Zurvanism was an ancient variant of Zoroastrianism. According to Zurvanism, the great powers of good and evil, Ahura Mazda and Angra Mainyu, were the sons of a greater god Zurvan, associated with time. According to Eudemus of Rhodes, some Persian thinkers, presumably Zurvanists, took there to be three great principles underlying the world: light, darkness, and greatest of all time (or perhaps, according to Eudemus, space). This paper explores what metaphysics might underlie these doctrines, and what contemporary options we have (...) for making sense of a metaphysics where time is the ultimate principle. Among the options explored is the option that despite appearance many of the entities of the concrete world are identical to stretches of time, or are somehow aspects of stretches of time; that they include times as parts, or are included in times as parts; that they are somehow properties of time; or hylomorphic compounds of which time is the matter; that the world is somehow a mixture of time, light, and dark; or that somehow the ends or teloi of everyday objects and processes are to be found among good, evil, and time. (shrink)

The dynamic nature of physics cannot be captured through an exclusive focus on the static mathematical formulations of physical theories. Instead, we can more fruitfully think of physics as a set of distinctively social, cognitive, and theoretical/methodological practices. An emphasis on practice has been one of the most notable aspects of the recent “naturalistic turn” in general philosophy of science, in no small part due to the arguments of many feminist philosophers of science. A major project of feminist philosophy of (...) physics has been to shine a critical light on the social and cognitive practices in physics, and how those ultimately influence other aspects of the science. Here we argue that traditional philosophy of physics has focused exclusively on the theoretical/methodological practices of physics, and that feminist philosophy of physics seeks to broaden the focus to include the social and cognitive practices as well. (shrink)

'The arrow of time' refers to the curious asymmetry that distinguishes the future from the past. Reversing the Arrow of Time argues that there is an intimate link between the symmetries of 'time itself' and time reversal symmetry in physical theories, which has wide-ranging implications for both physics and its philosophy. This link helps to clarify how we can learn about the symmetries of our world, how to understand the relationship between symmetries and what is real, and how to overcome (...) pervasive illusions about the direction of time. Roberts explains the significance of time reversal in a way that intertwines physics and philosophy, to establish what the arrow of time means and how we can come to know it. This book is both mathematically and philosophically rigorous yet remains accessible to advanced undergraduates in physics and the philosophy of physics. This title is also available as Open Access on Cambridge Core. (shrink)

The contemporary standard view of phenomenal consciousness —shared by reductionists and non-reductionists alike—takes it to be a simple, ‘low-level’, ‘pre-reflective’ feature of mental states,...

This dissertation is divided into two parts. In the first part I defend substantivalism. I do this by offering, in chapter 1, a counterpart-theoretic defense of substantivalism from Leibniz’ shift arguments. Then, in chapter 2, I defend substantivalism from the hole argument and argue, against the consensus, that the question of haecceitism is irrelevant to substantivalism in the context of general relativity. In the second part of the dissertation I defend supersubstantivalism. I do this by offering, in chapter 3, an (...) argument against dualistic substantivalism. The argument appeals to plausible principles of modal plenitude to show that the dualist is committed to a range of problematic possibilities. Then, in chapter 4, I consider a range of supersubstantivalist positions. I conclude by arguing for a version of supersubstantivalism I call compresence supersubstantivalism. (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”.

This paper examines a recent attempt by Evan Jobe to account for the asymmetric character of many scientific explanations. It is argued that a purported counterexample to Jobe's account, from Clark Glymour, is inconclusive, but that the account faces independent objections. It is also suggested, contrary to Jobe, that the explanatory relation is not always asymmetric. Sometimes a singular sentence C can figure in a DN derivation of another singular sentence E and E can also figure in a DN derivation (...) of C. Yet while we are inclined to regard the first derivation as an explanation of E, we are not inclined to regard the second derivation as an explanation of C. As Sylvain Bromberger pointed out in a now classic article (1966), one can explain the period of a pendulum by reference to its length and yet, although one can give a DN derivation of the length of a pendulum by reference to its period, this derivation does not seem to represent an explanation. Evan Jobe has recently offered an interesting account of such explanatory asymmetries and Clark Glymour has in turn proposed a counterexample which seems to show that Jobe's account is defective. The aim of this paper is two-fold. I shall attempt to show that (a) Glymour's proposed counterexample can be rejected on the grounds that it violates an independently plausible restriction on the role that equalities may play in DN explanation, and that (b) although Glymour's counterexample can be avoided in this way, Jobe's account is defective in several other respects. (shrink)

We examine critically the interdependence between science and philosophy which Sklar asserts in Space, Time, and Spacetime. We find that such a view makes it difficult to criticize the ideas of science, like that of absolute space, on their own merits, without importing extraneous philosophical associations. It also impedes appreciation of the importance, and subtlety, of explanation in scientific theory. As a result, particular explanations, such as the one Newton offered of his bucket experiment, are dismissed facilely-- indeed, all geometric (...) explanation appears illegitimate--, and such general attitudes as conventionalism appear to lack rationale. (shrink)

A popular method for comparing the structures of mathematical objects, which I call the ‘subset approach’, says that X has more structure than Y just in case X’s automorphisms form a proper subset of Y’s automorphisms. This approach is attractive, in part, because it seems to yield the right results in some comparisons of spacetime structure. But as I show, it yields the wrong results in a number of other cases. The problem is that the subset approach compares structure using (...) automorphism sets. So a different approach is needed: structure should be compared using automorphism groups. (shrink)

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)

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.

I argue that a criterion of theoretical equivalence due to Glymour :227–251, 1977) does not capture an important sense in which two theories may be equivalent. I then motivate and state an alternative criterion that does capture the sense of equivalence I have in mind. The principal claim of the paper is that relative to this second criterion, the answer to the question posed in the title is “yes”, at least on one natural understanding of Newtonian gravitation.

Unrestricted Composition (UC) is, roughly, the claim that given any objects at all, there is something which those objects compose. (UC) conflicts in an obvious way with common sense. It has as a consequence, for instance, that there is something which has as parts my nose and the moon. One of the more influential arguments for (UC) is Theodore Sider’s version of the Argument from Vagueness. (A version of the Argument from Vagueness was first presented by David Lewis (1986), pp. (...) 212–213). That argument purports to show that some plausible claims concerning the nature of vagueness entail (UC). In this paper I will suggest a response to this argument. I will show that the proponent of Supersubstantivalism (SS)—the view that material objects are identical to regions of spacetime—can reject a premise of Sider’s argument without denying the plausible claims concerning vagueness. Doing so requires only rejecting a certain view concerning the relationship between the proper sub-region relation and the proper parthood relation. So, proponents of (SS) are in a better position than many of us to side with common sense regarding composition. In the first section of the paper, I will present Sider’s argument. In the second section, I will introduce (SS) and briefly discuss some reasons one might have to believe that it is true. In the third section, I will show how the proponent of (SS) can avoid commitment to (UC) and reject a premise of Sider’s argument. Last, I’ll briefly consider and respond to some objections. (shrink)

The aim of this article is to analyse the relation between the second law of thermodynamics and the so-called arrow of time. For this purpose, a number of different aspects in this arrow of time are distinguished, in particular those of time-reversal (non-)invariance and of (ir)reversibility. Next I review versions of the second law in the work of Carnot, Clausius, Kelvin, Planck, Gibbs, Caratheodory and Lieb and Yngvason, and investigate their connection with these aspects of the arrow of time. It (...) is shown that this connection varies a great deal along with these formulations of the second law. According to the famous formulation by Planck, the second law expresses the irreversibility of natural processes. But in many other formulations irreversibility or even time-reversal non-invariance plays no role. I therefore argue for the view that the second law has nothing to do with the arrow of time. (shrink)

Background independence begins life as an informal property that a physical theory might have, often glossed as 'doesn't posit a fixed spacetime background'. Interest in trying to offer a precise account of background independence has been sparked by the pronouncements of several theorists working on quantum gravity that background independence embodies in some sense an essential discovery of the General Theory of Relativity, and a feature we should strive to carry forward to future physical theories. This paper has two goals. (...) The first is to investigate what a world must be like in order to be truly described by a background independent theory given extant accounts of background independence. The second is to argue that there are no non-empirical reasons to be more confident in theories that satisfy extant accounts of background independence than in theories that don't. The paper concludes by drawing a general moral about a way in which focussing primarily on mathematical formulations of our physical theories can adversely affect debates in the metaphysics of physics. (shrink)

Recent defenses of a priori knowledge can be applied to the idea of conventions in science in order to indicate one important sense in which conventionalism is correctsome elements of physical theory have a unique epistemological status as a functionally a priori part of our physical theory. I will argue that the former a priori should be treated as empirical in a very abstract sense, but still conventional. Though actually coming closer to the Quinean position than recent defenses of a (...) priori knowledge, the picture of science developed here is very different from that developed in Quinean holism in that categories of knowledge can be differentiated. (shrink)

Widespread reliance on representationalist understandings commit social scientists to either partially or totally decouple belief from reality, limiting the domain of phenomena that can be treated by belief as an analytic concept. Developing the contrastive notion of practical belief, we introduce the hysteresis effect as a situational phenomenon involving the systematic production of agent-environment mismatches and argue for its placement as a central problem for the theory of action. Revealing the dynamic, embodied conservation of belief in the temporality of practice, (...) hysteresis appears when environmental contexts change in a way that leaves actors without an ontologically complicit relationship to institutions as scaffolds of action. Under these circumstances, a past-inflected reflexiveness replaces a forward-inflecting practical belief in the actor's temporal relation to the world. Drawing from a variety of historical case studies, we locate hysteresis in routine disjunctures between the temporality of practice and the temporality of environments. Our analysis reveals four distinct types of reflexiveness produced the hysteresis effect, each with a unique dispositional impact on actors and extensions to group-level phenomena. We conclude the article by emphasizing the non-eliminativist relationship between belief as disposition and belief as representation. (shrink)

A material simple is a material object that has no proper parts. Some philosophers have argued for the possibility of extended simples. Some have even argued for the possibility of heterogeneous simples or simples that have intrinsic variations across their surfaces. There is a puzzle, though, that is meant to show that extended, heterogeneous simples are impossible. Although several plausible responses have been given to this puzzle, I wish to reopen the case against extended, heterogeneous simples. In this paper, I (...) briefly canvass responses to this puzzle which may be made in defense of extended, heterogeneous simples. I then present a new version of this puzzle which targets simples that occupy atomic yet extended regions of space. It seems that none of the traditional responses can be used to successfully save this particular kind of extended simple from the new puzzle. I also consider some non-traditional defenses of heterogeneous extended simples and argue that they too are unsuccessful. Finally, I will argue that a substantial case can be made against the possibility of extended heterogeneous simples of any kind. (shrink)

Rabbi Nachman of Bratslav describes the tzaddik as experiencing time in a distinctive, enlightened way: What is seventy years for the rest of us feels like a mere fifteen minutes for the tzaddik. Furthermore, even higher levels of enlightenment are possible—for a tzaddik on a higher level, what feels like seventy years for the first tzaddik is again but a mere fifteen minutes. This pattern continues, approaching a limit point which Rabbi Nachman calls “above time,” and which is the perspective (...) on time of the Divine. How might Rabbi Nachman’s claims about enlightened temporal experience be understood? In this paper, my aim is to examine some ways of understanding what it might mean to ‘experience time more quickly’ or to ‘experience 70 years as 15 minutes’ in light of contemporary theories of the structure of temporal experience. I then present a novel interpretation of Rabbi Nachman’s claims which appeals to the contemporary notion of the specious present —a nonzero temporal interval experienced in a unified way as present. (shrink)

This essay explores the use of platonist and nominalist concepts, derived from the philosophy of mathematics and metaphysics, as a means of elucidating the debate on spacetime ontology and the spatial structures endorsed by scientific realists. Although the disputes associated with platonism and nominalism often mirror the complexities involved with substantivalism and relationism, it will be argued that a more refined three-part distinction among platonist/nominalist categories can nonetheless provide unique insights into the core assumptions that underlie spatial ontologies, but it (...) also assists in critiquing alternative uses of nominalism, platonism, and both ontic and epistemic structural realism. (shrink)

This essay presents an alternative to contemporary substantivalist and relationist interpretations of quantum gravity hypotheses by means of an historical comparison with the ontology of space in the seventeenth century. Utilizing differences in the spatial geometry between the foundational theory and the theory derived from the foundational, in conjunction with nominalism and platonism, it will be argued that there are crucial similarities between seventeenth century and contemporary theories of space, and that these similarities reveal a host of underlying conceptual issues (...) that the substantival/relational dichotomy fails to distinguish. (shrink)

This essay explores the possibility of constructing a structural realist interpretation of spacetime theories that can resolve the ontological debate between substantivalists and relationists. Drawing on various structuralist approaches in the philosophy of mathematics, as well as on the theoretical complexities of general relativity, our investigation will reveal that a structuralist approach can be beneficial to the spacetime theorist as a means of deflating some of the ontological disputes regarding similarly structured spacetimes.

This paper investigates the question of, and the degree to which, Newton’s theory of space constitutes a third-way between the traditional substantivalist and relationist ontologies, i.e., that Newton judged that space is neither a type of substance/entity nor purely a relation among such substances. A non-substantivalist reading of Newton has been famously defended by Howard Stein, among others; but, as will be demonstrated, these claims are problematic on various grounds, especially as regards Newton’s alleged rejection of the traditional substance/accident dichotomy (...) concerning space. Nevertheless, our analysis of the metaphysical foundations of Newton’s spatial theory will strive to uncover its unique and innovative characteristics, most notably, the distinctive role that Newton’s “immaterialist” spatial ontology plays in his dynamics. (shrink)

This paper investigates Newton’s ontology of space in order to determine its commitment, if any, to both Cambridge neo-Platonism, which posits an incorporeal basis for space, and substantivalism, which regards space as a form of substance or entity. A non-substantivalist interpretation of Newton’s theory has been famously championed by Howard Stein and Robert DiSalle, among others, while both Stein and the early work of J. E. McGuire have downplayed the influence of Cambridge neo-Platonism on various aspects of Newton’s own spatial (...) hypotheses. Both of these assertions will be shown to be problematic on various grounds, with special emphasis placed on Stein’s influential case for a non-substantivalist reading. Our analysis will strive, nonetheless, to reveal the unique or forward-looking aspects of Newton’s approach, most notably, his critical assessment of substance ontologies, that help to distinguish his theory of space from his neo-Platonic contemporaries and predecessors. (shrink)

This paper explores the possibility of constructing a Cartesian space-time that can resolve the dilemma posed by a famous argument from Newton's early essay, De gravitatione. In particular, Huygens' concept of a center-of-mass reference frame is utilized in an attempt to reconcile Descartes' relationalist theory of space and motion with both the Cartesian analysis of bodily impact and conservation law for quantity of motion. After presenting a modern formulation of a Cartesian space-time employing Huygens' frames, a series of Newtonian counter-replies (...) are developed in order to estimate the viability of this relationalist project. (shrink)

This paper examines Descartes' problematic relational theory of motion, especially when viewed within the context of his dynamics, the Cartesian natural laws. The work of various commentators on Cartesian motion is also surveyed, with particular emphasis placed upon the recent important texts of Garber and Des Chene. In contrast to the methodology of most previous interpretations, however, this essay employs a modern "spacetime" approach to the problem. By this means, the role of dynamics in Descartes' theory, which has often been (...) neglected in favor of kinematic factors, is shown to be central to finding a solution to the puzzle of Cartesian motion. (shrink)

No one denies that time and space are different; and it is easy to catalog differences between them. I can point my finger toward the west, but I can’t point my finger toward the future. If I choose, I can now move to the left, but I cannot now choose to move toward the past. And (as D. C. Williams points out) for many of us, our attitudes toward time differ from our attitudes toward space. We want to maximize our (...) temporal extent and minimize our spatial extent: we want to live as long as possible but we want to be thin.1 But these differences are not very deep, and don’t get at the essence of the difference between time and space. That’s what I want to understand: I want to know what makes time different from space. I want to know which difference is the fundamental difference between them. (shrink)

Sklar ([1974]) claimed that relationalism about ontology-the doctrine that space and time do not exist-is compatible with Newtonian mechanics. To defend this claim he sketched a relationalist interpretation of Newtonian mechanics. In his interpretation, absolute acceleration is a fundamental, intrinsic property of material bodies; that a body undergoes absolute acceleration does not entail that space and time exist. But Sklar left his proposal as just a sketch; his defense of relationalism succeeds only if the sketch can be filled in. I (...) argue that this cannot be done. There can be no (relationalist) dynamical laws of motion based on Sklar's proposal that capture the content of Newton's theory. So relationalists must look elsewhere for a relationalist interpretation of Newtonian mechanics. (shrink)

It is widely believed that shapes are intrinsic properties. But this claim is hard to defend. I survey all known theories of shape properties, and argue that each theory is either incompatible with the claim that shapes are intrinsic, or can be shown to be false.

Several variant "Newtonian" theories of inertia and gravitation are described, and their scientific usefulness discussed. An examination of these theories is used to throw light on traditional epistemological and metaphysical questions about space and time. Finally these results are examined in the light of the changes induced by the transition from "Newtonian" to general relativistic spacetime.

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.

One of the issues dividing "absolutists" and "relationists" is the question whether all motion is relative motion or, in the words of Earman, spacetime has "structures that support absolute quantities of motion." This paper argues that, despite the enormous literature bearing on the topic, it is problematic to formulate a general criterion for when a quantity counts as absolute in contrast to merely relative in a way that is not hopelessly parasitic on other, presumably distinct, senses of "absolute." Furthermore, I (...) suggest that the vicissitudes of the evolution of the concept of absolute motion have contributed to this difficulty. (shrink)

We give a precise and modern mathematical characterization of the Newtonian spacetime structure (ℕ). Our formulation clarifies the concepts of absolute space, Newton's relative spaces, and absolute time. The concept of reference frames (which are “timelike” vector fields on ℕ) plays a fundamental role in our approach, and the classification of all possible reference frames on ℕ is investigated in detail. We succeed in identifying a Lorentzian structure on ℕ and we study the classical electrodynamics of Maxwell and Lorentz relative (...) to this structure, obtaining the important result that there exists only one intrinsic generalization of the Lorentz force law which is compatible with Maxwell equations. This is at variance with other proposed intrinsic generalizations of the Lorentz force law appearing in the literature. We present also a formulation of Newtonian gravitational theory as a curve spacetime theory and discuss its meaning. (shrink)

I elaborate and defend an interpretation of Leibniz on which he is committed to a stronger space-time structure than so-called Leibnizian space-time, with absolute speeds grounded in his concept of force rather than in substantival space and time. I argue that this interpretation is well-motivated by Leibniz's mature writings, that it renders his views on space, time, motion, and force consistent with his metaphysics, and that it makes better sense of his replies to Clarke than does the standard interpretation. Further, (...) it illuminates the way in which Leibniz took his physics to be grounded in his metaphysics. (shrink)

Throughout the late nineteenth and early twentieth centuries, philosophers of various sorts, including Helmholtz, Avenarius, Husserl, Russell, Carnap, Neurath, and Heidegger, were united in promulgating a new, “scientific” philosophy. This article documents some of the varieties of scientific philosophy and argues that the history of scientific philosophy is crucial to the development of analytic philosophy and the division between analytic and continental philosophy. Scientific philosophy defined itself via criticisms of old-fashioned systematic metaphysics and, in the twentieth century, of Lebensphilosophie. It (...) offered a modernist vision of philosophy participating in a progressive, problem-solving, piecemeal, and collaborative scientific ethos. The article argues that the rise of scientific philosophy indicates a change of the conception of science as well as philosophy in the late nineteenth century and notes some tensions in the accounts of science offered by scientific philosophers. The article offers some preliminary lessons for the interpretation of logical empiricism and phenomenology as episodes within a larger history of scientific philosophy. (shrink)

We find that E. J. Lowe’s resolution to David Lewis’s problem of temporary intrinsics is wrong, but not quite for the reasons adduced by Lewis himself. Our discussion hinges on a connection between state-independent properties and intrinsic properties.

The existence of fields besides gravitation may provide us with a way to decide empirically whether spacetime is really a nonflat Riemannian manifold or a flat Minkowskian manifold that appears curved as a result of gravitational distortions. This idea is explained using a modification of Poincaré's famous 'diskworld'.

This article motivates and develops a reductive account of the structure of certain physical quantities in terms of their mereology. That is, I argue that quantitative relations like "longer than" or "3.6-times the volume of" can be analyzed in terms of necessary constraints those quantities put on the mereological structure of their instances. The resulting account, I argue, is able to capture the intuition that these quantitative relations are intrinsic to the physical systems they’re called upon to describe and explain.

According to substantivalism, spacetime points and regions are real entities whose existence is not dependent on matter. In this paper, I motivate and defend a version of substantivalism which takes the totality of spacetime as fundamental, and show how this position avoids certain problem cases, in particular the objection from static Leibniz shifts, and better conforms to how we think about space in physics. I argue that, even though the static Leibniz shifts do not show ordinary substantivalism is committed to (...) in-principle undetectable physical structure ), they do indicate something problematic about the modal profile of space-time and its constituents. While the problem is modal, the solution cannot be solely a matter of revising the substantivalist's modal claims. Rather, I argue, the substantivalist must revise her background ontology of space-time. I show how this can be done by developing substantivalist theory that rejects this picture in favor of an alternative ontology of space-time in the spirit of priority monism. (shrink)

I explore some of the ways that assumptions about the nature of substance shape metaphysical debates about the structure of Reality. Assumptions about the priority of substance play a role in an argument for monism, are embedded in certain pluralist metaphysical treatments of laws of nature, and are central to discussions of substantivalism and relationalism. I will then argue that we should reject such assumptions and collapse the categorical distinction between substance and property.

The mainstream concept of death—the biological one—identifies death with the cessation of an organism. In this article, I challenge the mainstream position, showing that there is no single well-established concept of an organism and no universal concept of death in biological terms. Moreover, some of the biological views on death, if applied in the context of bedside decisions, might imply unacceptable consequences. I argue the moral concept of death—one similar to that of Robert Veatch—overcomes such difficulties. The moral view identifies (...) death with the irreversible cessation of a patient’s moral status, that is, a state when she can no longer be harmed or wronged. The death of a patient takes place when she is no longer capable of regaining her consciousness. In this regard, the proposal elaborated herein resembles that of Veatch yet differs from Veatch’s original project since it is universal. In essence, it is applicable in the case of other living beings such as animals and plants, provided that they have some moral status. (shrink)

We often use symmetries to infer outcomes’ probabilities, as when we infer that each side of a fair coin is equally likely to come up on a given toss. Why are these inferences successful? I argue against answering this with an a priori indifference principle. Reasons to reject that principle are familiar, yet instructive. They point to a new, empirical explanation for the success of our probabilistic predictions. This has implications for indifference reasoning in general. I argue that a priori (...) symmetries need never constrain our probability attributions, even when it comes to our initial credences. (shrink)

Left and right hands are incongruent counterparts. Yet each replicates the intrinsic properties of the other. This suggests that differing relations to space make the difference. Kant's and Weyl's discussions of the problem are critically discussed. It emerges that spatial relationism fails to explain how its relations may be interpreted. An excursion into visual geometry explains the basis of handedness in the orientable structure of space.

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)

We here present explicit relational theories of a class of geometrical systems (namely, inner product spaces) which includes Euclidean space and Minkowski spacetime. Using an embedding approach suggested by the theory of measurement, we prove formally that our theories express the entire empirical content of the corresponding geometric theory in terms of empirical relations among a finite set of elements (idealized point-particles or events) thought of as embedded in the space. This result is of interest within the general phenomenalist tradition (...) as well as the theory of space and time, since it seems to be the first example of an explicit phenomenalist reconstruction of a realist theory which is provably equivalent to it in observational consequences. The interesting paper "On the Space-Time Ontology of Physical Theories" by Ken Manders, Philosophy of Science, vol. 49, number 4, December 1982, p. 575-590, has significant affinities to this one. We both, in a sense, try to formally vindicate Leibniz's notion of a relational theory of space, by constructing theories of spatial relations among physical objects which are provably equivalent to the standard absolutist theories. The essential difference between our approaches is that Manders retains Leibniz's explicitly modal framework, whereas I do not. Manders constructs a spacetime theory which explicitly characterizes the totality of possible configurations of physical objects, using a modal language in which the notion of a possible configuration occurs as a primitive. There is no doubt that this is a more accurate realization of Leibniz's own conception of space than the embedding-based approach developed here. However, it also remains open to objections (such as those cited here from Sklar) on account of the special appeal to modal notions. Our approach here, by contrast, aims to avoid the special appeal to modal notions by giving directly a set of laws which are satisfied by a configuration individually, if and only if it is one of the allowable ones. One thus avoids the need for reference to possible but not actual configurations or objects, in the statement of the spacetime laws. We may then take this alternative set of laws as the actual geometric theory, and do away with the hypothetical entity called 'space'. Yet at the same time there is no invocation of modality, except in the ordinary sense in which every physical theory constrains what is possible. So that a relationalist is not forced to utilize a modal language (though Leibniz certainly does.). (shrink)