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)

Classical (Bayesian) probability (CP) theory has led to an influential research tradition for modeling cognitive processes. Cognitive scientists have been trained to work with CP principles for so long that it is hard even to imagine alternative ways to formalize probabilities. However, in physics, quantum probability (QP) theory has been the dominant probabilistic approach for nearly 100 years. Could QP theory provide us with any advantages in cognitive modeling as well? Note first that both CP and QP theory share the (...) fundamental assumption that it is possible to model cognition on the basis of formal, probabilistic principles. But why consider a QP approach? The answers are that (1) there are many well-established empirical findings (e.g., from the influential Tversky, Kahneman research tradition) that are hard to reconcile with CP principles; and (2) these same findings have natural and straightforward explanations with quantum principles. In QP theory, probabilistic assessment is often strongly context- and order-dependent, individual states can be superposition states (that are impossible to associate with specific values), and composite systems can be entangled (they cannot be decomposed into their subsystems). All these characteristics appear perplexing from a classical perspective. However, our thesis is that they provide a more accurate and powerful account of certain cognitive processes. We first introduce QP theory and illustrate its application with psychological examples. We then review empirical findings that motivate the use of quantum theory in cognitive theory, but also discuss ways in which QP and CP theories converge. Finally, we consider the implications of a QP theory approach to cognition for human rationality. (shrink)

— Niels Bohr, 19231 “There must be quite definite and clear grounds, why you repeatedly declare that one must interpret observations classically, which lie absolute ly in thei r essenc e. . . . It must belong to your deepest conviction—and I cannot understand on what you base it.”.

The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, including over 500 references. For example, we sketch how certain intuitive ideas of the founders of quantum theory have fared in the light of current mathematical knowledge. One such idea that has certainly stood the test of time is (...) Heisenberg's `quantum-theoretical Umdeutung (reinterpretation) of classical observables', which lies at the basis of quantization theory. Similarly, Bohr's correspondence principle (in somewhat revised form) and Schroedinger's wave packets (or coherent states) continue to be of great importance in understanding classical behaviour from quantum mechanics. On the other hand, no consensus has been reached on the Copenhagen Interpretation, but in view of the parodies of it one typically finds in the literature we describe it in detail. On the assumption that quantum mechanics is universal and complete, we discuss three ways in which classical physics has so far been believed to emerge from quantum physics, namely in the limit h -> 0 of small Planck's constant (in a finite system), in the limit N goes to infinity of a large system with $N$ degrees of freedom (at fixed h), and through decoherence and consistent histories. The first limit is closely related to modern quantization theory and microlocal analysis, whereas the second involves methods of C*-algebras and the concepts of superselection sectors and macroscopic observables. In these limits, the classical world does not emerge as a sharply defined objective reality, but rather as an approximate appearance relative to certain ``classical" states and observables. Decoherence subsequently clarifies the role of such states, in that they are ``einselected", i.e. robust against coupling to the environment. Furthermore, the nature of classical observables is elucidated by the fact that they typically define (approximately) consistent sets of histories. This combination of ideas and techniques does not quite resolve the measurement problem, but it does make the point that classicality results from the elimination of certain states and observables from quantum theory. Thus the classical world is not created by observation (as Heisenberg once claimed), but rather by the lack of it. (shrink)

The present work is focussed on the completeness of physics, or what is here called the Completeness Thesis: the claim that the domain of the physical is causally closed. Two major questions are tackled: How best is the Completeness Thesis to be formulated? What can be said in defence of the Completeness Thesis? My principal conclusions are that the Completeness Thesis can be coherently formulated, and that the evidence in favour if it significantly outweighs that against it. In opposition to (...) those who argue that formulation is impossible because no account of what is to count as physical can be provided, I argue that as long as the purpose of the argument in which the account is to be used are borne in mind there are no significant difficulties. The account of the physical which I develop holds as physical whatever is needed to fix the likelihood of pre-theoretically given physical effects, and hypothesises in addition that no chemical, biological or psychological factors will be needed in this way. The thus formulated Completeness Thesis is coherent, and has significant empirical content. In opposition to those who defend the doctrine of emergentism by means of philosophical arguments I contend that those arguments are flawed, setting up misleading dichotomies between needlessly attenuated alternatives and assuming the truth of what is to be proved. Against those who defend emergentism by appeal to the evidence, I argue that the history of science since the nineteenth century shows clearly that the empirical credentials of the view that the world is causally closed at the level of a small number of purely physical forces and types of energy is stronger than ever, and the credentials of emergentism correspondingly weaker. In opposition to those who argue that difficulties with reductionism point to the implausibility of the Completeness Thesis I argue that completeness in no way entails the kinds of reductionism which give rise to the difficulties in question. I argue further that the truth of the Completeness Thesis is in fact compatible with a great deal of taxonomic disorder and the impossibility of any general reduction of non-fundamental descriptions to fundamental ones. In opposition to those who argue that the epistemological credentials of fundamental physical laws are poor, and that those laws should in fact be seen as false, I contend that truth preserving accounts of fundamental laws can be developed. Developing such an account, I test it by considering cases of the composition of forces and causes, where what takes place is different to what is predicted by reference to any single law, and argue that viewing laws as tendencies allows their truth to be preserved, and sense to be made of both the experimental discovery of laws, and the fact that composition enables accurate prediction in at least some cases. (shrink)

Traditionally, “the operator calculus of Born and Wiener” has been considered one of the four formulations of quantum mechanics that existed in 1926. The present paper reviews the operator calculus as applied by Max Born and Norbert Wiener during the last months of 1925 and the early months of 1926 and its connections with the rise of the new quantum theory. Despite the relevance of this operator calculus, Born–Wiener’s joint contribution to the topic is generally bypassed in historical accounts of (...) quantum mechanics. In this study, we analyse the paper that epitomises the contribution, and we explain the main reasons for the apparent lack of interest in Born and Wiener’s work. We argue that they did not solve the main problem for which the tool was intended, that of linear motion, because of their reluctance to use Dirac delta functions. (shrink)

Einstein claimed that the fundamental dynamical insight of special relativity was the equivalence of mass and energy. I disagree. Not only are mass and energy not equivalent but talk of such equivalence obscures the real dynamical insight of special relativity, which concerns the nature of 4-forces and interactions more generally. In this paper I present and defend a new ontology of special relativistic particle dynamics that makes this insight perspicuous and I explain how alleged cases of mass–energy conversion can be (...) accommodated within that ontology. (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.

This paper analyses Bohr’s complementarity framework and applies it to biosemiotic studies by illustrating its application to three existing models of living systems: mechanistic biology, Barbieri’s version of biosemiotics in terms of his code biology and Markoš’s phenomenological version of hermeneutic biosemiotics. The contribution summarizes both Bohr’s philosophy of science crowned by his idea of complementarity and his conception of the phenomenon of the living. Bohr’s approach to the biological questions evolved – among other things – from the consequences of (...) an epistemological lesson of quantum theory and in light of complementarity of observer as a priori living creature and ex post scientific explanation of the living. In a manifestation of the phenomenon of the living, each model of living system and its description makes accessible – from its own presuppositions, contexts and concepts – some features which are not accessible from the others. Nevertheless, for a general understanding of that phenomenon, incompatible sophisticated approaches are equally necessary. Bohr’s epistemology of complementarity turns out to be a heuristic and methodical framework for testing the extent to which biosemiotics can become one of the special sciences or its potential as a cross-disciplinary branch of study. (shrink)

A theory’s fertility is one of the standard theoretical virtues. But how is it to be construed? In current philosophical discourse, particularly in the realism debate, theoretical fertility is usually understood in terms of novel success: a theory is fertile if it manages to make successful novel predictions. Another, more permissible, notion of fertility can be found in the work of Ernan McMullin. This kind of fertility, McMullin claims, gives us just as strong grounds for realism. My paper critically assesses (...) McMullin’s notion of fertility and its realist rationale. It concludes that McMullin’s preferred example, namely the fertile development of the Bohr-Sommerfeld model of the atom, does not support McMullin’s argument for realism. Although the implications for the realism debate are as of yet unclear, the case study offers some important methodological lessons. (shrink)

Humanity’s desire for change but not instability is explored. In this context, it is proposed that a key ‘balancing aid’ of society is openness. Converse attributes, such as secrecy, reserve and tact, are also discussed, following the ideas of Sissela Bok. A particular interest in openness can be traced to the thought and advocacy of Niels Bohr, at the beginning of the nuclear age, when the problems were thought about mainly in terms of security. His ideas and efforts to promote (...) an open world are reviewed in the light of subsequent developments. These developments are not restricted to nuclear matters. The qualitative proliferation of kinds of instability (perhaps combining into John Beddington’s ‘perfect storm’) is relevant. This proliferation justifies extension of Bohr’s concerns with security to the wider realm of stability. It is also proposed in this paper that Bohr’s use of the term confidence, which was an important element of his argument for an open world, requires refinement, with a distinction between confidence in others (trust) and self-confidence (necessary for openness). The paper ends with a section on ‘improving our prospects’. (shrink)

Bohr and Heisenberg suggested that the thermodynamical quantities of temperature and energy are complementary in the same way as position and momentum in quantum mechanics. Roughly speaking their idea was that a definite temperature can be attributed to a system only if it is submerged in a heat bath, in which case energy fluctuations are unavoidable. On the other hand, a definite energy can be assigned only to systems in thermal isolation, thus excluding the simultaneous determination of its temperature. Rosenfeld (...) extended this analogy with quantum mechanics and obtained a quantitative uncertainty relation in the form ΔU Δ(1/T) ≥ k, where k is Boltzmann's constant. The two “extreme” cases of this relation would then characterize this complementarity between isolation (U definite) and contact with a heat bath (T definite). Other formulations of the thermodynamical uncertainty relations were proposed by Mandelbrot (1956, 1989), Lindhard (1986), and Lavenda (1987, 1991). This work, however, has not led to a consensus in the literature. It is shown here that the uncertainty relation for temperature and energy in the version of Mandelbrot is indeed exactly analogous to modern formulations of the quantum mechanical uncertainty relations. However, his relation holds only for the canonical distribution, describing a system in contact with a heat bath. There is, therefore, no complementarily between this situation and a thermally isolated system. (shrink)

Quantum cognition research applies abstract, mathematical principles of quantum theory to inquiries in cognitive science. It differs fundamentally from alternative speculations about quantum brain processes. This topic presents new developments within this research program. In the introduction to this topic, we try to answer three questions: Why apply quantum concepts to human cognition? How is quantum cognitive modeling different from traditional cognitive modeling? What cognitive processes have been modeled using a quantum account? In addition, a brief introduction to quantum probability (...) theory and a concrete example is provided to illustrate how a quantum cognitive model can be developed to explain paradoxical empirical findings in psychological literature. (shrink)

Einstein's philosophy of physics (as clarified by Fine, Howard, and Held) was predicated on his Trennungsprinzip, a combination of separability and locality, without which he believed objectification, and thereby "physical thought" and "physical laws", to be impossible. Bohr's philosophy (as elucidated by Hooker, Scheibe, Folse, Howard, Held, and others), on the other hand, was grounded in a seemingly different doctrine about the possibility of objective knowledge, namely the necessity of classical concepts. In fact, it follows from Raggio's Theorem in algebraic (...) quantum theory that - within an appropriate class of physical theories - suitable mathematical translations of the doctrines of Bohr and Einstein are equivalent. Thus - upon our specific formalization - quantum mechanics accommodates Einstein's Trennungsprinzip if and only if it is interpreted a la Bohr through classical physics. Unfortunately, the protagonists themselves failed to discuss their differences in this constructive way, since their debate was dominated by Einstein's ingenious but ultimately flawed attempts to establish the "incompleteness" of quantum mechanics. This aspect of their debate may still be understood and appreciated, however, as reflecting a much deeper and insurmountable disagreement between Bohr and Einstein about the knowability of Nature. Using the theological controversy on the knowability of God as a analogy, we can say that Einstein was a Spinozist, whereas Bohr could be said to be on the side of Maimonides. Thus Einstein's off-the-cuff characterization of Bohr as a 'Talmudic philosopher' was spot-on. (shrink)

as the chief novelty in the quantum description of nature, Einstein for having found vindication in 3 relativity theory for either positivism or realism, depending upon whom one asks. Famous as is each in his own domain, they are famous also, together, for their decades-long disagreement over the future of fundamental physics, their respective embrace and rejection of quantum indeterminacy being only the most widely-known point of contention.

The concepts of complementarity and entanglement are considered with respect to their significance in and beyond physics. A formally generalized, weak version of quantum theory, more general than ordinary quantum theory of physical systems, is outlined and tentatively applied to two examples.

Nuclear models are incompatible in their thing-terms: terms that refer to static entities like objects, structures, and substances. Specifically, the two most prevalent models—the liquid drop and shell models—treat the nucleus, its internal structure, and the component nucleons as entities that contradict each other’s properties. These differences allow these two models to describe and explain different nuclear experiments: fission and scattering in the liquid drop model, and single-nucleon excitation and nuclear decay in the shell model. However, prima facie, these differences (...) also suggest that these models are incompatible in their ontology. However, by taking seriously the experimental methods by which these models are constructed and the calculational tools these models provide for interpreting experimental outcomes, I construct a new form of realism about these models that renders them ontologically compatible. Namely, I argue that nuclear models are consistent in the dynamic entities to which they refer. I therefore advocate a pure process realism with respect to nuclear models. Critical to this process realism is the recognition that the processes referred to within nuclear models are essential parts of the observation acts that form nuclear experiments. In particular, because the dynamics within the nucleus must always be a continuous intermediary of our experimental interventions and the receptions of signals from the system, these dynamics are essential dynamic parts of nuclear experiments. We are therefore licensed in inferring these dynamic parts on the basis of experimental practice alone. In contrast, the thing terms reified by the thing realist in these models require additional inferences, the premises of which cannot be supported on the basis of experiment alone. Thus, inferences to processes are experimentally supportable, whereas inferences to things are dubious at best. (shrink)

Resistance to the idea that phenomenology can be relevant to cognitive scientific explanation has faced two objections advanced, respectively, from both sides of the issue: from the scientific perspective it has been suggested that phenomenology, understood as an account of first-person experience, is ultimately reducible to cognitive neuroscientific explanation; and from a phenomenological perspective it has been argued that phenomenology cannot be naturalized. In this context it makes sense to consider that the notion of scientific reduction is linked to a (...) classic scientific conception of nature. I argue that if properly understood, the proposal to rethink the concept of nature itself, in enactivist phenomenological approaches, undermines the reductionist program and redefines what it means for phenomenology to be naturalized. (shrink)

This article offers a contribution to the history of scientific ideas by proposing an epistemological argument supporting the assumption made by Miller whereby Niels Bohr has been influenced by cubism when he developed his non-intuitive complementarity principle. More specifically, this essay will identify the Bergsonian durée as the conceptual bridge between Metzinger and Bohr. Beyond this conceptual link between the painter and the physicist, this paper aims to emphasize the key role played by art in the development of human knowledge.

This article is devoted to give reasons against the naturalization of logic, in a sense which entails a revision of this science. The paper criticizes each historical important attempt to revise logical laws – intuitionism, quantum logic, alternative logics – and also it tries to argue that the explanation problem of quantum mechanics has nothing to do with a naturalization of logic.

This article examines the problem of the origins of the correspondence principle formulated by Bohr in 1920 and intends to test the correctness of the argument that the essential elements of that principle were already present in the 1913 “trilogy”. In contrast to this point of view, moreover widely shared in the literature, this article argues that it is possible to find a connection between the formulation of the correspondence principle and the assessment that led Bohr to abandon the search (...) for a Planck-type theory. In fact, a thorough examination of Bohr’s works shows that the birth of this principle coincided with the depletion of a research program whose origins may date back to Bohr’s stay at the Rutherford’s laboratory (summer 1912). Finally, this article argues that original program of research was abandoned when it became clear that Planck’s quantum hypothesis for the harmonic oscillator was not an adequate support for the theoretical architecture of atomic physics; namely, there was evidence enough to justify a most drastic conclusion, according to Bohr: “I do not think that a theory of the Planck type can be made logical consistent”. (shrink)

De ontsluiting van de kosmos, de dynamiek van de schepping, de onrust in ons bestaan doortrekt de systematiek van Dooyeweerd. Zij is wetmatig, subjectief èn objectief. Zij heeft betrekking op de modale aspecten en op de structuren van de werkelijkheid. We kennen natuurlijke ontwikkeling, de evolutie zoals beschreven door de natuurwetenschappen, we kennen de beschavingsgeschiedenis van de mensheid, we kennen de artistieke ontsluiting in de kunsten, we kennen de juridische ontsluiting in de rechtsvorming, we kennen de wetenschappelijke ontsluiting. De ontsluiting (...) is normatief oorzover mensen er een leidende rol in spelen, het script van die rol is de wereldbeschouwing en het middel is de techniek. (shrink)

Scientific realism is discussed in a variety of quantum mechanical settings, and defended against rival views on a number of scores. The search for the hidden is the source of much scientific creativity.

During World War II, Niels Bohr realized that the nature of war had changed irrevocably due to the introduction of the atomic bomb. This, in his opinion, meant that nation states had to be open about nuclear knowledge and negotiate toward peace. The bomb presented a threat, yet at the same time, an opportunity, as Bohr would argue in his characteristic way. It is not too difficult to point to the epistemological origin of Bohr’s argument: One easily identifies resonances with (...) his ideas on “complementarity” from quantum mechanics. According to Bohr’s doctrine of complementarity, a quantum mechanical object shows certain qualities depending on the experimental perspective from which it is studied; and these qualities may be mutually exclusive. However, they should in fact be looked upon as “complementary” properties that together make up the full picture of the object under investigation.Initially, Bohr could express his ideas to the highest circles of power. This would soon change, howe .. (shrink)