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

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.

: 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)

In 1874, a strong controversy on the theory of bilinear and quadratic forms opposed Camille Jordan and Leopold Kronecker. The arithmetical ideal of Kronecker faced Jordan's claim for the simplicity of his algebraic canonical form. As the controversy combined mathematical and historical arguments, it gave rise to the writing of a history of the methods used by Lagrange, Laplace and Weierstrass in a century long mathematical discussion (1760-1860) around the "equation of secular inequalities".

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)

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)

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.

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 strengths and weaknesses of one of science's most pervasive and flexible metaprinciples;optimalityis used to explain utility maximization in economics, least effort principles in physics, entropy in chemistry, and survival of the fittest in biology. Fermat's principle of least time involves both teleological and causal considerations, two distinct modes of explanation resting on poorly understood psychological primitives. The rationality heuristic in economics provides an example from social science of the potential biases arising from the extreme flexibility of (...) optimality considerations, including selective search for confirming vidence, ex post rationalization, and the confusion of prediction with explanation. Commentators are asked to reflect on the extent to which optimality is an organizing principle of nature, a set of relatively unconnected techniques of science, a normative principle for rational choice and social organization, a metaphysical way of looking at the world, or something else still. (shrink)

Differential geometry, the contemporary heir of the infinitesimal calculus of the 17th century, appears today as the most appropriate language for the description of physical reality. This holds at every level: The concept of “connexion,” for instance, is used in the construction of models of the universe as well as in the description of the interior of the proton. Nothing is apparently more contrary to the wisdom of physicists; all the same, “it works.” The pages that follow show the conceptual (...) role played by this geometry in some examples—without entering into technical details. In order to achieve this, we shall often have to abandon the complete mathematical rigor and even full definitions; however, we shall be able to give a precise description of the connection of ideas thanks to some elements of group theory. (shrink)

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)

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)

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)

Em sua concepção da dinâmica como ciência das mudanças dos movimentos dos corpos, D'Alambert propõe-se a exprimir estas mudanças somente em função das grandezas do movimento. Ele estabelece assim a possibilidade de concebê-las fisicamente, em relação às suas causas efetivas, sem recorrer a conceitos externos como o de força, afirmado a co-naturalidade da causa física e de seus efeitos, traduzida pelaç noção de aceleração instantânea, cuja significação física vincula-se à forma diferencial da grandeza tempo e ao conceito de movimento virtual.

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)

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)

In this paper, we investigate the constitutive problems and other several aspects of what a research entitled 'formal epistemology' should be. The interest in this subject has to do with the possibility of reaching a privileged point of view or axis of research – i.e., the 'formal' one – that would allow a better grasp of the richness and variety of the facts and problems tackled by precise (local) epistemology of theories (for example, in physics). This approach is likely to (...) enable one to hold the main structural lines that organize those theories according to a more comprehensive, unifying and synthetic intelligibility. By the same token, it would eventually allow a better handling of the changes required in the organization of knowledge, putting emphasis on its main directions, drawing up a rational inventory of this knowledge, and perhaps anticipating others. At first, we deal with the 'thought of changes' that no approach of the 'form' can afford to leave aside, since the meaning of this concept is inseparable from the contents that come with constructions and modifications. We examine then the notion of 'epistemic operation' as an instrument to create new forms on the theoretical as well as on the meta-theoretical levels. In the wake of it, we analyze the characteristics of the form and of the formal, as well as their relationship with the contents of knowledge. We also take the notion of object into account, since it depends upon the decision of a subject and upon conventional choices. We finally inquire about the link between 'epistemic operations' as specified above and algorithmic functions for knowledge statements, and emphasize the risk of reductionism that might follow from a naturalistic conception of representation. (shrink)

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)

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)

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)

Les notions ou catégories de causalité et de déterminisme ont accompagné la formation des sciences modernes, et en premier lieu celle de la physique. L'usage courant de nos jours tend souvent, à tort, à les confondre, dans les remises en cause qui en sont faites en physique même. Nous nous proposons, dans ce travail, de clarifier la première de ces notions, plus exactement la causalité physique, en suivant son élaboration avec les débuts de la dynamique, à travers ses premières mises (...) en œuvre et conceptualisations qui accompagnent la mathématisation de la mécanique, avant d'être étendue à la physique d'une manière générale. Nous verrons comment, tout en s'appuyant sur l'un des aspects philosophiques traditionnels de l'idée de causalité (celui de « cause efficiente »), la causalité physique s'établit en rupture avec le sens métaphysique qui lui était précédemment attaché. Bien plutôt que dans les Principia de Newton, c'est dans la ré-élaboration par d'Alembert, dans son Traité de dynamique, des lois du mouvement formulés comme des principes, et exprimées par le calcul différentiel, que l'idée de causalité physique est expressément considérée indissociablement de son effet, qui est le changement de mouvement. Les pensées respectives de Newton et de d'Alembert sur les notions de cause et de force sont à cet égard en opposition en ce qui concerne la nature proprement physique de ce changement, considéré par d'Alembert comme immanent au mouvement, selon la cause circonscrite par son effet, alors qu'il reste mathématique et métaphysique dans la conception newtonienne de la force externe, comme substitut mathématique des causes, telle qu'elle se proposait avant Lagrange. C'est la conception physique, héritée de d'Alembert, qui devait par la suite prévaloir, à travers la mécanique analytique lagrangienne, qui permettait de réintégrer physiquement et rationnellement le concept de force dans sa transcription eulérienne différentielle. Les avatars ultérieurs de la notion de causalité, qui comprennent la causalité relativiste et les développements sur le déterminisme, font l'objet d'un travail complémentaire. (shrink)

It is shown how the historiographic purport of Lakatosian methodology of mathematics is structured on the theme of analysis and synthesis. This theme is explored and extended to the revolutionary phase around 1800. On the basis of this historical investigation it is argued that major innovations, crucial to the appraisal of mathematical progress, defy reconstruction as irreducibly rational processes and should instead essentially be understood as processes of social-cognitive interaction. A model of conceptual change is developed whose essential ingredients are (...) the variability of rational responses to new intellectual and practical challenges arising in the cultural environment of mathematics, and the shifting selective pressure of society. The resulting view of mathematical development is compared with Kuhn's theory of scientific paradigms in the light of some personal communications. (shrink)

Generally speaking, virtual displacement or work concerns to a timely idea according to which a motion of a certain body is not the unique possible motion. The process of reducing this motion to a particular magnitude and concept, eventually minimizing as a hypothesis, can be traced back to the Aristotelian school. In the history and philosophy of science one finds various enunciations of the Principle of Virtual Laws and its virtual displacement or work applications, i.e., from Aristotle to Leibniz’s vis (...) viva, from Maupertuis’ least action to Euler and Lagrange with calculus of variations to Lazare Carnot’s mechanics. In this case study, I will demonstrate that a particular approach used by Lazare Carnot is original by explaining within the historical context of rival approaches such as the development of the Principle of virtual Laws. I will also discuss Carnot’s geometric motion as one of the possible but invertible movements applied to virtual displacement as employed in his theories of machines and collisions. I will then go on to explore how the originality of an invertible motion within his mechanical and, in general, mathematical research program permitted Carnot to introduce a new way of structuring a scientific theory and making mechanics, with respect to the Newtonian paradigm, to scholars and his students of the École polytechnique de Paris. (shrink)

The author proposes to show that the actual crisis in microphysics is principally due to the fact that, as quantum mechanics is a theory of stationary states and reversible movements, it fundamentally ignores the notion of a transitory process. The essential characteristic of quantum theories is the result of an evolution of more than two centuries; a period of development essentially devoted to the description of stationary and reversible phenomena. The author's point of view, which reflects that of the school (...) of Louis de Broglie, is that microphysics must now cross a new threshold in giving up the description of stationary states and the calculation of their transition probabilities in favor of attempting to describe the transitions themselves and explain the origin and stability of stationary states. The future seems to him to be one of a microphysics based on irreversibility. (shrink)

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)