Epistemology of General Relativity

For Einstein, simplicity is the main criterion in the theoretical choice when the experiments and observations do not give sufficiently clear indications . Univocity in the theoretical representation of nature should not be confused with a denial of the underdetermination thesis. The principle of univocality played a central role in Einstein's formulation of general relativity. According to Einstein, a constructive theory offers a constructive model for phenomena of interest. A principle theory consists of a set of well-substantiated individual empirical generalizations. He states that this was his methodology in discovering the theory of relativity as the main theory, the other two principles being the principle of relativity and the principle of light. DOI: 10.13140/RG.2.2.17942.5024

Is Geometry Analytic?

In this paper I present critical evaluations of Ayer and Putnam's views on the analyticity of geometry. By drawing on the historico-philosophical work of Michael Friedman on the relativized apriori; and Roberto Torretti on the foundations of geometry, I show how we can make sense of the assertion that pure geometry is analytic in Carnap's sense

Leibniz Equivalence. On Leibniz's (Bad) Influence on the Logical Empiricist Interpretation of General Relativity

Einstein’s “point-coincidence argument'” as a response to the “hole argument” is usually considered as an expression of “Leibniz equivalence,” a restatement of indiscernibility in the sense of Leibniz. Through a historical-critical analysis of Logical Empiricists' interpretation of General Relativity, the paper attempts to show that this labeling is misleading. Logical Empiricists tried explicitly to understand the point-coincidence argument as an indiscernibility argument of the Leibnizian kind, such as those formulated in the 19th century debate about geometry, by authors such as Poincaré, Helmholtz or Hausdorff. However, they clearly failed to give a plausible account of General Relativity. Thus the point-coincidence/hole argument cannot be interpreted as Leibnizian indiscernibility argument, but must be considered as an indiscernibility argument of a new kind. Weyl's analysis of Leibniz's and Einstein's indiscernibility arguments is used to support this claim

Differentiation with stratification: a principle of theoretical physics in the tradition of the memory art

The Art of Memory started with Aristotle's questions on memory. During its long evolution, it had important contributions from alchemist, was transformed by Ramon Llull and apparently ended with Giordano Bruno, who was considered the best known representative of this art. This tradition did not disappear, but lives in the formulations of our modern scientific theories. From its initial form as a method of keeping information via associations, it became a principle of classification and structuring of knowledge. This principle, which we here name {\it differentiation with stratification}, is a structural design behind classical mechanics. Integrating two different traditions of science in one structure, this physical theory became the modern paradigm of science. In this paper, we show that this principle can also be formulated as a set of questions. This is done via an analysis of theories, based on the epistemology of observational realism. A combination of Rudolph Carnap's concept of theory as a system of observational and theoretical languages, with a criterion for separating observational languages, based on analytical psychology, shapes this epistemology. The `nuclear' role of the observational laws and the differentiations from these nucleus, reproducing the general cases of phenomena, reveals the memory art's heritage in the theories. Here in this paper we argue that this design is also present in special relativity and in quantum mechanics.Comment: 6 pages, no figures; "Quantum theory from Problems to Advances", June 9-12, 2014, Linnaeus University, Vaxjo, Swede

The Kantian Grounding of Einstein’s Worldview: (I) The Early Influence of Kant’s System of Perspectives

Recent perspectival interpretations of Kant suggest a way of relating his epistemology to empirical science that makes it plausible to regard Einstein’stheory of relativity as having a Kantian grounding. This first of two articles exploring this topic focuses on how the foregoing hypothesis accounts for variousresonances between Kant’s philosophy and Einstein’s science. The great attention young Einstein paid to Kant in his early intellectual development demonstrates the plausibility of this hypothesis, while certain features of Einstein’s cultural-political context account for his reluctance to acknowledge Kant’s influence, even though contemporary philosophers who regarded themselves as Kantians urged him to do so. The sequel argues that this Kantian grounding probably had a formative influence not only on Einstein’s discovery of the theory of relativity and his view of the nature of science, but also on his quasi-mystical, religious disposition

Categories and the Foundations of Classical Field Theories

I review some recent work on applications of category theory to questions concerning theoretical structure and theoretical equivalence of classical field theories, including Newtonian gravitation, general relativity, and Yang-Mills theories.Comment: 26 pages. Written for a volume entitled "Categories for the Working Philosopher", edited by Elaine Landr

The Kantian Framework of Complementarity

A growing number of commentators have, in recent years, noted the important affinities in the views of Immanuel Kant and Niels Bohr. While these commentators are correct, the picture they present of the connections between Bohr and Kant is painted in broad strokes; it is open to the criticism that these affinities are merely superficial. In this essay, I provide a closer, structural, analysis of both Bohr's and Kant's views that makes these connections more explicit. In particular, I demonstrate the similarities between Bohr's argument, on the one hand, that neither the wave nor the particle description of atomic phenomena pick out an object in the ordinary sense of the word, and Kant's requirement, on the other hand, that both 'mathematical' (having to do with magnitude) and 'dynamical' (having to do with an object's interaction with other objects) principles must be applicable to appearances in order for us to determine them as objects of experience. I argue that Bohr's 'Complementarity interpretation' of quantum mechanics, which views atomic objects as idealizations, and which licenses the repeal of the principle of causality for the domain of atomic physics, is perfectly compatible with, and indeed follows naturally from a broadly Kantian epistemological framework.Comment: Slight change between this version and previous in the wording of the first paragraph of the section 'Complementarity

Physical Geometry and Special Relativity: Einstein and Poincaré

The problem of the relation between Geometry and Physics has been the object of extensive discussions, through the present century, by mathematicians, physicists and philosophers of science, who have considered the possibility to decide which geometry corresponds to physical space, with respect to the General Theory of Relativity. At first sight, the Special Theory of Relativity seems to be independent from this problem. In this debate, which made reference to Poincaré's philosophy of Geometry, Einstein has been directly involved. Although he concludes positively about the decidability of Geometry, he is not a rejoinder of empiricism. He himself invokes frequently Poincaré in his arguments against empiricists, in particular Poincaré's alleged "indissociability between Geometry and Physics", which sounds like Poincaré's indissociability between space and dynamics contrary to Einstein's separation of kinematics from dynamics in Special Relativity. It is thus tempting to compare his own position to Poincaré's one before and after his elaboration of the General Theory of Relativity. We would like to know, in particular, whether Einstein's conception of the relations between Geometry and Physics has drastically changed when he has passed from Special to General Theory of Relativity, adopting henceafter the essential of Poincaré's conception which he did not share at the time of Special Relativity. This inquiry has led us to a reevaluation of Poincaré's conception of the relation between Geometry and Physics, quite at variance with the received view. It also has led us to consider again the problem of why Poincaré did not fully develop Special Relativity as we now understand it, i.e. in Einstein's sense, and to show evidence for a strong influence of his conception of Geometry when dealing with classical and relativistic Mechanics. Finally we show what has been actually - in our view - the evolution of Einstein's thought concerning the relations of Physics and Geometry, which is indeed an adaptation of his previous implicit conception, at work with Special Relativity, to the requirements of the general theory. This adaptation revealed to him the complexity of a problem he had considered previously in a simplified way, and made him conscious of the well-foundedness of important aspects of Poincaré's conceptions, which he translated, then adapted, for the use of his own physical thinking.Le problème des relations entre la géométrie et la physique a fait l'objet de nombreuses discussions, tout au long de ce siècle, entre les mathématiciens, les physiciens et les philosophes des sciences. Ces discussions étaient centrées pour l'essentiel sur le problème de la décidabilité expérimentale de la géométrie, c'est-à-dire sur la possibilité, ou non, de décider de la géométrie qui correspond à l'espace du monde physique, en prenant en considération la théorie de la Relativité générale. La Relativité restreinte semble à première vue rester étrangère à ce problème. Einstein a pris directement part à ce débat, dans lequel la philosophie de la géométrie de Poincaré était fréquemment invoquée. Lui-même y faisait volontiers référence : tout en concluant à la possibilité de décider expérimentalement de la géométrie du monde physique, il s'opposait à l'empirisme et reprenait, dans son débat contre ce dernier, des arguments rapportés à Poincaré, comme celui de l'"indissociabilité de la géométrie et de la physique". Cette dernière n'est pas sans rappeler l'indissociabilité de l'espace et de la dynamique, qui marquent l'approche de la Relativité par Poincaré, au contraire de la séparation de la cinématique et de la dynamique opérée par Einstein pour parvenir à sa théorie de la Relativité restreinte. Il était tentant de comparer sa propre position, avant et après son élaboration de la Relativité générale, à celle de Poincaré. Il serait intéressant de savoir, en particulier, si la conception d'Einstein sur les relations entre la géométrie et la physique a radicalement changé quand il est passé de la Relativité restreinte à la Relativité générale, s'alignant purement et simplement, après cette dernière, sur la position de Poincaré, alors qu'il en différait à l'époque de la Relativité restreinte. Cette enquête nous a conduit à remettre en question la description généralement admise des conceptions de Poincaré sur les rapports entre la géométrie et la physique. Nous avons également été amené à reprendre le problème de savoir pourquoi Poincaré n'a pas développé dans toutes ses implications la Relativité restreinte telle que nous la comprenons aujourd'hui, c'est-à-dire au sens d'Einstein, et à mettre en évidence à cet égard l'influence de sa pensée de la géométrie sur des problèmes pourtant aussi différents en nature que ceux de la mécanique, classique et relativiste. Enfin, quant à l'évolution effective de la pensée d'Einstein sur les rapports de la physique et de la géométrie, nous montrons comment elle consiste en une adaptation de sa conception implicite lors de l'élaboration de la Relativité restreinte aux exigences de la théorie de la Relativité généralisée. Cette adaptation lui fit une nécessité de prendre en compte la complexité du problème qu'il avait pu (et même dû) simplifier pour la première théorie, lui faisant voir en même temps le bien-fondé de certains aspects importants des conceptions de Poincaré, que dès lors il traduisit, puis adapta, dans les termes de sa propre pensée de la physique