Este trabalho teve por objetivo investigar alguns aspectos dinâmicos de modelos de gravidade generalizada escalares-tensoriais e f(R), que pretendem resolver de modo mais natural o problema da existência da energia escura, que seria a componente do Universo responsável por sua expansão acelerada. Num espaço-tempo de Friedmann-Lemaître-Robertson-Walker com curvatura espacial nula foi possível escrever as equações de movimento de forma a se obter um sistema dinâmico com um número menor de variáveis e cujo espaço de fase foi estudado genericamente e esboçado para alguns modelos em particular. Em seguida, as regiões dinamicamente proibidas e os pontos fixos do espaço de fase foram analisados. Para os modelos f(R), apresentamos Lagrangianas e Hamiltonianas efetivas e deduzimos uma expressão geral para o parâmetro de equação de estado w. Discutimos ainda a equivalência entre os modelos f(R) e os escalares-tensoriais. Por fim, introduzimos o Princípio de Maupertuis-Jacobi, que permite relacionar a Lagrangiana de um sistema mecânico a uma métrica numa determinada variedade Riemanniana, para determinar singularidades que podem surgir nos modelos f(R), tanto numa métrica isotrópica como numa anisotrópica do tipo mais simples (Bianchi tipo I). Encontramos, de maneira mais direta, as mesmas singularidades já conhecidas através de métodos de análise dinâmica. / This work aims the investigation of some dynamical aspects of generalized gravity models, namely scalar-tensor and f(R) models. These models intend to solve in a more natural way the problem of the existence of the dark energy, which is supposedly the component of the Universe that causes its accelerated expansion. In a null spatial curvature Friedmann-Lemaître-Robertson-Walker spacetime, it has been possible to write the equations of movement in a fashion that allowed us to obtain a dynamical system with a reduced number of variables, whose phase space has been generically studied and depicted for some particular models. In sequence, the dynamically forbidden regions and the fixed points of the phase space have been analyzed. For f(R) models, we have presented effective Lagrangians and Hamiltonians and derived a general expression for the equation of state parameter w. Furthermore, we have discussed the equivalence between f(R) and scalar-tensor models. Finally, we have introduced the Maupertuis-Jacobi Principle, which allows one to relate the Lagrangian for a mechanical system to a metric in a certain Riemannian manifold, to determine singularities which may appear in f(R) models, in an isotropic metric as well as in an anisotropic one of the simplest kind (Bianchi type I). We have found, in a more direct way, the same singularities that arise by using dynamical analysis methods.

Este trabalho teve por objetivo investigar alguns aspectos dinâmicos de modelos de gravidade generalizada escalares-tensoriais e f(R), que pretendem resolver de modo mais natural o problema da existência da energia escura, que seria a componente do Universo responsável por sua expansão acelerada. Num espaço-tempo de Friedmann-Lemaître-Robertson-Walker com curvatura espacial nula foi possível escrever as equações de movimento de forma a se obter um sistema dinâmico com um número menor de variáveis e cujo espaço de fase foi estudado genericamente e esboçado para alguns modelos em particular. Em seguida, as regiões dinamicamente proibidas e os pontos fixos do espaço de fase foram analisados. Para os modelos f(R), apresentamos Lagrangianas e Hamiltonianas efetivas e deduzimos uma expressão geral para o parâmetro de equação de estado w. Discutimos ainda a equivalência entre os modelos f(R) e os escalares-tensoriais. Por fim, introduzimos o Princípio de Maupertuis-Jacobi, que permite relacionar a Lagrangiana de um sistema mecânico a uma métrica numa determinada variedade Riemanniana, para determinar singularidades que podem surgir nos modelos f(R), tanto numa métrica isotrópica como numa anisotrópica do tipo mais simples (Bianchi tipo I). Encontramos, de maneira mais direta, as mesmas singularidades já conhecidas através de métodos de análise dinâmica. / This work aims the investigation of some dynamical aspects of generalized gravity models, namely scalar-tensor and f(R) models. These models intend to solve in a more natural way the problem of the existence of the dark energy, which is supposedly the component of the Universe that causes its accelerated expansion. In a null spatial curvature Friedmann-Lemaître-Robertson-Walker spacetime, it has been possible to write the equations of movement in a fashion that allowed us to obtain a dynamical system with a reduced number of variables, whose phase space has been generically studied and depicted for some particular models. In sequence, the dynamically forbidden regions and the fixed points of the phase space have been analyzed. For f(R) models, we have presented effective Lagrangians and Hamiltonians and derived a general expression for the equation of state parameter w. Furthermore, we have discussed the equivalence between f(R) and scalar-tensor models. Finally, we have introduced the Maupertuis-Jacobi Principle, which allows one to relate the Lagrangian for a mechanical system to a metric in a certain Riemannian manifold, to determine singularities which may appear in f(R) models, in an isotropic metric as well as in an anisotropic one of the simplest kind (Bianchi type I). We have found, in a more direct way, the same singularities that arise by using dynamical analysis methods.

Si la pensée des lumières a parfois été célébrée par l’historiographie pour sa contribution significative au développement culturel et scientifique de la modernité, elle a le plus souvent été critiquée pour sa superficialité spéculative, ainsi que pour sa confiance aveugle dans les résultats des enquêtes scientifiques. La figure de Pierre-Louis Moreau de Maupertuis (1698-1759), à laquelle notre travail est consacré, rentre de plein droit dans ce cadre interprétatif : mentionné dans quelques récits historiques comme scientifique de premier plan, notamment pour sa contribution décisive à la diffusion des théories newtoniennes en France, il est relégué au second plan dans les travaux d’histoire de la philosophie et de l’épistémologie. L’un des objectifs principaux de notre travail est précisément de proposer une relecture de l’œuvre de Maupertuis qui emphatise l’intérêt spéculatif de ses doctrines, afin de montrer la place éminente qu’il occupe dans l’histoire de la pensée moderne. Nous nous pencherons ainsi sur quelques textes importants de Maupertuis, en soulignant le rôle capital qu’y jouent les questions épistémologiques et métaphysiques. L’analyse critique de la pensée scientifique et philosophique de Maupertuis n’est pourtant pas le seul aspect significatif de notre recherche : notre ambition est de proposer un récit plus vaste que la simple étude des travaux de Maupertuis, qui puisse contextualiser son œuvre dans les dynamiques de la République des Lettres au début du XVIIIe siècle. En ce sens, nous attribuons une importance toute particulière à l’étude des controverses de Maupertuis avec d’autres savants et philosophes. Il sera notamment question de deux controverses. La première, qui concerne la forme de la Terre, éclate au sein de l’Académie des Sciences de Paris entre 1733 et 1740. La deuxième, qui porte sur les monades et la philosophie wolffienne, a pour cadre l’Académie de Berlin entre 1746 et 1750. L’intérêt du travail sur les controverses de Maupertuis est double. Tout d’abord, il s’agit d’un aspect de la vie et de l’œuvre du savant que les commentateurs ont peu étudié : certes, il existe quelques études particulières sur les controverses maupertuisiennes, notamment de celle qui porte sur la figure de la Terre, mais la question n’est jamais thématisée de manière systématique dans les monographies publiées jusqu’ici. Ensuite, les controverses de Maupertuis nous paraissent intéressantes comme étude de cas pour comprendre le fonctionnement concret des controverses scientifiques et philosophiques. Nous ne prétendons évidemment pas présenter les conclusions que nous allons tirer de l’examen de ces controverses en tant que normes universelles pour l’étude de toute controverse scientifique ou philosophique du passé. Toutefois, comme les historiens travaillant sur les controverses privilégient souvent les scientifiques et les philosophes du XVIIe siècle, il nous semble intéressant de présenter une étude de cas provenant du XVIIIe siècle, qui appartient à un contexte intellectuel et social profondément différent de celui du siècle précédent. Nous pourrons ainsi apporter de nouveaux éléments de réflexion sur la nature du désaccord scientifique et philosophique, qui puissent intégrer et compléter les travaux existants. Ce que nous présentons ici, en définitive, n’est pas seulement une étude sur Maupertuis, mais un travail qui, à travers l’analyse de sa pensée et des controverses qu'elle a suscitées, vise à la reconstruction des rapports et des échanges qui constituent le réseau de la République des Lettres au début du XVIIIe siècle. L’œuvre de Maupertuis est ainsi envisagée comme un prisme, à travers lequel nous observons les lignes principales de développement de la science et de la philosophie de son époque. / Whereas historians have sometimes acknowledged the momentous contribution the Enlightenment provided to the cultural and scientific development of the modern world, more often they have criticized its speculative shallowness, and its overconfidence in the results of the scientific inquiry. The figure of Pierre-Louis Moreau de Maupertuis (1698-1759), holding a central place in our study, suffered the same fate as many other Enlightenment thinkers: mentioned in some historical narratives as a leading scientist and experimenter, most notably for the decisive contribution he gave to the circulation of Newtonian theories in France, he is relegated to the background in histories of modern philosophy and epistemology. One of the main objectives of the present research is to advance an interpretation of Maupertuis’ works which insists on the speculative depth of his doctrines, in order to display the preeminent place epistemological and metaphysical stakes occupy therein. The critical analysis of Maupertuis’ texts, however, is not the only important aspect of our study: we aim indeed at creating a wider narrative, which might contribute to clarify Maupertuis’ place within the intellectual network of the early 18th-century Republic of Letters. In this sense, we attribute a special importance to the study of Maupertuis’ controversies with other scientists and philosophers. The two controversies on which we concentrate are the controversy over the shape of the Earth, which took place at the Paris Academy of Sciences between 1733 and 1740, and the controversy over monads and Christian Wolff’s philosophy, taking place at the Berlin Academy of Sciences between 1746 and 1750. The interest of studying Maupertuis’ controversies is twofold. Firstly, it is an aspect of Maupertuis’ life and work commentators have overlooked: although there are a few essays dealing with Maupertuis’ controversies, which are for the most part focused on the question of shape of the Earth, monographs hitherto published do not discuss this aspect in detail. Secondly, Maupertuis’ controversies are an interesting case study to understand how scientific and philosophical controversies concretely work. We do not intend to claim that our study of Maupertuis’ controversies might function as a universally valid model for the study of each and every controversy in the history of science and philosophy. However, since historians studying controversies privilege case studies drawn from the 17th century, it seems useful to discuss an episode from another century, which belongs therefore to a different intellectual and social context. In this way, we will provide new elements of reflection on the nature of philosophical and scientific disagreement, which might integrate the existing literature on the subject. Ultimately, our study is not only a work on Maupertuis’ thought, but a survey that, through the analysis of Maupertuis’ texts and controversies, reconstructs the network of relations and exchanges which constitute the early 18th-century Republic of Letters. The work of Maupertuis functions therefore as a prism through which we observe the main lines of development of science and philosophy of his time.

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Co-tutelle de thèse avec l'École Normale Supérieure de Lyon / Dans cette thèse, j'étudie la réception singulière de la philosophie de Leibniz dans le corpus matérialiste français du 18e siècle. Il s'agit ainsi de repérer, dans les textes de La Mettrie, Diderot, Helvétius et d'Holbach, les éléments (concepts, arguments ou images) leibniziens dont ces auteurs usent de manière à élaborer leur propre doctrine. L'objectif est alors triple : premièrement, comprendre les sources du matérialisme moderne et notamment reconsidérer ses rapports avec la métaphysique du 17e siècle. On montrera ainsi, avec l'exemple particulier du recours à la philosophie de Leibniz, que le matérialisme est moins une doctrine du rejet de la métaphysique classique que de son détournement et de sa subversion. Deuxièmement, montrer l'importance de la figure de Leibniz dans la constitution d'une philosophie dite « radicale », c'est-à-dire nuancer le schéma largement admis actuellement d'une identité entre « radicalité » et « spinozisme ». Enfin, cette étude des usages matérialistes de Leibniz vise, par l'analyse des réceptions, à déterminer des interprétations possibles de la philosophie de Leibniz, ou du moins de certains de ses éléments. Il s'agit ainsi de considérer le devenir historique de la philosophie leibnizienne comme le lieu de la révélation de ses potentialités théoriques. La thèse comporte deux parties. La première analyse les médiations par lesquelles la philosophie de Leibniz est introduite en France au 18e siècle (Wolff, Du Châtelet, Maupertuis). La seconde présente quatre usages de la philosophie leibnizienne repérables chez La Mettrie, Diderot, D'Holbach et Helvétius ainsi que le processus de démembrement que ces auteurs lui font subir. / In this dissertation, I study the unexpected reception of Leibniz's philosophy in the 18th century French materialism. The aim is to identify the leibnizian concepts, arguments or images that are used by La Mettrie, Diderot, d'Holbach and Helvétius to build their own thoughts. Three kinds of results are shown. Firstly, to understand better the origins of French modern materialisme and particularly its relationship to 17th century metaphysics. In this perspective, this stydy shows that materialists do not necessarilyu reject metaphysics but rather use it for their own goals. Secondly, to show the role of Leibniz in the in the elaboration of a so-called radical philosophy, which means to question the common idea that radicalism originates from spinozism. Lastly, by looking at the materialists uses of Leibniz's concepts, it tries to identify new possible interpretations of his philosophy, more precisely to consider the historical reception of leibnizian philosophy as a way to reveal his theoretical potential. This work is divided in two parts : in the first one, it studies the mediations by which Leibniz's philosophy was introduced in France in the 18th century (Wolff, Du Châtelet, Maupertuis). In the second one, it examines four different uses of the leibnizian philosophy, namely, in La Mettrie, Diderot, d'Holbach and Helvétius.