This chapter contains sections titled: Relationism, Substantivalism and Space‐time Conventionalism about Space‐time Black Holes and Singularities Horizons and Uniformity Conclusion.

Kant's argument from incongruent counterparts for substantival space is examined; it is concluded that the argument has no force against a relationist. The argument does suggest that a relationist cannot give an account of enantiomorphism, incongruent counterparts and orientability. The prospects for a relationist account of these notions are assessed, and it is found that they are good provided the relationist is some kind of modal relationist. An illustration and interpretation of these modal commitments is given.

In this paper I argue that the positivist–conventionalist interpretation of the Restricted Principle of Relativity is flawed, due to the positivists’ own understanding of conventions and their origins. I claim in the paper that, to understand the conventionalist thesis, one has to diambiguate between three types of convention; the linguistic conventions stemming from the fundamental role of mathematical axioms (conceptual conventions), the conventions stemming from the coordination betweeh theoretical statements and physical, observable facts or entities (coordinative definitions), and conventions that (...) are made possible by possible revisions to theory (the thesis of empirical underdetermination). I claim that it is not possible to interpret the Principle of Relativity as based on one of these three types of convention. This renders the conventionalist interpretation of the Principle of Relativity untenable. The paper is part of a larger project that aims to understand the philosophical significance of the Principle of Relativity. (shrink)

Space—an essential dimension of our life—is analyzable from different viewpoints, which often gives rise to contrasting conceptualizations. Perceptual analyses shed light on the intrinsic anisotropy and deformations of perceived space, raising the issue of which geometry may be able to represent perceptual space. Pictorial drawings and painting have been relevant sources of information about the nature of living and perceived space. Although the geometry of perceptual space is still in its infancy, contributions are beginning to appear. This special issue contributes (...) to the development of the geometry of perceptual space. (shrink)

I argue for a four dimensional, non-dynamical view of space-time, where becoming is not an intrinsic property of reality. This view has many features in common with the Parmenidean conception of the universe. I discuss some recent objections to this position and I offer a comparison of the Parmenidean space-time with an interpretation of Heraclitus’ thought that presents no major antagonism.

All physical theories, from classical Newtonian mechanics to relativistic quantum field theory, entail propositions concerning the geometric structure of spacetime. To give an example, the general theory of relativity entails that spacetime is curved, smooth, and four-dimensional. In this dissertation, I take the structural commitments of our theories seriously and ask: how is such structure instantiated in the physical world? Mathematically, a property like 'being curved' is perfectly well-defined insofar as we know what it means for a mathematical space to (...) be curved. But what could it mean to say that the physical world is curved? Call this the problem of physical geometry. The problem of physical geometry is a plea for foundations--a request for fundamental truth conditions for physical-geometric propositions. My chief claim is that only a substantival theory of spacetime--a theory according to which spacetime is an entity in its own right, existing over and above the material content of the world--can supply the necessary truth conditions. (shrink)

I argue that the best interpretation of the general theory of relativity has need of a causal entity, and causal structure that is not reducible to light cone structure. I suggest that this causal interpretation of GTR helps defeat a key premise in one of the most popular arguments for causal reductionism, viz., the argument from physics.

What is the relation between material objects and spacetime regions? Supposing that spacetime regions are one sort of substance, there remains the question of whether or not material objects are a second sort of substance. This is the question of dualistic versus monistic substantivalism. I will defend the monistic view. In particular, I will maintain that material objects should be identified with spacetime regions. There is the spacetime manifold, and the fundamental properties are pinned directly to it.

I examine two claims that arise in Brown’s account of inertial motion. Brown claims there is something objectionable about the way in which the motions of free particles in Newtonian theory and special relativity are coordinated. Brown also claims that since a geodesic principle can be derived in Einsteinian gravitation, the objectionable feature is explained away. I argue that there is nothing objectionable about inertia and that while the theorems that motivate Brown’s second claim can be said to figure in (...) a deductive-nomological explanation, their main contribution lies in their explication rather than their explanation of inertial motion. (shrink)

The empirical study of visual space has centered on determining its geometry, whether it is a perspective projection, flat or curved, Euclidean or non-Euclidean, whereas the topology of space consists of those properties that remain invariant under stretching but not tearing. For that reason distance is a property not preserved in topological space whereas the property of spatial order is preserved. Specifically the topological properties of dimensionality, orientability, continuity, and connectivity define “real” space as studied by physics and are the (...) spatial properties that characterize the physical universe as being an integral whole. By contrast the geometrical analysis of VS has taken little cognizance of its topology. Instead such properties have been presupposed a priori rather than being established a posteriori by empirical means, perhaps because these properties are self-evident. Applying the method of coordinative definition expounded by Hans Reichenbach for determining geometrical and topological properties of physical space, it can be shown that VS fulfills the topological criteria of being a “real” space sui generis. Though theorized to be produced by the brain, the topology of VS is not topologically equivalent with the structure and activity of the brain because, as will be shown, the topology of VS cannot be formed from the topology of the brain without tearing and/or cutting and pasting. (shrink)

This article argues that time‐asymmetric processes in spacetime are enantiomorphs. Subsequently, the Kantian puzzle concerning enantiomorphs in space is reviewed to introduce a number of positions concerning enantiomorphy, and to arrive at a dilemma: one must either reject that orientations of enantiomorphs are determinate, or furnish space or objects with orientation. The discussion on space is then used to derive two problems in the debate on the direction of time. First, it is shown that certain kinds of reductionism about the (...) direction of time are at variance with the claim that orientation of enantiomorphic objects is intrinsic. Second, it is argued that reductive explanations of time‐asymmetric processes presuppose that enantiomorphic processes do not have determinate orientation. (shrink)

A critical re-examination of the history of the concepts of space (including spacetime of general relativity and relativistic quantum field theory) reveals a basic ontological elusiveness of spatial extension, while, at the same time, highlighting the fact that its epistemic primacy seems to be unavoidably imposed on us (as stated by A.Einstein “giving up the extensional continuum … is like to breathe in airless space”). On the other hand, Planck’s discovery of the atomization of action leads to the fundamental recognition (...) of an ontology of non-spatial, abstract entities (Quine) for the quantum level of reality (QT), as distinguished from the necessarily spatio-temporal, experimental revelations (measurements). The elementary quantum act (measured by Planck’s constant) has neither duration nor extension, and any genuinely quantum process literally does not belong in the Raum and time of our experience. As Heisenberg stresses: “Während also die klassische Physik ein objectives Geschehen in Raum and Zeit zum Gegenstand hat, für dessen Existenz seine Beobachtung völlig irrelevant war, behandelt die Quantentheorie Vorgänge, die sozusagen nur in den Momenten der Beobachtung als raumzeitliche Phänomene aufleuchten, und über die in der zwischenzeit anschaulische physikalische Aussagen sinloss sind”. An admittedly speculative, hazardous conjecture is then advanced concerning the relation of such quantum ontology with the role of the pre-phenomenal continuum (Husserl) in the perception of macroscopically distinguishable objects in the Raum and time of our experience. Although rather venturesome, it brings together important philosophical issues. Coherently with recent general results in works on the foundations of QT, it is assumed that the linearity of quantum dynamical evolution does not apply to the central nervous system of living beings at a certain level of the evolutionary ramification and at the pre-conscious stage of subjectivity. Accordingly, corresponding to the onset of a non-linear dynamic evolution, a ‘primary spatial’ reduction is ‘continually’ taking place, thereby constituting the neural precondition for the experience of distinguishable macroscopic objects in the continuous spatial extension. While preventing the theoretically possible quantum superpositions of macroscopic objects from being perceivable by living beings, the ‘primary reduction’ has no effect on the standard processes concerning quantum level entities involved in laboratory man-made experiments. In this connection, an experimental check which might falsify the conjecture is briefly discussed. The approach suggested here, if sound, leads to a naturalization of that part of Kant’s Transcendental Aesthetics than can survive the Euclidean catastrophe. According to such naturalized transcendentalism, “space can well be transcendental without the axioms being so”, in agreement with a well-known statement by Boltzman. Finally, as far as QT is concerned, the conjecture entails that a scheme for quantum measurement of the von Neumann type cannot even ‘leave the ground’, vindicating Bohr’s viewpoint. A quantum theory of measurement, in a proper sense, turns out to be unnecessary and in fact impossible. (shrink)

Paragraph 6 of Newtons Scholium argues that the parts of space cannot move. A premise of the argument – that parts have individuality only through an order of position – has drawn distinguished modern support yet little agreement among interpretations of the paragraph. I argue that the paragraph offers an a priori, metaphysical argument for absolute motion, an argument which is invalid. That order of position is powerless to distinguish one part of Euclidean space from any other has gone virtually (...) unremarked. It remains uncertain what the import of the paragraph is but it is not close to apparently similar arguments of Leibniz. (shrink)

Geometry was a main source of inspiration for Carnap’s conventionalism. Taking Poincaré as his witness Carnap asserted in his dissertation Der Raum (Carnap 1922) that the metrical structure of space is conventional while the underlying topological structure describes "objective" facts. With only minor modifications he stuck to this account throughout his life. The aim of this paper is to disprove Carnap's contention by invoking some classical theorems of differential topology. By this means his metrical conventionalism turns out to be indefensible (...) for mathematical reasons. This implies that the relation between to-pology and geometry cannot be conceptualized as analogous to the relation between the meaning of a proposition and its expression in some language as logical empiricists used to say. (shrink)

A common adage runs that, given a theory manifesting symmetries, the syntax of that theory should be modified in order to construct a new theory, from which symmetry-variant structure of the original theory has been excised. Call this strategy for explicating the underlying ontology of symmetry-related models reduction. Recently, Dewar has proposed an alternative to reduction as a means of articulating the ontology of symmetry-related models—what he calls sophistication, in which the semantics of the original theory is modified, and symmetry-related (...) models of that theory are treated as if they are isomorphic. In this paper, we undertake a critical evaluation of sophistication about symmetries—we find the programme underdeveloped in a number of regards. In addition, we clarify the interplay between sophistication about symmetries, and a separate debate to which Dewar has contributed—viz., that between interpretational versus motivational approaches to symmetry transformations. (shrink)

One of the few authors to have explicitly connected the physical issue of the expansion of the universe with the philosophical topic of the metaphysical status of space is Gerald James Whitrow. This paper examines his view and tries to highlight its strong and weak points, thereby clarifying its obscure aspects. In general, this really interesting philosophical approach to one of the most important phenomena concerning our universe, and therefore modern cosmology, has been very rarely tackled. This unicity increases the (...) value, from a physical, philosophical and historical point of view, of Whitrow’s attempt and calls for new research. (shrink)

The traditional absolutist-relationist debate is still clearly formulable in the context of General Relativity Theory (GTR), despite the important differences between Einstein's theory and the earlier context of Newtonian physics. This paper answers recent arguments by Robert Rynasiewicz against the significance of the debate in the GTR context. In his (1996) (‘Absolute vs. Relational Spacetime: An Outmoded Debate?’), Rynasiewicz argues that already in the late nineteenth century, and even more so in the context of General Relativity theory, the terms of (...) the original Descartes–Newton–Leibniz dispute about space are not to be found. Nineteenth-century ether theories of electromagnetism, and the metric field of GTR, he claims, do not lend themselves to being interpreted clearly as either absolute space à la Newton, or relational structures à la either Descartes or Leibniz. I argue that, while in some imaginable theories Rynasiewicz's claim that the classical debate dissolves would be correct, in fact in the most important historical theories he discusses, this is not the case. In particular, I argue that in both Lorentz's ether theory and General relativity theory, there is a clear and compelling way to establish connections to the classical absolutist-relationist disputes, and that in both these theories it is the absolutist position that is prima facie victorious. To support my arguments and give a clear overview of the whole debate, I end by offering definitional sketches of relationism and absolutism (substantivalism) about spacetime in the context of contemporary physics. The sketches show the clear connections between these views today and their ancestors in Newton and Leibniz. But at the same time, they indicate how both views are not just claims about existing physical theories, but rather also bets about how future physics will clarify the ontological picture. (shrink)

I discuss a rarely mentioned correspondence between Einstein and Swann on the constructive approach to the special theory of relativity, in which Einstein points out that the attempts to construct a dynamical explanation of relativistic kinematical effects require postulating a fundamental length scale in the level of the dynamics. I use this correspondence to shed light on several issues under dispute in current philosophy of spacetime that were highlighted recently in Harvey Brown’s monograph Physical Relativity, namely, Einstein’s view on the (...) distinction between principle and constructive theories, and the consequences of pursuing the constructive approach in the context of spacetime theories. r 2008 Elsevier Ltd. All rights reserved. (shrink)

Panenetheism is the claim that God and the cosmos are intimately inter-related, with the cosmos being in God and God being in the cosmos. What does this exactly mean? The aim of this paper is to address this question by sheding light on four possible models of God-world-inter-relatedness. Being critical of those models, which understand maximal immanence in a literal, spatial sense, the paper argues in favor of a model, which cashes out immanence in terms of divine activity. God is, (...) where God acts. Since God acts upon all of creation everywhere and anytime, God is omnipresent to it at all times. Thus, the proposal is to read the ‘en’ in ‘panetheism’ in an ‘agential sense’: God is in the cosmos by creating and sustaining it and the cosmos is in God by constantly being within the sphere of divine activity. (shrink)

By briefly reviewing three well-known scientific revolutions in fundamental physics (the discovery of inertia, of special relativity and of general relativity), I claim that problems that were supposed to be crying for a dynamical explanation in the old paradigm ended up receiving a structural explanation in the new one. This claim is meant to give more substance to Kuhn’s view that revolutions are accompanied by a shift in what needs to be explained, while suggesting at the same time the existence (...) of a pattern that is common to all of the discussed case-studies. It remains to be seen whether also quantum mechanics, in particular entanglement, conforms to this pattern. (shrink)

The debate on the ontological status of spacetime in General Relativity has historically seen two principal philosophical contenders: substantivalism, roughly the view that holds that spacetime exists apart from the material contents of the universe, and relationism, the doctrine that spacetime does not exist, i.e., it is a mere abstract web of spatiotemporal relations among bodies. This dispute, however, has rarely been fought on a cosmological battlefield. In this paper an attempt in this direction is made. The question at issue (...) is the following: is there any feature of our universe that requires or is best explained in terms of a substantival space? I claim that there is indeed: the expansion of the universe, perhaps the most important phenomenon in cosmology, can play such a role. (shrink)

This paper explores early Australasian philosophy in some detail. Two approaches have dominated Western philosophy in Australia: idealism and materialism. Idealism was prevalent between the 1880s and the 1930s, but dissipated thereafter. Idealism in Australia often reflected Kantian themes, but it also reflected the revival of interest in Hegel through the work of ‘absolute idealists’ such as T. H. Green, F. H. Bradley, and Henry Jones. A number of the early New Zealand philosophers were also educated in the idealist tradition (...) and were influential in their communities, but produced relatively little. In Australia, materialism gained prominence through the work of John Anderson, who arrived in Australia in 1927, and continues to be influential. John Anderson had been a student of Henry Jones, who might therefore be said to have influenced both main strands of Australian philosophical thought. (shrink)

In this paper we discuss Priest’s account of change and motion, contrasting it with its more orthodox rival, the Russellian account. The paper is divided in two parts. In first one we take a stance that is more sympathetic to the Russellian view, arguing that Priest’s arguments against it are inconclusive. In the second part, instead, we take a more sympathetic attitude towards Priest’s objections. We argue, however, that if these objections pose insurmountable difficulties to the Russellian account, then they (...) pose the same difficulties also to Priest’s favoured Hegelian account, and for the same reasons. (shrink)