We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in [Maudlin 2012] and [Malament, unpublished]. It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of [Tarski 1959]: a predicate of betwenness and a (...) four place predicate to compare the square of the relativistic intervals. Minkowski spacetime is described as a four dimensional ‘vector space’ that can be decomposed everywhere into a spacelike hyperplane - which obeys the Euclidean axioms in [Tarski and Givant, 1999] - and an orthogonal timelike line. The length of other ‘vectors’ are calculated according to Pythagora’s theorem. We conclude with a Representation Theorem relating models of our system that satisfy second order continuity to the mathematical structure called ‘Minkowski spacetime’ in physics textbooks. (shrink)

The debate on the conventionality of simultaneity and the debate on the dimensionality of the world have been central in the philosophy of special relativity. The link between both debates however has rarely been explored. The purpose of this paper is to gauge what implications the former debate has for the latter. I show the situation to be much more subtle than was previously argued, and explain how the ontic versus epistemic distinction in the former debate impacts the latter. Despite (...) claims to the contrary, I conclude that special relativity leaves the debate on the dimensionality of the world underdetermined. (shrink)

The problem of underdetermination is thought to hold important lessons for philosophy of science. Yet, as Kyle Stanford has recently argued, typical treatments of it offer only restatements of familiar philosophical problems. Following suggestions in Duhem and Sklar, Stanford calls for a New Induction from the history of science. It will provide proof, he thinks, of “the kind of underdetermination that the history of science reveals to be a distinctive and genuine threat to even our best scientific theories” (Stanford 2001, (...) p. S12). This paper examines Stanford’s New Induction and argues that it – like the other forms of underdetermination that he criticizes – merely recapitulates familiar philosophical conundra. (shrink)

Thermodynamics is the science that describes much of the time asymmetric behavior found in the world. This entry's first task, consequently, is to show how thermodynamics treats temporally ‘directed’ behavior. It then concentrates on the following two questions. (1) What is the origin of the thermodynamic asymmetry in time? In a world possibly governed by time symmetric laws, how should we understand the time asymmetric laws of thermodynamics? (2) Does the thermodynamic time asymmetry explain the other temporal asymmetries? Does it (...) account, for instance, for the fact that we know more about the past than the future? The discussion thus divides between thermodynamics being an explanandum or explanans. In the former case the answer will be found in philosophy of physics; in the latter case it will be found in metaphysics, epistemology, and other fields, though in each case there will be blurring between the disciplines. (shrink)

In this paper I wish to make some headway on understanding what \emph{kind} of problem the ``problem of time'' is, and offer a possible resolution---or, rather, a new way of understanding an old resolution. The response I give is a variation on a theme of Rovelli's \emph{evolving constants of motion} strategy. I argue that by giving correlation strategies a \emph{structuralist} basis, a number of objections to the standard account can be blunted. Moreover, I show that the account I offer provides (...) a suitable ontology for time in both classical and quantum canonical general relativity. (shrink)

Schulman (Entropy 7(4):221–233, 2005) has argued that Boltzmann’s intuition, that the psychological arrow of time is necessarily aligned with the thermodynamic arrow, is correct. Schulman gives an explicit physical mechanism for this connection, based on the brain being representable as a computer, together with certain thermodynamic properties of computational processes. Hawking (Physical Origins of Time Asymmetry, Cambridge University Press, Cambridge, 1994) presents similar, if briefer, arguments. The purpose of this paper is to critically examine the support for the link between (...) thermodynamics and an arrow of time for computers. The principal arguments put forward by Schulman and Hawking will be shown to fail. It will be shown that any computational process that can take place in an entropy increasing universe, can equally take place in an entropy decreasing universe. This conclusion does not automatically imply a psychological arrow can run counter to the thermodynamic arrow. Some alternative possible explanations for the alignment of the two arrows will be briefly discussed. (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.

My main aim in this paper is to show that influential antireductionist arguments such as Fodor's, Kitcher's, and Dupré's state stronger conclusions than they actually succeed in establishing. By putting to the fore the role of metaphysical presuppositions in these arguments, I argue that they are convincing only as 'temporally qualified argument', and not as 'generally valid ones'. I also challenge the validity of the strategy consisting in drawing metaphysical lessons from the failure of reductionist programmes. What most of these (...) antireductionist standpoints have in common is a pretension to methodological imports. I conclude by explaining why, in order to remain relevant for scientific practice, antireductionist arguments should stay clear of metaphysics, for the latter, I argue, does not mix well with a taste for methodological prescriptions. (shrink)

There are two ways that we might respond to the underdetermination of theory by data. One response, which we can call the agnostic response, is to suspend judgment: "Where scientific standards cannot guide us, we should believe nothing". Another response, which we can call the fideist response, is to believe whatever we would like to believe: "If science cannot speak to the question, then we may believe anything without science ever contradicting us". C.S. Peirce recognized these options and suggested evading (...) the dilemma. It is a Logical Maxim, he suggests, that there could be no genuine underdetermination. This is no longer a viable option in the wake of developments in modern physics, so we must face the dilemma head on. The agnostic and fideist responses to underdetermination represent fundamentally different epistemic viewpoints. Nevertheless, the choice between them is not an unresolvable struggle between incommensurable worldviews. There are legitimate considerations tugging in each direction. Given the balance of these considerations, there should be a modest presumption of agnosticism. This may conflict with Peirce's Logical Maxim, but it preserves all that we can preserve of the Peircean motivation. (shrink)

Der Artikel setzt sich mit Cassirers Erklärung für die durch die Relativitätstheorie aufgestellten philosophischen Probleme auseinander. Die Hauptfrage richtet sich darauf, wie Cassirer als Neukantianer auf Einsteins Entdeckungen antwortet. Das Problem, das hierbei aufkommt, ist die Präsupposition von der aprioristischen Natur der euklidischen Geometrie. Cassirers Antwort liegt in der Begründung, dass Kants Philosophie ausreichend breit angelegt sei, um auch nicht-euklidische Geometrien in die Determinierung der physikalischen Welt mit einzubeziehen. Er tut es, indem er aufweist, dass Kant, auch wenn er sie (...) für Formen der reinen Intuition hielt, Zeit und Raum mit bestimmten theoretischen Faktoren, mit Erkenntnisregeln in Verbindung brachte. Der Raum als reine Koexistenzform und die Zeit als reine Sukzessionsform implizieren keine besonderen Messrelationen, und es wäre folglich falsch, eine aprioristische Natur der Euklid’schen Geometrie anzunehmen. Die Art der Anwendung verschiedener Geometrien bei der Determinierung der physikalischen Welt wird erklärt in Anlehnung an Kleins Geometrieansatz, bei dem geometrische Eigenschaften vor dem Hintergrund einer bestimmten Gruppe von Transformationen als invariant bleibende angesehen werden. Das Konzept der Gruppe stellt das eigentliche Konzept a priori dar. Die Gruppentheorie spielt sogar eine größere Rolle sowohl in physikalischen Theorien als auch in Cassirers Epistemologie. Denn mit der Relativitätstheorie wird offenkundig, dass physikalische Theorien gegenüber einer Transformationsgruppe Invarianztheorien sind. Cassirer behauptet, dass die allgemeine Lehre von der Unveränderlichkeit bestimmter Werte in irgendeiner Form in jeglicher Theorie der Natur zurückkehren müsse, weil sie zur logischen und epistemologischen Natur einer solchen Theorie gehöre. (shrink)

The paper considers Cassirer’s account of the philosophical problems raised by the theory of relativity. The main question the paper addresses is how Cassirer, as a Neokantian, responds to the discoveries made by Einstein. The problem here is especially the presupposition of the a priori nature of Euclidean geometry. Cassirer’s answer lies in showing that Kant’s philosophy is broad enough to include also non-Euclidean geometries in the determination of the physical world. He does this by showing that though Kant conceived (...) space and time as forms of pure intuition he already connected them with certain theoretical factors, with the rules of the understanding. Space as the pure form of coexistence and time as the pure form of succession imply no special relations of measurement and it is thus a mistake to assume the a priori nature of Euclidean geometry. The way different geometries can figure in the determination of the physical world is explained in reference to the Klein approach to geometry, which defines geometrical properties as those that stay invariant according to a certain group of transformations. It is the concept of a group that is the real concept a priori. Group theory plays an even larger role in physical theories as well as Cassirer’s epistemology. Namely, with the theory of relativity it becomes evident that physical theories are theories of invariants according to a group of transformations. Cassirer claims that the general doctrine of invariability of certain values must recur in some form in any theory of nature, because it belongs to the logical and epistemological nature of such a theory. (shrink)

This is an excerpt from a report on the Temporal Experience Workshop at the University of Toronto in May of 2013. This portion of the report explores the question: What can we learn about the nature of time from the nature of ordinary experience?

This report highlights and explores four questions that arose from the workshop on temporal experience at the University of Toronto, May 20th and 21st, 2013.

Ontology is taken by Moulines as supervenient on science: what kinds of things there are is determined by our well-confirmed theories. But the fact is that today, science provides us with a multiplicity of well-confirmed theories, each having its own ontological commitments. The modest, ontological form of reduction advocated by Moulines (this volume) restores hope of putting some ontological order in the “huge chaotic supermarket of science”. In this paper I show that any claim on the amount of order obtained (...) by reduction does not only always remain “temporally qualified” but, worse for the reductionist with a taste for ontological order, that the very notion of orderliness must be relativized to the capacities and interests of knowers. (shrink)

It has been argued that the fundamental laws of physics are deceitful in that they give the impression of greater unity and coherence in our theories than is actually found to be the case. Causal stories and phenomenological relationships are claimed to provide a more acceptable account of the world, and only theoretical entities — not laws — are considered as perhaps corresponding to real features of the world.This paper examines these claims in the light of the author's own field (...) of research: high energy physics. Some of the distinctions upon which the above conclusions are based are found not to be tenable in practice. Examples from experimental particle physics are presented which suggest an important role of the underlying theoretical structure which cannot be overlooked. It is argued that the fundamental theories must, in fact, be treated as being as worthy or unworthy of ontological commitment as the entities they postulate or the phenomenological relationships they inspire. Whilst it is conceded that aspects of the current theoretical formalism belie literal interpretation, it is maintained that revision in these particular areas need not affect the symmetry principles, particle spectra, or coupling strengths that largely determine the empirical content of the theory. (shrink)

Abstract: Situations that social scientists and others explain by using concepts like "custom" and "norm" often tend to be situations in which many other kinds of explanations (for example, biological, psychological, economic, historical) seem plausible as well. Do these other explanations compete with the custom or norm explanations, or do they complement them? We need to consider this question carefully and not just assume that various accounts are all permissible at different levels of analysis. In this article I describe two (...) families of noncompeting accounts: (1) explanations of different (but similarly described) facts, and (2) accounts that seem to differ but are really different parts or versions of the same underlying explanation. I argue that while many types of apparent competitors don't really compete with norms, there are usually some that do. These competing accounts will usually undermine the norm account. (shrink)

In the exuberance that followed Einstein’s discoveries, philosophers at one time or another have proposed that his theories support virtually every conceivable moral in ontology. I present an opinionated assessment, designed to avoid this overabundance. We learn from Einstein’s theories of novel entanglements of categories once held distinct: space with time; space and time with matter; and space and time with causality. We do not learn that all is relative, that time in the fourth dimension in any non-trivial sense, that (...) coordinate systems and even geometry are conventional or that spacetime should be reduced ontologically to causal, spatio-temporal or other relations. (shrink)

In this essay I address the issue of whether Einstein's Special Theory of Relativity counts against a tensed or "A-series" understanding of time. Though this debate is an old one, it continues to be lively with many prominent authors recently arguing that a genuine A-series is compatible with a relativistic world view. My aim in what follows is to outline why Special Relativity is thought to count against a tensed understanding of time and then to address the philosophical attempts to (...) reconcile the two theories. I conclude that while modern physics on its own does not rule out the possibility of a real A-series, the combination of Einstein's theory and the philosophical arguments against tense is decisive. The upshot is that the tenseless or "B-series" view of time is the best one. (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)

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)

We divide analytic metaphysics into naturalistic and non-naturalistic metaphysics. The latter we define as any philosophical theory that makes some ontological (as opposed to conceptual) claim, where that ontological claim has no observable consequences. We discuss further features of non-naturalistic metaphysics, including its methodology of appealing to intuition, and we explain the way in which we take it to be discontinuous with science. We outline and criticize Ladyman and Ross's 2007 epistemic argument against non-naturalistic metaphysics. We then present our own (...) argument against it. We set out various ways in which intellectual endeavours can be of value, and we argue that, in so far as it claims to be an ontological enterprise, non-naturalistic metaphysics cannot be justified according to the same standards as science or naturalistic metaphysics. The lack of observable consequences explains why non-naturalistic metaphysics has, in general, failed to make progress, beyond increasing the standards of clarity and precision in expressing its theories. We end with a series of objections and replies. (shrink)

Artigo traduzido do original inglês " Is the Best Good Enough ?", publicado em Proceedings of the Aristotelian Society , vol. XCIII, parte 2, 1993, pp. 89-104. Todos os direitos do artigo estáo reservados aos editores de Aristotelian Society , a quem os tradutores agradecem, na pessoa de Mark Tavis, a licença para a traduçáo deste artigo. Reprinted by courtesy of the Editor of the Aristotelian Society: © [1993].

Time passes; sometimes swiftly, sometimes interminably, but always it passes. We see the world change as events emerge from the shroud of the future, clandestinely slinking into the past almost immediately as though they are reluctant to meet our gaze: children are born, old friends and relatives die, governments once full of youthful enthusiasm wane. If the Earth were sentient, it might feel itself being torn apart as tectonic plates diverge, and chuckle as it outlived species upon species of transient (...) parasites. How could anyone possibly deny that time passes? (shrink)

I examine the issue of persistence over time in thecontext of the special theory of relativity (SR). Thefour-dimensional ontology of perduring objects isclearly favored by SR. But it is a different questionif and to what extent this ontology is required, andthe rival endurantist ontology ruled out, by thistheory. In addressing this question, I take theessential idea of endurantism, that objects are whollypresent at single moments of time, and argue that itcommits one to unacceptable conclusions regardingcoexistence, in the context of SR. (...) I then propose anddiscuss a plausible account of coexistence forperduring objects, which is free of these defects. This leaves the endurantist room for some maneuvers. I consider them and show that they do not really helpthe endurantist out. She can accommodate the notionof coexistence in the relativistic framework only atthe cost of renouncing central endurantist intuitions. (shrink)