Relative motion of particles is examined in the context of relational space-time. It is shown that de Broglie waves may be derived as a representation of the coordinate maps between the rest-frames of these particles. Energy and momentum are not absolute characteristics of these particles, they are understood as parameters of the coordinate maps between their rest-frames. It is also demonstrated the position of a particle is not an absolute, it is contingent on the frame of reference used to (...) observe the particle. (shrink)

This is a revised and shortened version of ‘Relational Space and Places of Value’, Logical Analysis and History of Philosophy, 14 (2011), 89-106.

Drawing on a Leibnizian panpsychist ontology of living beings that have a body and a soul, this paper outlines a theory of space based on the perceptual and appetitive relations among these creatures’ souls. In parallel with physical space founded on relations among bodies subject to efficient causation, teleological space results from relations among souls subject to final causation and is described qualitatively in terms of creatures’ pleasure and pain, wellbeing and happiness. Particular places within this space include the kingdom (...) of grace, where morally responsible, rational beings act as far as possible in accord with the ideal of justice as universal love and wise benevolence. However, while Leibniz considered love as properly directed only towards rational beings, it is argued here that the truly wise person will direct their love and benevolence towards all living things. Ausgehend von Leibniz’ panpsychistischer Ontologie von Lebewesen, die einen Körper und eine Seele haben, skizziert dieser Beitrag eine Theorie des Raumes, der auf den perzeptuellen und appetitiven Relationen zwischen den Seelen der Geschöpfe beruht. Parallel zum physikalischen Raum, der in Relationen zwischen den effizient kausal interagierenden Körper begründet liegt, ergibt sich aus den Relationen zwischen den Seelen, die finaler Verursachung unterliegen und in qualitativen Begriffen von Freude und Schmerz wie von Wohl und Zufriedenheit beschrieben werden, ein teleologischer Raum. Besondere Regionen dieses Raumes bilden das Königreich der Gnade, wo moralisch verantwortliche, rationale Wesen so weit wie möglich in Übereinstimmung mit dem Ideal der Gerechtigkeit als universale Liebe und weise Güte handeln. Während Leibniz jedoch meinte, dass sich echte Liebe nur auf rationale Wesen richte, wird hier argumentiert, dass eine wahrhaft weise Person ihre Liebe und Güte auf alle Lebewesen beziehen wird. (shrink)

The present paper aims to contribute to the substantivalism versus relationalism debate and to defend general relativity (GR) against pseudoscientific attacks in a novel, especially inclusive way. This work was initially motivated by the desire to establish the incompatibility of any ether theories with accelerated cosmic expansion and inflation (motto: where would a hypothetical medium supposedly come from so fast?). The failure of this program is of interest for emergent GR concepts in high energy particle physics. However, it becomes increasingly (...) important to guard scientific results against their misrepresentation by fundamentally anti-scientific agendas. We therefore argue that although it is not known whether the perceived space-time is fundamental (rather than a condensed state or a particular membrane), in a fundamental theory, space-time must be abstract relational: fundamental space-time is the consistent spatial-temporal arrangement of events. To pursue its own goals, this work should be accessible to a wide audience: physicists, philosophers of science, those being tempted by anti-relativity theories, but also those who vigorously defend some orthodox relativity that is not actually supported by GR. It must thus be extensive in order to satisfy the different parties’ desire to have included and understood their respective positions. (shrink)

As Pooley (2001) explains, the challenge of giving a relational account of orientability (and topology more generally) is not an easy one. This paper criticizes Pooley's and other proposals, raises a range of problems for the project, and then proposes a novel way for the relationist to understand not only topology, but also the geometry of space. This proposal is the `regularity account' since it claims that geometry and topology supervene on the regular ways in which relations evolve.

Post-structuralist Geography is a highly accessible introduction to post-structuralist theory that critically assesses how post-structuralism can be used to study space and place. The text comprises: - a thorough appraisal of the work of key post-structuralist thinkers, including Gilles Deleuze, Michel Foucault, and Bruno Latour - case studies to elucidate, illustrate, and apply the theory - boxed summaries of complex arguments which - with the engaging writing style - provide a clear overview of post-structuralist approaches to the study of space (...) and place. Comprehensive and comprehensible - communicating a new and exciting agenda for human geography - Post-structuralist Geography is the students’ essential guide to the theoretical literature. (shrink)

The public/private dichotomy has long been the object of considerable attention for feminists. We argue that, by focusing their attention on a divide which has declined in importance, feminists may fail to keep up with the current means by which sexual inequalities are perpetuated. Furthermore, by concentrating on this divide feminists risk reproducing such dichotomous thinking in their own work, discursively perpetuating that which they had initially hoped to displace. We begin by surveying feminist critiques of the public/private dichotomy, consider (...) recent moves to go beyond critique, yet suggest that the dichotomy continues to be a framing concern within feminist work. We then survey the way in which space has been understood within geography, and consider the implications of adopting a relational conception of space for analysis of public and private in political theory. We offer a broader framework for examining the ways in which sexual inequalities are reproduced in contemporary society. We therefore open up the possibility that over time inequalities may be mediated to a greater or lesser degree by spatial divisions. This places a further pressure on the assumption that the public/private divide, or some variation thereof, must be at the heart of feminist theorizing. (shrink)

Originally published in 1921, this book presents a concise study of time and space relations by the renowned British physicist Alfred Robb (1873-1936). The text is one of a series of works on the topic of special relativity written by Robb from 1911 onwards. An appendix section is included. This book will be of value to anyone with an interest in special relativity, the development of physics and the history of science.

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)

This book proposes the foundation of the relational approach to biology, rejecting the deterministic and reductionist approach of molecular biology. Although biology has made enormous progress in the last seventy years, onto genesis is still conceived as a “revelation” of information (DNA). Recovering the geometric tradition, relational biology conceives scientific and epistemological tools (cause, probability, space etc.) of science in a new way. If probabilistic biology and organicism still proposes a biology based on physics, with a fundamental invariant, (...) relational biology is based on variation: its fundamental invariant is variation, one of the most important elements of life. This is an indispensable book for academics who consider biology from a new theoretical approach, in particular for those working in the domains of cancer, ontogenesis and evolution. (shrink)

. A space for ‘who’ – a culture of ‘two’: speculations related to an ‘in-between knowledge’. Ethics and Education: Vol. 7, Creating spaces, pp. 251-260. doi: 10.1080/17449642.2013.767084.

This chapter considers three substantivalist theories, namely, the theory of spatial qualities, spatial monism, and body‐space dualism, and two relationist theories, namely, Aristotelian relationism and modern relationism. Spatial Substantivalism comes in two forms, depending on whether places are properties or not. Assuming that places are properties amounts to the theory of spatial qualities; the alternative version of substantivalism is spatial particularism. Spatial particularism in turn comes in two forms, body‐space dualism and spatial monism. Spatial relationists also come in two forms, (...) Aristotelian and modern. modern relationists believe that the fundamental spatial relation is the distance between dimensionless point‐masses. Aristotelian Relationists take the fundamental spatial properties to be volume and shape, and the only fundamental spatial relation to be contiguity. A critical difference between spatial substantivalists and spatial relationists concerns their treatments of empty space. (shrink)

In this chapter, I evaluate various conceptions of distance. Of the two most prominent, one takes distance relations to be intrinsic, the other extrinsic. I recommend pluralism: different conceptions can peacefully coexist as long as each holds sway over a distinct region of logical space. But when one asks which conception holds sway at the actual world, one conception stands out. It is the conception of distance embodied in differential geometry, what I call the Gaussian conception. On this conception, all (...) fundamental facts about distance are “local” facts.” But there is a problem: the Gaussian conception, notwithstanding its mathematical and physical credentials, appears metaphysically suspicious on Humean grounds. In the final section, I suggest that the Gaussian conception can be given a sound metaphysical footing in terms of non-standard analysis. (shrink)

We construct a computable vector space with the trivial computable automorphism group, but with the dependence relations as complicated as possible, measured by their Turing degrees. As a corollary, we answer a question asked by A.S. Morozov in [Rigid constructive modules, Algebra and Logic, 28 570–583 ; 379–387 ].

The epistemological rupture of Copernicus, the laws of planetary motions of Kepler, the comprehensive physical observations of Galileo and Huygens, the conception of relativity, and the physical theory of Newton were components of an extremely fertile and influential cognitive environment that prompted the restless Leibniz to shape an innovative theory of space and time. This theory expressed some of the concerns and intuitions of the scientific community of the seventeenth century, in particular the scientific group of the Academy of Sciences (...) of Paris, but remained relatively unknown until the twentieth century. After Einstein, however, the relational theory of Leibniz gained wider respect and fame. The aim of this article is to explain how Leibniz foresaw relativity, through his critique of contemporary mechanistic philosophy. (shrink)

In previous work, we introduced a version of distributed temporal logic that is well-suited both for verifying security protocols and as a metalogic for reasoning about, and relating, different security protocol models. In this paper, we formally investigate the relationship between our approach and strand spaces, which is one of the most successful and widespread formalisms for analyzing security protocols. We define translations between models in our logic and strand-space models of security protocols, and we compare the results obtained (...) with respect to the level of abstraction that is inherent in each of the formalisms. This allows us to clarify different aspects of strand spaces that are often left implicit, as well as pave the way to transfer results, techniques and tools across the two approaches. (shrink)

It has often been suggested that the meaning of terms is theory dependent. Bas van Fraassen has proposed a particular way of inferring which sentences are true in virtue of meaning, given a theory in so-called state-space format. I examine his claims by means of simple examples.

Clark & Thornton have demonstrated the paradox between the opacity of the transformations that underlie relational mappings and the ease with which people learn such mappings. However, C&T's trading-spaces proposal resolves the paradox only in the broadest outline. The general-purpose algorithm promised by C&T remains to be developed. The strategy of doing so is to analyze and formulate computational mechanisms for known cases of recoding.

We extend Bishopʼs concept of function spaces to the concept of pre-function spaces. We show that there is an adjunction between the category of neighbourhood spaces and the category of Φ-closed pre-function spaces. We also show that there is an adjunction between the category of uniform spaces and the category of Ψ-closed pre-function spaces.

Since antiquity, natural philosophers have struggled to comprehend the nature of three tightly interconnected concepts: space, time, and motion. A proper understanding of motion, in particular, has been seen to be crucial for deciding questions about the natures of space and time, and their interconnections. Since the time of Newton and Leibniz, philosophers’ struggles to comprehend these concepts have often appeared to take the form of a dispute between absolute conceptions of space, time and motion, and relational conceptions. This (...) article guides the reader through some of the history of these philosophical struggles. Rather than taking sides in the (alleged) ongoing debates, or reproducing the standard dialectic recounted in most introductory texts, we have chosen to scrutinize carefully the history of the thinking of the canonical participants in these debates — principally Descartes, Newton, Leibniz, Mach and Einstein. Readers interested in following up either the historical questions or current debates about the natures of space, time and motion will find ample links and references scattered through the discussion and in the Other Internet Resources section below. (shrink)