It is commonly thought that before the introduction of quantum mechanics, determinism was a straightforward consequence of the laws of mechanics. However, around the nineteenth century, many physicists, for various reasons, did not regard determinism as a provable feature of physics. This is not to say that physicists in this period were not committed to determinism; there were some physicists who argued for fundamental indeterminism, but most were committed to determinism in some sense. However, for them, determinism was often not (...) a provable feature of physical theory, but rather an a priori principle or a methodological presupposition. Determinism was strongly connected with principles of causality and continuity and the principle of sufficient reason; this thesis examines the relevance of these principles in the history of physics. Moreover, the history of determinism in this period shows that there were essential changes in the relation between mathematics and physics: whereas in the eighteenth century, there were metaphysical arguments which lent support to differential calculus, by the early twentieth century the development of rigorous foundations of differential calculus led to concerns about its applicability in physics. The thesis consists of six papers. In the first paper, "On the origins and foundations of Laplacian determinism", I argue that Laplace, who is usually pointed out as the first major proponent of scientific determinism, did not derive his statement of determinism directly from the laws of mechanics; rather, his determinism has a background in eighteenth century Leibnizian metaphysics, and is ultimately based on the law of continuity and the principle of sufficient reason. These principles also provided a basis for the idea that one can find laws of nature in the form of differential equations which uniquely determine natural processes. In "The Norton dome and the nineteenth century foundations of determinism", I argue that an example of indeterminism in classical physics which has attracted attention in philosophy of physics in recent years, namely the Norton come, was already discussed during the nineteenth century. However, the significance which this type of indeterminism had back then is very different from the significance which the Norton dome currently has in philosophy of physics. This is explained by the fact that determinism was conceived of in an essentially different way: in particular, the nineteenth century authors who wrote about this type of indeterminism regarded determinism as an a priori principle rather than as a property of the equations of physics. In "Vital instability: life and free will in physics and physiology, 1860-1880", I show how Maxwell, Cournot, Stewart and Boussinesq used the possibility of unstable or indeterministic mechanical systems to argue that the will or a vital principle can intervene in organic processes without violating the laws of physics, so that a strictly dualist account of life and the mind is possible. Moreover, I show that their ideas can be understood as a reaction to the law of conservation of energy and to the way it was used in physiology to exclude vital and mental causes. In "The nineteenth century conflict between mechanism and irreversibility", I show that in the late nineteenth century, there was a widespread conflict between the aim of reducing physical processes to mechanics and the recognition that certain processes are irreversible. Whereas the so-called reversibility objection is known as an objection that was made to the kinetic theory of gases, it in fact appeared in a wide range of arguments, and was susceptible to very different interpretations. It was only when the project of reducing all of physics to mechanics lost favor, in the late nineteenth century, that the reversibility objection came to be used as an argument against mechanism and against the kinetic theory of gases. In "Continuity in nature and in mathematics: Boltzmann and Poincaré", I show that the development of rigorous foundations of differential calculus in the nineteenth century led to concerns about its applicability in physics: through this development, differential calculus was made independent of empirical and intuitive notions of continuity and was instead based on mathematical continuity conditions, and for Boltzmann and Poincaré, the applicability of differential calculus in physics depended on whether these continuity conditions could be given a foundation in intuition or experience. In the final paper, "Determinism around 1900", I briefly discuss the implications of the developments described in the previous two papers for the history of determinism in physics, through a discussion of determinism in Mach, Poincaré and Boltzmann. I show that neither of them regards determinism as a property of the laws of mechanics; rather, for them, determinism is a precondition for science, which can be verified to the extent that science is successful. (shrink)

The late 19th-century Ignorabimus controversy over the limits of scientific knowledge has often been characterized as proclaiming the end of intellectual progress, and by implication, as plunging Germany into a crisis of pessimism from which Liberalism never recovered. My research supports the opposite interpretation. The initiator of the Ignorabimus controversy, Emil du Bois-Reymond, was a physiologist who worked his whole life against the forces of obscurantism, whether they came from the Catholic and Conservative Right or the scientistic and millenarian Left. (...) Du Bois-Reymond’s doubt that scientists would ever elucidate consciousness must therefore be seen as an endorsement, and not a rejection, of his faith in reason. (shrink)

The recent discovery of an indeterministic system in classical mechanics, the Norton dome, has shown that answering the question whether classical mechanics is deterministic can be a complicated matter. In this paper I show that indeterministic systems similar to the Norton dome were already known in the nineteenth century: I discuss four nineteenth century authors who wrote about such systems, namely Poisson, Duhamel, Boussinesq and Bertrand. However, I argue that their discussion of such systems was very different from the contemporary (...) discussion about the Norton dome, because physicists in the nineteenth century conceived of determinism in essentially different ways: whereas in the contemporary literature on determinism in classical physics, determinism is usually taken to be a property of the equations of physics, in the nineteenth century determinism was primarily taken to be a presupposition of theories in physics, and as such it was not necessarily affected by the possible existence of systems such as the Norton dome. (shrink)

ArgumentThis paper explores how the Belgian mathematician Paul Mansion became interested in probability theory. In comparison to many other countries at the time, probability theory had a much stronger presence in Belgium. In addition, Mansion, who was an avowed Catholic militant, had found probability theory to be a useful means of reflecting on certain problems pertaining to determinism and randomness that were arising in scientific debates at the time. Mansion’s work took place during a time of consolidation of mathematical education (...) in Belgium, as well as a new interest in probabilistic results and the foundation of the Institute for Philosophy in Louvain by his friend Désiré Mercier. The present paper addresses how these aspects intersected at the turn of the twentieth century. (shrink)

RESUMO: O objetivo deste artigo é examinar o que entendemos ser uma prova original da existência de Deus na obra de Pierre Duhem. Cremos que a originalidade dessa prova consiste especialmente nas premissas usadas pelo filósofo. Quanto à forma, a mesma assemelha-se ao conhecido argumento do desígnio, mas a sua versão se caracteriza por buscar na história das teorias físicas a matéria da qual a existência de uma Providência é derivada. É a complexa evolução das teorias e, a despeito dela, (...) a sua espantosa progressividade em direção a estágios sempre mais perfeitos que servem de premissa para a via duhemiana de acesso a Deus. Tudo se passa como se houvesse uma suposta pré-ordenação divina do curso das teorias, uma finalidade intrínseca a ele.ABSTRACT: The aim of this paper is to examine what we believe to be an original proof of the existence of God in the work of Pierre Duhem. We think that the originality of this proof consists especially in the assumptions used by the French philosopher in his argumentation. Regarding the form, it resembles the well-known design argument, but his version is characterized by seeking in the history of physical theories the matter from which the existence of a Providence is derived. It is the complex evolution of theories and, despite it, its amazing progress towards ever more perfect theories that serves as the premise for Duhem's way of access to God. Everything goes as if it had been a divine preordainment and an intrinsic goal ruling the evolution of theories. (shrink)

ArgumentThis article contributes to a global history of relativity, by exploring how Einstein’s theory was appropriated in Belgium. This may sound like a contradiction in terms, yet the early-twentieth-century Belgian context, because of its cultural diversity and reflectiveness of global conditions (the principal example being the First World War), proves well-suited to expose transnational flows and patterns in the global history of relativity. The attempts of Belgian physicist Théophile de Donder to contribute to relativity physics during the 1910s and 1920s (...) illustrate the role of the war in shaping the transnational networks through which relativity circulated. The local attitudes of conservative Belgian Catholic scientists and philosophers, who denied that relativity was philosophically significant, exemplify a global pattern: while critics of relativity feared to become marginalized by the scientific, political, and cultural revolutions that Einstein and his theory were taken to represent, supporters sympathized with these revolutions. (shrink)

ArgumentIn 1877, a young mathematician named Joseph Boussinesq presented amémoireto theAcadémiedes sciences which demonstrated that some differential equations may have more than one solution. Boussinesq linked this fact to indeterminism and to a possible solution to the free will versus determinism debate. Boussinesq's main interest was to reconcile his philosophical and religious views with science by showing that matter and motion do not suffice to explain all there is in the world. His argument received mixed criticism that addressed both his (...) philosophical views and the scientific content of his work, pointing to the physical “realisticness” of multiple solutions. While Boussinesq proved to be able to face the philosophical criticism, the scientific objections became a serious problem, thus slowly moving the focus of the debate from the philosophical plane to the scientific one. This change of perspective implied a wide discussion on topics such as instability, the sensitivity to initial conditions, and the conservation of energy. The Boussinesq debate is an example of a philosophically motivated debate that transforms into a scientific one, an example of the influence of philosophy on the development of science. (shrink)

Much speculation on the sources of Duhem's historical interests fails to account for the major shifts in these interests: neither his belief in the continuous development of physics nor his Catholicism, when his Church was encouraging the study of generally Aristotelian scholastic thought, led to any interest in mediaeval science before 1904. Equally, his own claim that he was merely testing his views on the nature of physical theory is easily squared only with earlier work with no trace of mediaeval (...) science. Behind this discontinuity lies a major crisis. Though not a positivist, Duhem had based all his work on assumptions acceptable to positivists. One of these, the sterility of the Middle Ages, was refuted by his chance discovery of evidence of genuine mediaeval science in the autumn of 1903, but that left the doctrine of scholastic sterility intact. (shrink)