This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the (...) field, it lays down a much-needed marker of progress to date and provides a platform for informed and coherent future analysis and research of the subject. -/- The publication comes at a time of heightened worldwide concern over the standard of science and mathematics education, attended by fierce debate over how best to reform curricula and enliven student engagement in the subjects There is a growing recognition among educators and policy makers that the learning of science must dovetail with learning about science; this handbook is uniquely positioned as a locus for the discussion. -/- The handbook features sections on pedagogical, theoretical, national, and biographical research, setting the literature of each tradition in its historical context. Each chapter engages in an assessment of the strengths and weakness of the research addressed, and suggests potentially fruitful avenues of future research. A key element of the handbook’s broader analytical framework is its identification and examination of unnoticed philosophical assumptions in science and mathematics research. It reminds readers at a crucial juncture that there has been a long and rich tradition of historical and philosophical engagements with science and mathematics teaching, and that lessons can be learnt from these engagements for the resolution of current theoretical, curricular and pedagogical questions that face teachers and administrators. (shrink)

The ArgumentRecent archival research has brought about a new understanding of the import of Einstein's puzzling remarks (1916) attributing a physical meaning to general covariance. Debates over the scope and meaning of general covariance still persist, even within physics. But already in 1921 Cassirer identified the significance of general covariance as a novel stage in the development of the criterion of objectivity within physics; an account of this development, and its implications, is the primary task undertaken in his monograph of (...) “epistemological considerations” on the theory of relativity. Cassirer's assessment is correct: general covariance, understood as an injunction against dynamical theories with background elements, is a “limiting heuristic principle” guiding Einstein's fundamental conception of a “complete field theory”; as such, it underlies a “separation principle” built into the conceptual framework of the EPR criticism of quantum mechanics. In conclusion, a further parallel is noted: mutual recognition that the principle of general covariance is but a form of “anthropomorphism.”. (shrink)

Substantivalists believe that spacetime and its parts are fundamental constituents of reality. Relationalists deny this, claiming that spacetime enjoys only a derivative existence. I begin by describing how the Galilean symmetries of Newtonian physics tell against both Newton's brand of substantivalism and the most obvious relationalist alternative. I then review the obvious substantivalist response to the problem, which is to ditch substantival space for substantival spacetime. The resulting position has many affinities with what are arguably the most natural interpretations of (...) special and general relativity. I move on to consider and reject two recent antisubstantivalist lines of thought. The interim conclusion is that the best argument for relationalism is an appeal to Ockham's razor. However, for this to be successful there must be genuine relationalist theories that share the theoretical virtues of their substantivalist rivals but without the additional ontological commitment. The bulk of the paper is therefore an investigation of various concrete relationalist proposals. I distinguish three options for the relationalist in the face of the success of Galilean invariant physics and trace how these generalise to relativistic physics. One of the options is particularly promising but, since its basic objects end up being spacetime points, this does not help the prospects of relationalism as traditionally conceived. I end with some reflections on the fate of substantivalism in the aftermath of the Hole Argument, concluding that we have as yet to be given good reasons to abandon the natural, substantivalist interpretation of current physics. (shrink)

Karl Popper is famous for having proposed that science advances by a process of conjecture and refutation. He is also famous for defending the open society against what he saw as its arch enemies – Plato and Marx. Popper’s contributions to thought are of profound importance, but they are not the last word on the subject. They need to be improved. My concern in this book is to spell out what is of greatest importance in Popper’s work, what its failings (...) are, how it needs to be improved to overcome these failings, and what implications emerge as a result. The book consists of a collection of essays which dramatically develop Karl Popper’s views about natural and social science, and how we should go about trying to solve social problems. Criticism of Popper’s falsificationist philosophy of natural science leads to a conception of science that I call aim-oriented empiricism. This makes explicit metaphysical theses concerning the comprehensibility and knowability of the universe that are an implicit part of scientific knowledge – implicit in the way science excludes all theories that are not explanatory, even those that are more successful empirically than accepted theories. Aim-oriented empiricism has major implications, not just for the academic discipline of philosophy of science, but for science itself. Popper generalized his philosophy of science of falsificationism to arrive at a new conception of rationality – critical rationalism – the key methodological idea of Popper’s profound critical exploration of political and social issues in his The Open Society and Its Enemies, and The Poverty of Historicism. This path of Popper, from scientific method to rationality and social and political issues is followed here, but the starting point is aim-oriented empiricism rather than falsificationism. Aim-oriented empiricism is generalized to form a conception of rationality I call aim-oriented rationalism. This has far-reaching implications for political and social issues, for the nature of social inquiry and the humanities, and indeed for academic inquiry as a whole. The strategies for tackling social problems that arise from aim-oriented rationalism improve on Popper’s recommended strategies of piecemeal social engineering and critical rationalism, associated with Popper’s conception of the open society. This book thus sets out to develop Popper’s philosophy in new and fruitful directions. The theme of the book, in short, is to discover what can be learned from scientific progress about how to achieve social progress towards a better world. (shrink)

This target article presents a new computational theory of explanatory coherence that applies to the acceptance and rejection of scientific hypotheses as well as to reasoning in everyday life, The theory consists of seven principles that establish relations of local coherence between a hypothesis and other propositions. A hypothesis coheres with propositions that it explains, or that explain it, or that participate with it in explaining other propositions, or that offer analogous explanations. Propositions are incoherent with each other if they (...) are contradictory, Propositions that describe the results of observation have a degree of acceptability on their own. An explanatory hypothesis is acccpted if it coheres better overall than its competitors. The power of the seven principles is shown by their implementation in a connectionist program called ECHO, which treats hypothesis evaluation as a constraint satisfaction problem. Inputs about the explanatory relations are used to create a network of units representing propositions, while coherende and incoherence relations are encoded by excitatory and inbihitory links. ECHO provides an algorithm for smoothly integrating theory evaluation based on considerations of explanatory breadth, simplicity, and analogy. It has been applied to such important scientific cases as Lovoisier's argument for oxygen against the phlogiston theory and Darwin's argument for evolution against creationism, and also to cases of legal reasoning. The theory of explanatory coherence has implications for artificial intelligence, psychology, and philosophy. (shrink)

Abstract Einstein intended the general theory of relativity to be a generalization of the relativity of motion and, therefore, a radical departure from previous spacetime theories. It has since become clear, however, that this intention was not fulfilled. I try to explain Einstein's misunderstanding on this point as a misunderstanding of the role that spacetime plays in physics. According to Einstein, earlier spacetime theories introduced spacetime as the unobservable cause of observable relative motions and, in particular, as the cause of (...) inertial effects of ?absolute? motion. I use a comparative analysis of Einstein and Newton to show that spacetime is not introduced as an explanation of observable effects, but rather is defined through those effects in arguments like Newton's ?water bucket? argument and Einstein's argument for special relativity. I then argue that to claim that a spacetime theory is true, or to claim that a spacetime structure is ?real?, is not to claim that a theoretical object explains the observable. Rather, it is to claim that the fundamental definitions that link spacetime structure to physical phenomena are empirically sound, i.e. that they can be successfully applied empirically. This leads to a new and clearer view of the empirical content of spacetime theories and of the meaning of ?realism? about spacetime. (shrink)

Discussions of the metaphysical status of spacetime assume that a spacetime theory offers a causal explanation of phenomena of relative motion, and that the fundamental philosophical question is whether the inference to that explanation is warranted. I argue that those assumptions are mistaken, because they ignore the essential character of spacetime theory as a kind of physical geometry. As such, a spacetime theory does notcausally explain phenomena of motion, but uses them to construct physicaldefinitions of basic geometrical structures by coordinating (...) them with dynamical laws. I suggest that this view of spacetime theories leads to a clearer view of the philosophical foundations of general relativity and its place in the historical evolution of spacetime theory. I also argue that this view provides a much clearer and more defensible account of what is entailed by realism concerning spacetime. (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.

The foundation of irreversible, probabilistic time -- the classical time of conscious observation -- is the reversible and deterministic time of the quantum wave function. The tendency in physics is to regard time in the abstract, a mere parameter devoid of inherent direction, implying that a concept of real time begins with irreversibility. In reality time has no need for irreversibility, and every invocation of time implies becoming or flow. Neither symmetry under time reversal, of which Newton was well aware, (...) nor the absence of an absolute parameter, as in relativity, negates temporal passage. Far from encapsulating time, irreversibility is a secondary property dependent on the emergence of distinct moments from the ceaseless presence charted by the wave function. (shrink)

What does it mean for a hypothesis to be ad hoc? One prominent account has it that ad hoc hypotheses have no independent empirical support. Others have viewed ad hoc judgements as subjective. Here I critically review both of these views and defend my own Coherentist Conception of Ad hocness by working out its conceptual and descriptive attractions.

South Korean high school students are being taught Einstein’s Special Theory of Relativity. In this article, I examine the portrayal of this theory in South Korean high school physics textbooks and discuss an alternative method used to solve the analyzed problems. This examination of how these South Korean textbooks present this theory has revealed two main flaws: First, the textbooks’ contents present historically fallacious backgrounds regarding the origin of this theory because of a blind dependence on popular undergraduate textbooks, which (...) ignore the revolutionary aspects of the theory in physics. And second, the current ingredients of teaching this theory are so simply enumerated and conceptually confused that students are not provided with good opportunities to develop critical capacities for evaluating scientific theories. Reviewing textbooks used in South Korea, I will, first, claim that the history of science contributes to understand not merely the origins but also two principles of this theory. Second, in addition to this claim, I argue that we should distinguish not only hypotheses from principles but also phenomena from theoretical consequences and evidence. Finally, I suggest an alternative way in which theory testing occurs in the process of evaluation among competitive theories on the basis of data, not in the simple relation between a hypothesis and evidence. (shrink)

We put forward a new view of relativity theory that makes the existence of a flow of time compatible with the four-dimensional block universe. To this end, we apply the creation-discovery view elaborated for quantum mechanics to relativity theory and in such a way that time and space become creations instead of discoveries and an underlying non temporal and non spatial reality comes into existence. We study the nature of this underlying non temporal and non spatial reality and reinterpret many (...) aspects of the theory within this new view. We show that data of relativistic measurements are sufficient to derive the three-dimensionality of physical space. The nature of light and massive entities is reconsidered, and an analogy with human cognition is worked out. (shrink)

This essay aims to provide a self-contained introduction to time in relativistic cosmology that clarifies both how questions about the nature of time should be posed in this setting and the extent to which they have been or can be answered empirically. The first section below recounts the loss of Newtonian absolute time with the advent of special and general relativity, and the partial recovery of absolute time in the form of cosmic time in some cosmological models. Section II considers (...) the beginning and end of time in a broader class of models in which there is not an analog of Newtonian absolute time. As we will see, reasonable physical assumptions imply that the universe is finite to the past, and Section III turns to consideration of the “beginning” itself. We critically review conventional wisdom that a “singularity” reveals flaws in general relativity and briefly assess ways of avoiding the singularity. (shrink)

This paper proposes a parallel in the forms of Aristotle’s and Einstein’s physics. It’s an exercise on conceptual analysis rather than history. The possible similarity between Aristotle’s world and the form (global geometry) of Einstein’s universe is discussed. The correlation between kinematics, dynamics and gravity in their respective theories is also studied. Finally, Aristotle’s ontology of space is compared to the relativistic ontology spacetime.

The stochastic phase-space solution of the particle localizability problem in relativistic quantum mechanics is reviewed. It leads to relativistically covariant probability measures that give rise to covariant and conserved probability currents. The resulting particle propagators are used in the formulation of stochastic geometries underlying a concept of quantum spacetime that is operationally based on stochastically extended quantum test particles. The epistemological implications of the intrinsic stochasticity of such quantum spacetime frameworks for microcausality, the EPR paradox, etc., are discussed.

“Branching space-times” is intended as a representation of objective, event-based indeterminism. As such, BST exhibits both a spatio-temporal aspect and an indeterministic “modal” aspect of alternative possible historical courses of events. An essential feature of BST is that it can also represent spatial or space-like relationships as part of its relativistic theory of spatio-temporal relations; this ability is essential for the representation of local indeterminism. This essay indicates how BST might be seen to grow out of Newton ’s deterministic and (...) non-relativistic theory by two independent moves: Taking account of indeterminism, and attending to spatio-temporal relationships in a spirit derived from Einstein’s theory of special relativity. Since and are independent, one can see that there is room for four theories: Newtonian determinism, branching time indeterminism, relativistic determinism, and branching space-times indeterminism. (shrink)

Interpretations of Einstein’s equation differ primarily concerning whether E = mc2 entails that mass and energy are the same property of physical systems, and hence whether there is any sense in which mass is ever ‘converted’ into energy. In this paper, I examine six interpretations of Einstein’s equation and argue that all but one fail to satisfy a minimal set of conditions that all interpretations of physical theories ought to satisfy. I argue that we should prefer the interpretation of Einstein’s (...) equation that holds that mass and energy are distinct properties of physical systems. This interpretation also carries along the view that while most cases of ‘conversion’ are not genuine examples of mass being ‘converted’ into energy, it is possible that the there are such ‘conversions’ in the sense that a certain amount of energy ‘appears’ and an equivalent of mass ‘disappears’. Finally, I suggest that the interpretation I defend is the only one that does not blur the distinction between what Einstein called ‘principle’ and ‘constructive’ theories. This is philosophically significant because it emphasizes that explanations of Einstein’s equation and the ‘conversion’ of mass and energy must be top‐down explanations. (shrink)

“Branching space-times” (BST) is intended as a representation of objective, event-based indeterminism. As such, BST exhibits both a spatio-temporal aspect and an indeterministic “modal” aspect of alternative possible historical courses of events. An essential feature of BST is that it can also represent spatial or space-like relationships as part of its (more or less) relativistic theory of spatio-temporal relations; this ability is essential for the representation of local (in contrast with “global”) indeterminism. This essay indicates how BST might be seen (...) to grow out of Newton’s deterministic and non-relativistic theory by two independent moves: (1) Taking account of indeterminism, and (2) attending to spatio-temporal relationships in a spirit derived from Einstein’s theory of special relativity. Since (1) and (2) are independent, one can see that there is room for four theories: Newtonian determinism, branching time indeterminism, relativistic determinism, and (finally) branching space-times indeterminism. (shrink)

Abstract Schlick quite clearly maintains that the shift from classical physics to the theories of relativity is not necessitated by experience, but motivated by the pragmatic payoff of simplifying space-time ontology. However, there is in his work another, heretofore unrecognized argument for the revolutionary shift from classical to relativistic physics. According to this conceptual line of argument, the principles that define simultaneity and motion in classical physics fail to establish a univocal correspondence to physical quantities, and therefore must be revised, (...) along with the notions of absolute space and time that they underpin. Though these insights appear only intermittently in Schlick’s work, I will seek to elaborate on them in an effort to clarify his views on conventions within physics and the nature of revolutionary science, and to suggest that these views are invulnerable to the criticisms of pragmatic empiricists such as Quine. Content Type Journal Article Pages 1-17 DOI 10.1007/s12136-011-0131-3 Authors Steven Bland, Department of Philosophy, Huron University College, 1349 Western Rd, London, Ontario, Canada N6G 1H3 Journal Acta Analytica Online ISSN 1874-6349 Print ISSN 0353-5150. (shrink)

In the interwar period there was a significant school of thought that repudiated Einstein's theory of relativity on the grounds that it contained elementary inconsistencies. Some of these critics held extreme right-wing and anti-Semitic views, and this has tended to discredit their technical objections to relativity as being scientifically shallow. This paper investigates an alternative possibility: that the critics were right and that the success of Einstein's theory in overcoming them was due to its strengths as an ideology rather than (...) as a science. The clock paradox illustrates how relativity theory does indeed contain inconsistencies that make it scientifically problematic. These same inconsistencies, however, make the theory ideologically powerful. The implications of this argument are examined with respect to Thomas Kuhn and Karl Popper's accounts of the philosophy of science. (shrink)

This is the chapter on general relativity for the Cambridge Companion to Einstein which I am co-editing with Christoph Lehner.

In studying causation, many examples are presented assuming that determinism holds in the world of the example such as the notoriously difficult to resolve preemptive and preventative situations. We show that for deterministic examples that this conditional preemptive situation is either (i)vacuously true, (ii)contradictory, or (iii) implies indeterminism. Along the way we formulate a specific block space-time definition of determinism, and suggest that commonsense causation theories need focus on unphysical quantities and indeterminism.

In this critical notice we argue against William Craig's recent attempt to reconcile presentism (roughly, the view that only the present is real) with relativity theory. Craig's defense of his position boils down to endorsing a ‘neo-Lorentzian interpretation’ of special relativity. We contend that his reconstruction of Lorentz's theory and its historical development is fatally flawed and that his arguments for reviving this theory fail on many counts. 1 Rival theories of time 2 Relativity and the present 3 Special relativity: (...) one theory, three interpretations 4 Theories of principle and constructive theories 5 The relativity interpretation: explanatorily deficient? 6 The relativity interpretation: ontologically fragmented? 7 The space-time interpretation: does God need a preferred frame of reference? 8 The neo-Lorentzian interpretation: at what price? 9 The neo-Lorentzian interpretation: with what payoff? 10 Why we should prefer the space-time interpretation over the neo-Lorentzian interpretation 11 What about general relativity? 12 Squaring the tenseless space-time interpretation with our tensed experience. (shrink)

This article deals with the question whether aesthetic considerations affected Einstein in formulating both his theories of relativity. The opinions of philosophers and historians alike are divided on this matter. Thus, Gerald Holton supports the view that Einstein employed aesthetic considerations in formulating his theory of special relativity whereas Jim Shelton opposes it, one of his reasons being that Einstein did not mention such considerations. The other theory, namely, that of general relativity, is discussed by John D. Norton. He asserts (...) that the successful completion of this theory was due to Einstein's adherence to mathematical simplicity resulting from experience, as Einstein himself stated, and not from an aesthetic drive, to which he did not refer. The present work attempts to overcome this deficiency indirectly by investigating Einstein's aesthetic awareness and its consequences for his work. It is found that this awareness was imbedded in his perception of nature and is linked to the criteria (such as simplicity) that guided him in formulating his theories. The conclusion thus reached is that aesthetic considerations did play a role in Einstein's endeavour, contrary to the assertions of Shelton and Norton. (shrink)

This paper is a review of the canonical proper-time approach to relativistic mechanics and classical electrodynamics. The purpose is to provide a physically complete classical background for a new approach to relativistic quantum theory. Here, we first show that there are two versions of Maxwell’s equations. The new version fixes the clock of the field source for all inertial observers. However now, the (natural definition of the effective) speed of light is no longer an invariant for all observers, but depends (...) on the motion of the source. This approach allows us to account for radiation reaction without the Lorentz-Dirac equation, self-energy (divergence), advanced potentials or any assumptions about the structure of the source. The theory provides a new invariance group which, in general, is a nonlinear and nonlocal representation of the Lorentz group. This approach also provides a natural (and unique) definition of simultaneity for all observers.The corresponding particle theory is independent of particle number, noninvariant under time reversal (arrow of time), compatible with quantum mechanics and has a corresponding positive definite canonical Hamiltonian associated with the clock of the source.We also provide a brief review of our work on the foundational aspects of the corresponding relativistic quantum theory. Here, we show that the standard square-root and Dirac equations are actually two distinct spin- $\frac{1}{2}$ particle equations. (shrink)

The relation of the special and the general principle of relativity to the principle of covariance, the principle of equivalence and Mach's principle, is discussed. In particular, the connection between Lorentz covariance and the special principle of relativity is illustrated by giving Lorentz covariant formulations of laws that violate the special principle of relativity: Ohm's law and what we call “Aristotle's first and second laws.” An “Aristotelian” universe in which all motion is relative to “absolute space” is considered. The first (...) law: a free particle is at rest. The second law: force is proportional to velocity. Ohm's law: the current density is proportional to the electrical field strength. Neither of these laws fulfills the principle of relativity. The examples illustrate, in the context of Lorentz covariance and special relativity, Kretschmann's critique of founding Einstein's general principle of relativity on the principle of general covariance. A modification of the principle of covariance is suggested, which may serve as a restricted criterium for a physical law to satisfy Einstein's general principle of relativity. Other objections that have been raised to the validity of Einstein's general principle of relativity are based upon the preferred state of inertial frames in the general, as well as in the special theory, the existence of tidal effects in “true” gravitational fields, doubts as to the validity of Mach's principle, whether electromagnetic phenomena obey the principle, and, finally, the anisotropy of the cosmic background radiation. These objections are reviewed and discussed. (shrink)

Saying so can make it so, J. L. Austin taught us long ago. Famously, John Searle has developed this Austinian insight in an account of the construction of institutional reality. Searle maintains that so-called Status Function Declarations, allegedly having a “double direction of fit”, synchronically create worldly institutional facts, corresponding to the propositional content of the declarations. I argue that Searle’s account of the making of institutional reality is in tension with the special theory of relativity—irrespective of whether the account (...) is interpreted as involving causal generation or non-causal grounding of worldly institutional facts—and should be replaced by a more modest theory which interprets the results of Status Function Declarations in terms of mere Cambridge change and institutional truth. I end the paper by indicating the import of this more modest theory for theorizing about the causal potency of institutional phenomena generated by declarations. (shrink)

Density matrices for mixed state qubits, parametrized by the Bloch vector in the open unit ball of the Euclidean 3-space, are well known in quantum computation theory. We bring the seemingly structureless set of all these density matrices under the umbrella of gyrovector spaces, where the Bloch vector is treated as a hyperbolic vector, called a gyrovector. As such, this article catalizes and supports interdisciplinary research spreading from mathematical physics to algebra and geometry. Gyrovector spaces are mathematical objects that form (...) the setting for the hyperbolic geometry of Bolyai and Lobachevski just as vector spaces form the setting for Euclidean geometry. It is thus interesting, in geometric quantum computation, to realize that the set of all qubit density matrices has rich structure with strong link to hyperbolic geometry. Concrete examples for the use of the gyro-structure to derive old and new, interesting identities for qubit density matrices are presented. (shrink)

The debate concerning the relations between matter and motion has the same age as philosophy itself. In modern times this problem was transformed into the one concerning the relations between mass and energy. Newton identified mass with matter. Classical thermodynamics brought this conception to its logical conclusion, establishing an ontic dichotomy between mass-matter and energy. On the basis of this pre-relativistic conception, Einstein's famous equation has been interpreted as a relation of equivalence between mass-matter and energy. Nevertheless, if we reject (...) this epistemologically illegitimate identification, it is possible to elaborate a unitary conception of matter, which at the same time is an argument for the unity between matter and motion. In particular, the classical antithesis between matter and field becomes obsolete in the frame of the proposed interpretation. (shrink)

This paper attempts to analyze the concept of quantum statistical determinism. This is done after we have clarified the epistemic difference between causality and determinism and discussed the content of classical forms of determinism—mechanical and dynamical. Quantum statistical determinism transcends the classical forms, for it expresses the multiple potentialities of quantum systems. The whole argument is consistent with a statistical interpretation of quantum mechanics.

In early major works, Cassirer and Schlick differently recast traditional doctrines of the concept and of the relation of concept to intuitive content along the lines of recent epistemological discussions within the exact sciences. In this, they attempted to refashion epistemology by incorporating as its basic principle the notion of functional coordination, the theoretical sciences' own methodological tool for dispensing with the imprecise and unreliable guide of intuitive evidence. Examining their respective reconstructions of the theory of knowledge provides an axis (...) of comparison along which to locate Cassirer's Neo-Kantianism and Schlick's pre-positivist empiricism, and an immediate background of contrast to the subsequent rise of logical empiricism. For in the absence of intuition all our knowledge is without objects and therefore remains entirely empty. (Kant A62/B87) And how awkward is the human mind in diving the nature of things when forsaken by the analogy of what we see and touch directly? (Boltzmann 1895). (shrink)