Before the discovery of the expanding universe, one of the challenges faced in early relativistic cosmology was the determination of the finite and constant curvature radius of space-time by using astronomical observations. Great interest in this specific question was shown by de Sitter, Silberstein, and Lundmark. Their ideas and methods for measuring the cosmic curvature radius, at that time interpreted as equivalent to the size of the universe, contributed to the development of the empirical approach to relativistic cosmology. Their works (...) are a noteworthy example of the efforts made by modern cosmologists toward the understanding of the universe as a whole, its properties, and its content. (shrink)

After a survey of disagreements among Thomists on the nature of mathematical abstraction, the author cites Aquinas's text Scriptum super libros Sententiarum, I, d. 2, a.3 (a late text inserted in an older work). It assimilates the objects of mathematics to those of logic, thus admitting a remote foundation in reality but not the direct one of the concepts of the physical sciences.

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...) structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions. (shrink)

I argue that, contrary to folklore, Einstein never really cared for geometrizing the gravitational or the electromagnetic field; indeed, he thought that the very statement that General Relativity geometrizes gravity "is not saying anything at all". Instead, I shall show that Einstein saw the "unification" of inertia and gravity as one of the major achievements of General Relativity. Interestingly, Einstein did not locate this unification in the field equations but in his interpretation of the geodesic equation, the law of motion (...) of test particles. (shrink)

In der vorliegenden Arbeit werden diejenigen Aspekte der Philosophie von Moritz Schlick behandelt, die eng mit der Entwicklung der modernen Naturwissenschaft, Logik und Mathematik verknüpft sind. Es wird gezeigt, in welchem großen Ausmaß Schlick zur Entstehung einer modernen empirischen Phüosophie beigetragen hat. Folgende Problemkreise werden ausführlich behandelt: Raum und Zeit, besonders die Kritik am synthetisch^priorischen Charakter der Geometrie. Das Verhältnis von Erleben und Erkennen und die darauf aufbauende Metaphysikkritik; das Außenwelt- und das Kausalitätsproblem; das psychophysische Problem und schließlich das Problem (...) der Fundierung der Erkenntnis. (shrink)

Pierre Duhem's often unrecognized influence on twentieth-century philosophy of science is illustrated by an analysis of his significant if also largely unrecognized influence on Albert Einstein. Einstein's first acquaintance with Duhem's La Théorie physique, son objet et sa structure around 1909 is strongly suggested by his close personal and professional relationship with Duhem's German translator, Friedrich Adler. The central role of a Duhemian holistic, underdeterminationist variety of conventionalism in Einstein's thought is examined at length, with special emphasis on Einstein's deployment (...) of Duhemian arguments in his debates with neo-Kantian interpreters of relativity and in his critique of the empiricist doctrines of theory testing advanced by Schlick, Reichenbach, and Carnap. Most striking is Einstein's 1949 criticism of the verificationist conception of meaning from a holistic point of view, anticipating by two years the rather similar, but more famous criticism advanced independently by Quine in Two Dogmas of Empiricism. (shrink)

We argue that current constructive approaches to the special theory of relativity do not derive the geometrical Minkowski structure from the dynamics but rather assume it. We further argue that in current physics there can be no dynamical derivation of primitive geometrical notions such as length. By this we believe we continue an argument initiated by Einstein.

This paper attempts to show how the logical empiricists’ interpretation of the relation between geometry and reality emerges from a “collision” of mathematical traditions. Considering Riemann’s work as the initiator of a 19th century geometrical tradition, whose main protagonists were Helmholtz and Poincaré, the logical empiricists neglected the fact that Riemann’s revolutionary insight flourished instead in a non-geometrical tradition dominated by the works of Christoffel and Ricci-Curbastro roughly in the same years. I will argue that, in the attempt to interpret (...) general relativity as the last link of the chain Riemann–Helmholtz–Poincaré–Einstein, logical empiricists were led to argue that Einstein’s theory of gravitation mainly raised a problem of mathematical under-determination, i.e. the discovery that there are physical differences that cannot be expressed in the relevant mathematical structure of the theory. However, a historical reconstruction of the alternative Riemann–Christoffel–Ricci–Einstein line of evolution shows on the contrary that the main philosophical issue raised by Einstein’s theory was instead that of mathematical over-determination, i.e. the recognition of the presence of redundant mathematical differences that do not have any correspondence in physical reality. (shrink)

By inserting the dialogue between Einstein, Schlick and Reichenbach into a wider network of debates about the epistemology of geometry, this paper shows that not only did Einstein and Logical Empiricists come to disagree about the role, principled or provisional, played by rods and clocks in General Relativity, but also that in their lifelong interchange, they never clearly identified the problem they were discussing. Einstein’s reflections on geometry can be understood only in the context of his ”measuring rod objection” against (...) Weyl. On the contrary, Logical Empiricists, though carefully analyzing the Einstein–Weyl debate, tried to interpret Einstein’s epistemology of geometry as a continuation of the Helmholtz–Poincaré debate by other means. The origin of the misunderstanding, it is argued, should be found in the failed appreciation of the difference between a “Helmholtzian” and a “Riemannian” tradition. The epistemological problems raised by General Relativity are extraneous to the first tradition and can only be understood in the context of the latter, the philosophical significance of which, however, still needs to be fully explored. (shrink)

This study reconstructs the 1928–1929 correspondence between Reichenbach and Einstein about the latter’s latest distant parallelism-unified field theory, which attracted considerable public attention at the end of the 1920s. Reichenbach, who had recently become a Professor in Berlin, had the opportunity to discuss the theory with Einstein and therefore sent him a manuscript with some comments for feedback. The document has been preserved among Einstein’s papers. However, the subsequent correspondence took an unpleasant turn after Reichenbach published a popular article on (...) distant parallelism in a newspaper. Einstein directly wrote to the Editorial Board complaining about Reichenbach’s unfair use of off-the-record information. While Reichenbach’s reply demonstrates a sense of personal betrayal at Einstein’s behavior, his published writings of that period point to a sense of intellectual betrayal of their shared philosophical ideals. In his attempts to unify both electricity and gravitation, Einstein had abandoned the physical heuristic that guided him to the relativity theory, to embrace a more speculative, mathematical heuristic that he and Reichenbach had both previously condemned. A decade-long personal and intellectual friendship grew fainter and then never recovered. This study, relying on archival material, aims to revisit the Reichenbach–Einstein relationship in the late 1920s in light of Reichenbach’s neglected contributions to the epistemology of the unified field theory program. Thereby, it hopes to provide a richer account of Reichenbach’s philosophy of space and time. (shrink)

The paper offers a historical overview of Einstein's oscillating attitude towards a "phenomenological" and "dynamical" treatment of rods and clocks in relativity theory. Contrary to what it has been usually claimed in recent literature, it is argued that this distinction should not be understood in the framework of opposition between principle and constructive theories. In particular Einstein does not seem to have plead for a "dynamical" explanation for the phenomenon rods contraction and clock dilation which was initially described only "kinematically". (...) On the contrary textual evidence shows that, according to Einstein, a realistic microscopic model of rods and clocks was needed to account for the very existence of measuring devices of "identical construction" which always measure the same unit of time and the same unit of length. In fact, it will be shown that the empirical meaningfulness of both relativity theories depends on what, following Max Born, one might call the "principle of the physical identity of the units of measure". In the attempt to justify the validity of such principle, Einstein was forced by different interlocutors, in particular Hermann Weyl and Wolfgang Pauli, to deal with the genuine epistemological, rather then physical question whether a theory should be able or not to described the material devices that serve to its own verification. (shrink)

In 1922 the University of Buenos Aires (UBA) Council approved a motion to send an invitation to Albert Einstein to visit Argentina and give a course of lectures on his theory of relativity. The motion was proposed by Jorge Duclout (1856–1927), who had been educated at the Eidgenössische Technische Hochschule, Zurich (ETH). This proposal was the culmination of a series of initiatives of various Argentine intellectuals interested in the theory of relativity. In a very short time Dr. Mauricio Nirenstein (1877–1935), (...) then the university's administrative secretary, fulfilled all the requirements for the university's invitation to be endorsed and delivered to the sage in Berlin. The visit took place three years later, in March–April 1925. (shrink)

This paper considers Kant's understanding of conceptual representation in light of his view of geometry.

The geometro-stochastic quantization of a gauge theory based on the (4,1)-de Sitter group is presented. The theory contains an intrinsic elementary length parameter R of geometric origin taken to be of a size typical for hadron physics. Use is made of a soldered Hilbert bundle ℋ over curved spacetime carrying a phase space representation of SO(4, 1) with the Lorentz subgroup related to a vierbein formulation of gravitation. The typical fiber of ℋ is a resolution kernel Hilbert space ℋ $_{\bar (...) \eta }^{(\rho )} $ constructed in terms of generalized coherent states $\bar \eta $ ρ related to the principal series of unitary irreducible representations of SO(4, 1), namely de Sitter horospherical waves for spinless particles characterized by the parameter ρ. The framework is, finally, extended to a quantum field-theoretical formalism by using bundles with Fock space fibers constructed from ℋ $_{\bar \eta }^{(\rho )} $. (shrink)

Discussions of the metaphysical status of spacetime assume that a spacetime theory offers a causal explanation of phenomena of relative motion, and that the fundamental philosophical question is whether the inference to that explanation is warranted. I argue that those assumptions are mistaken, because they ignore the essential character of spacetime theory as a kind of physical geometry. As such, a spacetime theory does notcausally explain phenomena of motion, but uses them to construct physicaldefinitions of basic geometrical structures by coordinating (...) them with dynamical laws. I suggest that this view of spacetime theories leads to a clearer view of the philosophical foundations of general relativity and its place in the historical evolution of spacetime theory. I also argue that this view provides a much clearer and more defensible account of what is entailed by realism concerning spacetime. (shrink)

Abstract: This article contends that the relation of early logical empiricism to Kant was more complex than is often assumed. It argues that Reichenbach's early work on Kant and Einstein, entitled The Theory of Relativity and A Priori Knowledge (1920) aimed to transform rather than to oppose Kant's Critique of Pure Reason. One the one hand, I argue that Reichenbach's conception of coordinating principles, derived from Kant's conception of synthetic a priori principles, offers a valuable way of accounting for the (...) historicity of scientific paradigms. On the other hand, I show that even Reichenbach, in line with Neo-Kantianism, associated Kant's view of synthetic a priori principles too closely with Newtonian physics and, consequently, overestimated the difference between Kant's philosophy and his own. This is even more so, I point out, in the retrospective account logical empiricism presented of its own history. Whereas contemporary reconstructions of this history, including Michael Friedman's, tend to endorse this account, I offer an interpretation of Kant's conception of a priori principles that contrasts with the one put forward by both Neo-Kantianism and logical empiricism. On this basis, I re-examine the early Reichenbach's effort to accommodate these principles to the paradigm forged by Einstein. (shrink)

The physicist's conception of space-time underwent two major upheavals thanks to the general theory of relativity and quantum mechanics. Both theories play a fundamental role in describing the same natural world, although at different scales. However, the inconsistency between them emerged clearly as the limitation of twentieth-century physics, so a more complete description of nature must encompass general relativity and quantum mechanics as well. The problem is a theorists' problem par excellence. Experiment provide little guide, and the inconsistency mentioned above (...) is an important problem which clearly illustrates the intermingling of philosophical, mathematical, and physical thought. In fact, in order to unify general relativity with quantum field theory, it seems necessary to invent a new mathematical framework which will generalise Riemannian geometry and therefore our present conception of space and space-time. Contemporary developments in theoretical physics suggest that another revolution may be in progress, through which a new kind of geometry may enter physics, and space-time itself can be reinterpreted as an approximate, derived concept. The main purpose of this article is to show the great significance of space-time geometry in predetermining the laws which are supposed to govern the behaviour of matter, and further to support the thesis that matter itself can be built from geometry, in the sense that particles of matter as well as the other forces of nature emerges in the same way that gravity emerges from geometry. Scientific research is not a process of steady accumulation of absolute truths, which has culminated in present theories, but rather a much more dynamic kind of process in which there are no final theoretical concepts valid in unlimited domains. (David Bohm). (shrink)

What role does the imagination play in scientific progress? After examining several studies in cognitive science, I argue that one thing the imagination does is help to increase scientific understanding, which is itself indispensable for scientific progress. Then, I sketch a transcendental justification of the role of imagination in this process.

The purpose of this paper is to evaluate the `Lorentzian Pedagogy' defended by J.S. Bell in his essay ``How to teach special relativity'', and to explore its consistency with Einstein's thinking from 1905 to 1952. Some remarks are also made in this context on Weyl's philosophy of relativity and his 1918 gauge theory. Finally, it is argued that the Lorentzian pedagogy---which stresses the important connection between kinematics and dynamics---clarifies the role of rods and clocks in 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. (shrink)

In a comparison of the principles of special relativity and of quantum mechanics, the former theory is marked by its relative economy and apparent explanatory simplicity. A number of theorists have thus been led to search for a small number of postulates - essentially information theoretic in nature - that would play the role in quantum mechanics that the relativity principle and the light postulate jointly play in Einstein's 1905 special relativity theory. The purpose of the present paper is to (...) resist this idea, at least in so far as it is supposed to reveal the fundamental form of the theory. It is argued that the methodology of Einstein's 1905 theory represents a victory of pragmatism over explanatory depth; and that its adoption only made sense in the context of the chaotic state state of physics at the start of the 20th century - as Einstein well knew. (shrink)

It is argued that an unheralded moment marking the beginnings of relativity theory occurred in 1889, when G. F. FitzGerald, no doubt with the puzzling 1887 Michelson-Morley experiment fresh in mind, wrote to Heaviside about the possible effects of motion on inter-molecular forces in bodies. Emphasis is placed on the difference between FitzGerald's and Lorentz's independent justifications of the shape distortion effect involved. Finally, the importance of the their `constructive' approach to kinematics---stripped of any commitment to the physicality of the (...) ether--- will be defended, in the spirit of Pauli, Swann and Bell. (shrink)

Such are those thick & gloomie shadows dampe Oft seene in charnel vaults, & sepulchers, Lingering, & sitting by a new made grave, As loath to leave the bodie that it lov'd, & link’t it selfe by carnall sensualtie To a degenerate, & degraded state.

By inserting the dialogue between Einstein, Schlick and Reichenbach in a wider network of debates about the epistemology of geometry, the paper shows, that not only Einstein and Logical Empiricists came to disagree about the role, principled or provisional, played by rods and clocks in General Relativity, but they actually, in their life-long interchange, never clearly identified the problem they were discussing. Einstein’s reflections on geometry can be understood only in the context of his “measuring rod objection” against Weyl. Logical (...) Empiricists, though carefully analyzing the Einstein-Weyl debate, tried on the contrary to interpret Einstein’s epistemology of geometry as a continuation of the Helmholtz-Poincaré debate by other means. The origin of the misunderstanding, it is argued, should be found in the failed appreciation of the difference between a “Helmhotzian” and a “Riemannian” tradition. The epistemological problems raised by General Relativity are extraneous to the first tradition and can only be understood in the context of the latter, whose philosophical significance, however, still needs to be fully explored. (shrink)