in 1966 at the Free University in Brussels, convened to pay homage to Martin Buber. The first essay, by Gabriel Marcel, attempts to edify the reader on Buber's philosophical anthropology, his philosophy of dialogue, political philosophy, and his philosophy of religion. There are frequent comparisons between Marcel's point of view and Buber's. The essay is particularly strong where Marcel analyzes Buber's notion of the "we." His perceptive examination of this (...) subject points up the affinity between his own and the Jewish philosopher's thought. The essay by Emmanuel Levinas, "La Pensée de Martin Buber et le Judaïsme Contemporain," sketches current Jewish thought and finds that it was Buber who gave it direction. Levinas provides also an account of the enormous work which Buber did in establishing Hassidism as an important stage in Hebraic thought. The last essay, by André Lacocque, deals with Protestant theology and the possible application of Buber's ideas to it. There is an extended comparison between the views of Kierkegaard and those of Buber on man's relationship with God and the author concludes that Buber's point of view is more compatible with modern Christianity than was Kierkegaard's.--S. J. B. (shrink)

A printing of the lecture notes of a course on moral philosophy that Perelman taught for many years at the University of Brussels, which has not changed the simple oral style. As a sketch of the history of ethics the book is briefer than, but comparable to, René Le Senne’s Traité de morale générale and Jacques Maritain’s Moral Philosophy. A book for beginners, Perelman’s work offers a clear analysis of more than thirty ethical positions from the ancient, medieval, and modern (...) periods. (shrink)

The development of the typical cladomothallus of the red algae Antithaminion plumula (Ellis) Le Jolis [= Pterothamnion plumula (Ellis) Nägcli], (Rhodophyceae, Ceramiales) is simulated with the help of a formal language called L-systems. Two types of uniseriate filaments are distinguished: axial filaments of cladomes with indefinite growth and branching and pleuridia with definite growth and branching. The rythmical acropetal formation of secondary axes with basitonic arrangement contrasts with the intercalary basitonic formation of pleuridia, resulting in an acrotonic arrangement within an (...) axial segment. Five types of cells and two types of cell divisions intervene in the system. In addition, for the graphical representations, some morphological particularities of A. plumula are taken into account: the curvature of axial filaments, the extension of growth zones, variable cell generation times, and segment length variability along an axis. The incidence of these variables on the generated thallus form is emphasized, pointing to the singularities of A. plumula. (shrink)