This article pursues the question whether and inasmuch theories of corporate responsibility are dependent on conceptions of managerial freedom. I argue that neglect of the idea of freedom in economic theory has led to an inadequate conceptualization of the ethical responsibilities of corporations within management theory. In a critical review of the history of economic ideas, I investigate why and how the idea of freedom was gradually removed from the canon of economics. This reconstruction aims at a deconstruction of certain (...) axioms of neoclassical economics that hamper contemporary efforts in integrating ethics firmly into management education. I intend to show by these deconstructive endeavors that a constructive use of the idea of responsible freedom could correct and complement the current quantitative focus in business theory through qualitative orientations. I argue that with the help of qualitative success criteria, the strategic integration of the tenets of both business ethics and Corporate Social Responsibility into business practice can be advanced by further research. (shrink)

The conservation of energy and momentum have been viewed as undermining Cartesian mental causation since the 1690s. Modern discussions of the topic tend to use mid-nineteenth century physics, neglecting both locality and Noether’s theorem and its converse. The relevance of General Relativity has rarely been considered. But a few authors have proposed that the non-localizability of gravitational energy and consequent lack of physically meaningful local conservation laws answers the conservation objection to mental causation: conservation already fails in GR, so there (...) is nothing for minds to violate. This paper is motivated by two ideas. First, one might take seriously the fact that GR formally has an infinity of rigid symmetries of the action and hence, by Noether’s first theorem, an infinity of conserved energies-momenta. Second, Sean Carroll has asked how one should modify the Dirac–Maxwell–Einstein equations to describe mental causation. This paper uses the generalized Bianchi identities to show that General Relativity tends to exclude, not facilitate, such Cartesian mental causation. In the simplest case, Cartesian mental influence must be spatio-temporally constant, and hence 0. The difficulty may diminish for more complicated models. Its persuasiveness is also affected by larger world-view considerations. The new general relativistic objection provides some support for realism about gravitational energy-momentum in GR. Such realism also might help to answer an objection to theories of causation involving conserved quantities, because energies-momenta would be conserved even in GR. (shrink)

Recent work on the history of General Relativity by Renn, Sauer, Janssen et al. shows that Einstein found his field equations partly by a physical strategy including the Newtonian limit, the electromagnetic analogy, and energy conservation. Such themes are similar to those later used by particle physicists. How do Einstein's physical strategy and the particle physics derivations compare? What energy-momentum complex did he use and why? Did Einstein tie conservation to symmetries, and if so, to which? How did his work (...) relate to emerging knowledge of the canonical energy-momentum tensor and its translation-induced conservation? After initially using energy-momentum tensors hand-crafted from the gravitational field equations, Einstein used an identity from his assumed linear coordinate covariance x'=Mx to relate it to the canonical tensor. Usually he avoided using matter Euler-Lagrange equations and so was not well positioned to use or reinvent the Herglotz-Mie-Born understanding that the canonical tensor was conserved due to translation symmetries, a result with roots in Lagrange, Hamilton and Jacobi. Whereas Mie and Born were concerned about the canonical tensor's asymmetry, Einstein did not need to worry because his Entwurf Lagrangian is modeled not so much on Maxwell's theory as on a scalar theory. Einstein's theory thus has a symmetric canonical energy-momentum tensor. But as a result, it also has 3 negative-energy field degrees of freedom. Thus the Entwurf theory fails a 1920s-30s a priori particle physics stability test with antecedents in Lagrange's and Dirichlet's stability work; one might anticipate possible gravitational instability. This critique of the Entwurf theory can be compared with Einstein's 1915 critique of his Entwurf theory for not admitting rotating coordinates and not getting Mercury's perihelion right. One can live with absolute rotation but cannot live with instability. Particle physics also can be useful in the historiography of gravity and space-time, both in assessing the growth of objective knowledge and in suggesting novel lines of inquiry to see whether and how Einstein faced the substantially mathematical issues later encountered in particle physics. This topic can be a useful case study in the history of science on recently reconsidered questions of presentism, whiggism and the like. Future work will show how the history of General Relativity, especially Noether's work, sheds light on particle physics. (shrink)

We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind, and Weierstrass; to the reconstruction of Cauchy’s foundational work associated with the work of Boyer and Grabiner; and to Bishop’s constructivist reconstruction of classical analysis. We examine the effects of a nominalist disposition on historiography, teaching, and research.

One of the most influential scientific treatises in Cauchy's era was J.-L. Lagrange's Mécanique Analytique, the second edition of which came out in 1811, when Cauchy was barely out of his teens. Lagrange opens his treatise with an unequivocal endorsement of infinitesimals. Referring to the system of infinitesimal calculus, Lagrange writes:Lorsqu'on a bien conçu l'esprit de ce système, et qu'on s'est convaincu de l'exactitude de ses résultats par la méthode géométrique des premières et dernières raisons, ou par la méthode analytique (...) des fonctions dérivées, on peut employer les infiniment petits comme un instrument sûr et commode pour abréger et simplifier les demonstrations.Lagrange's renewed enthusiasm for .. (shrink)

An overlap between the general relativist and particle physicist views of Einstein gravity is uncovered. Noether's 1918 paper developed Hilbert's and Klein's reflections on the conservation laws. Energy-momentum is just a term proportional to the field equations and a "curl" term with identically zero divergence. Noether proved a \emph{converse} "Hilbertian assertion": such "improper" conservation laws imply a generally covariant action. Later and independently, particle physicists derived the nonlinear Einstein equations assuming the absence of negative-energy degrees of freedom for stability, along (...) with universal coupling: all energy-momentum including gravity's serves as a source for gravity. Those assumptions imply that the energy-momentum is only a term proportional to the field equations and a symmetric curl, which implies the coalescence of the flat background geometry and the gravitational potential into an effective curved geometry. The flat metric, though useful in Rosenfeld's stress-energy definition, disappears from the field equations. Thus the particle physics derivation uses a reinvented Noetherian converse Hilbertian assertion in Rosenfeld-tinged form. The Rosenfeld stress-energy is identically the canonical stress-energy plus a Belinfante curl and terms proportional to the field equations, so the flat metric is only a convenient mathematical trick without ontological commitment. Neither generalized relativity of motion, nor the identity of gravity and inertia, nor substantive general covariance is assumed. The more compelling criterion of lacking ghosts yields substantive general covariance as an output. Hence the particle physics derivation, though logically impressive, is neither as novel nor as ontologically laden as it has seemed. (shrink)

A widespread view in physics holds that the implementation of time reversal in standard quantum mechanics must be given by an anti-unitary operator. In foundations and philosophy of physics, however, there has been some discussion about the conceptual grounds of this orthodoxy, largely relying on either its obviousness or its mathematical-physical virtues. My aim in this paper is to substantively change the traditional structure of the debate by highlighting the philosophical commitments underlying the orthodoxy. I argue that the persuasive force (...) of the orthodoxy can benefit from a relational metaphysics of time and a by-stipulation view on symmetries. Within such philosophical background, I submit, the orthodoxy of time reversal in standard quantum mechanics could find a fertile terrain to lay the groundwork for a more thorough conceptual justification. (shrink)

The widespread idea that infinitesimals were “eliminated” by the “great triumvirate” of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum (...) with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d’Alembert, Cauchy, and others. (shrink)

Misconceptions about energy conservation abound due to the gap between physics and secondary school chemistry. This paper surveys this difference and its relevance to the 1690s–2010s Leibnizian argument that mind-body interaction is impossible due to conservation laws. Justifications for energy conservation are partly empirical, such as Joule’s paddle wheel experiment, and partly theoretical, such as Lagrange’s statement in 1811 that energy is conserved if the potential energy does not depend on time. In 1918 Noether generalized results like Lagrange’s and proved (...) a converse: symmetries imply conservation laws and vice versa. Conservation holds if and only if nature is uniform. The rise of field physics during the 1860s–1920s implied that energy is located in particular places and conservation is primordially local: energy cannot disappear in Cambridge and reappear in Lincoln instantaneously or later; neither can it simply disappear in Cambridge or simply appear in Lincoln. A global conservation law can be inferred in some circumstances. Einstein’s General Relativity, which stimulated Noether’s work, is another source of difficulty for conservation laws. As is too rarely realized, the theory admits conserved quantities due to symmetries of the Lagrangian, like other theories. Indeed General Relativity has more symmetries and hence more conserved energies. An argument akin to Leibniz’s finally gets some force. While the mathematics is too advanced for secondary school, the ideas that conservation is tied to uniformities of nature and that energy is in particular places, are accessible. Improved science teaching would serve the truth and enhance the social credibility of science. (shrink)

I examine here if Kant can explain our knowledge of duration by showing that time has metric structure. To do so, I spell out two possible solutions: time’s metric could be intrinsic or extrinsic. I argue that Kant’s resources are too weak to secure an intrinsic, transcendentally-based temporal metrics; but he can supply an extrinsic metric, based in a metaphysical fact about matter. I conclude that Transcendental Idealism is incomplete: it cannot account for the durative aspects of experience—or it can (...) do so only with help from a non-trivial metaphysics of material substance. (shrink)

ABSTRACT An overview of some of the main modes of making images of natural objects and processes, as they have appeared in the history of science, leads to two main conclusions. First, the dichotomies that have traditionally distinguished, for example, art from science, museums from laboratories, and geometrical from algebraic methods have produced a poverty of understanding of visualization. It is at the intersections of these dichotomies where much of the creative work of science occurs, and it is into those (...) intersections that this Focus section leads us. Second, the section suggests that we need to understand images as arguments. Generalizing, we need to develop a “materialized epistemology” that reunites sensual with ideational knowing. Recent work in the history of science is already pointing the way and producing a dramatically new historiography. (shrink)

An account is given of the emergence of the concept of work as a basic component of mechanics. It was largely an achievement of engineer savants in France during the Bourbon Restoration , with Navier, Coriolis and Poncelet playing the major roles. Some aspects of the eighteenth-century prehistory are described, and also concurrent developments in French engineering. The principal problem areas were friction, hydraulics, machine performance and ergonomics, and especially in the last context the developments became involved with social and (...) even philosophical movements in the 1820s. Education played an important role throughout; several of the principal sources are textbooks. (shrink)

We reconstruct essential features of Lagrange’s theory of analytical functions by exhibiting its structure and basic assumptions, as well as its main shortcomings. We explain Lagrange’s notions of function and algebraic quantity, and we concentrate on power-series expansions, on the algorithm for derivative functions, and the remainder theorem—especially on the role this theorem has in solving geometric and mechanical problems. We thus aim to provide a better understanding of Enlightenment mathematics and to show that the foundations of mathematics did not, (...) for Lagrange, concern the solidity of its ultimate bases, but rather purity of method—the generality and internal organization of the discipline. (shrink)

This chapter looks at Euler’s relation to Newton, and at his role in the rise of ‘Newtonian’ mechanics. It aims to give a sense of Newton’s complicated legacy for Enlightenment science, and to raise awareness that some key ‘Newtonian’ results really come from Euler.

: This paper first discusses the current historical and philosophical framework forged during the last century to account for both the history and the epistemic status of Newton's theory of general gravitation. It then examines the conflict surrounding this theory at the close of the seventeenth century and the first steps towards the revolutionary shift in rational mechanics in the eighteenth century. From a historical point of view, it shows the crucial contribution of the Cartesian mechanistic philosophy and Leibnizian analytic (...) methods to the emergence of so-called Newtonian mechanics which can also be fairly characterized as a synthetic theory of attraction. From a philosophical standpoint, the paper suggests that the reworking of Newton's theory in the 18th century is better understood in a theoretical framework that reconciles Kuhn's notion of "invisible revolution" rather than his notion of "normal science" with Whewell's ascription of the completion of dynamical studies to the post Newtonian period. (shrink)

We can distinguish between two different ways in which mathematics is applied in science: when mathematics is introduced and developed in the context of a particular scientific application; when mathematics is used in the context of a particular scientific application but it has been developed independently from that application. Nevertheless, there might also exist intermediate cases in which mathematics is developed independently from an application but it is nonetheless introduced in the context of that particular application. In this paper I (...) present a case study, that of the Lagrange multipliers, which concerns such type of intermediate application. I offer a reconstruction of how Lagrange developed the method of multipliers and I argue that the philosophical significance of this case-study analysis is twofold. In the context of the applicability debate, my historically-driven considerations pull towards the reasonable effectiveness of mathematics in science. Secondly, I maintain that the practice of applying the same mathematical result in different scientific settings can be regarded as a form of crosschecking that contributes to the objectivity of a mathematical result. (shrink)

Symmetry fundamentalism claims that symmetries should be taken metaphysically seriously as part of the fundamental ontology. The main aim of this paper is to bring some novel objections against this view. I make two points. The first places symmetry fundamentalism within a broader network of philosophical commitments. I claim that symmetry fundamentalism entails idealization realism which, in turn, entails the reification of further theoretical structures. This might lead to an overloaded ontology as well as open the way to criticisms from (...) metaphysical frameworks that reject such reifications. The second point contrasts symmetry fundamentalism with the now common view that regards symmetries as stipulations guiding empirical research and theory construction. I claim that both views clash each other and cannot be held together. I finish the paper with a more positive prospect that will be developed in future work—symmetry deflationism. (shrink)

A comment on Paul Schoemaker's target article in Behavioral and Brain Sciences, 14 (1991), p. 205-215, "The Quest for Optimality: A Positive Heuristic of Science?" (https://doi.org/10.1017/S0140525X00066140). This comment argues that the optimizing model of decision leads to an infinite regress, once internal costs of decision (i.e., information and computation costs) are duly taken into account.

This paper examines the contribution of Gabrio Piola to continuum mechanics.Though he was undoubtably a skilled mathematician and a good mechanician, little is commonly known about his papers within the international scientific community, principally because a large part of the Italian school of mechanics was isolated in the first half of the XIXth century.We examine and comment on Piola’s most important papers, and compare them with those of his contemporaries Cauchy, Poisson and Kirchhoff.

The idea of a canonical transformation emerged in 1837 in the course of Carl Jacobi's researches in analytical dynamics. To understand Jacobi's moment of discovery it is necessary to examine some background, especially the work of Joseph Lagrange and Siméon Poisson on the variation of arbitrary constants as well as some of the dynamical discoveries of William Rowan Hamilton. Significant figures following Jacobi in the middle of the century were Adolphe Desboves and William Donkin, while the delayed posthumous publication in (...) 1866 of Jacobi's full dynamical corpus was a critical event. François Tisserand's doctoral dissertation of 1868 was devoted primarily to lunar and planetary theory but placed Hamilton–Jacobi mathematical methods at the forefront of the investigation. Henri Poincaré's writings on celestial mechanics in the period 1890–1910 succeeded in making canonical transformations a fundamental part of the dynamical theory. Poincaré offered a mathematical vision of the subject that differed from Jacobi's and would become influential in subsequent research. Two prominent researchers around 1900 were Carl Charlier and Edmund Whittaker, and their books included chapters devoted explicitly to transformation theory. In the first three decades of the twentieth century Hamilton–Jacobi theory in general and canonical transformations in particular would be embraced by a range of researchers in astronomy, physics and mathematics. (shrink)

This thesis is a study of the notion of time in modern physics, consisting of two parts. Part I takes seriously the doctrine that modern physics should be treated as the primary guide to the nature of time. To this end, it offers an analysis of the various conceptions of time that emerge in the context of various physical theories and, furthermore, an analysis of the relation between these conceptions of time and the more orthodox philosophical views on the nature (...) of time. In Part II I explore the interpretation of nonrelativistic quantum mechanics in light of the suggestion that an overly Newtonian conception of time might be contributing to some of the difficulties that we face in interpreting the quantum mechanical formalism. In particular, I argue in favour of introducing backwards-in-time causal influences as part of an alternative conception of time that is consistent with the picture of reality that arises in the context of the quantum formalism. Moreover, I demonstrate that this conception of time can already be found in a particular formulation of classical mechanics. One might see that one of the central themes of Part II originates from a failure to heed properly the doctrine of Part I: study into the nature of time should be guided by modern physics and thus we should be careful not to insert a preconceived Newtonian conception of time unwittingly into our interpretation of the quantum mechanical formalism. Thus, whereas Part I is intended as a demonstration of methodology with respect to the study of time, Part II in a sense explores a confusion that can be seen as arising in the absence of this methodology. (shrink)

The examples and concepts that Shoemaker cites are rather heterogeneous. Some distinctions need to be drawn. An optimality thesis involves not just an ordering of options, but a value judgment about them. So let us begin by distinguishing minimality from optimality. And the concept of minimality can play a variety of roles, among which I distinguish between extremum descriptions, statements hypothesizing an optimizing process, and methodological recommendations. Finally, I consider how the three categories relate to Shoemaker’s question that “Who is (...) optimizing: the scientist or nature?” . (shrink)

Tratamos neste artigo de algumas questões concernentes aos aspectos do pensamento nas obras científicas e à relação entre ciência e filosofia.

This article describes the emergence of formal methods in theory of partial differential equations in the French school of mathematics through Janet’s work in the period 1913–1930. In his thesis and in a series of articles published during this period, Janet introduced an original formal approach to deal with the solvability of the problem of initial conditions for finite linear PDE systems. His constructions implicitly used an interpretation of a monomial PDE system as a generating family of a multiplicative set (...) of monomials. He introduced an algorithmic method on multiplicative sets to compute compatibility conditions, and to study the problem of the existence and the uniqueness of a solution to a linear PDE system with given initial conditions. The compatibility conditions are formulated using a refinement of the division operation on monomials defined with respect to a partition of the set of variables into multiplicative and non-multiplicative variables. Janet was a pioneer in the development of these algorithmic methods, and the completion procedure that he introduced on polynomials was the first one in a long and rich series of works on completion methods which appeared independently throughout the twentieth-century in various algebraic contexts. (shrink)