A case study of the development of quantum field theory and of S-matrix theory, from their inceptions to the present, is presented. The descriptions of science given by Kuhn and by Lakatos are compared and contrasted as they apply to this case study. The episodes of the developments of these theories are then considered as candidates for competing research programs in Lakatos' methodology of scientific research programs. Lakatos' scheme provides a reasonable overall description and a plausible assessment of the relative (...) value of these two programs in terms of progressive and degenerating problem shifts. Also discussed are the roles of various types of models as they have been used in these areas of theoretical high-energy physics. (shrink)

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can be (...) also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators on it. One can interpret special Minkowski space involved by special relativity and the qubit Hilbert space of quantum information as Fourier counterparts immediately noticing that general relativity means gravitation as the Fourier counterpart of non-Hermitian operators implying non-unitarity and the violation of energy conservation and thus destroying Pauli’s particle paradigm. Since the Standard model obeys it, this explains the impossibility of “quantum gravitation” in any framework conservatively generalizing the Standard model so that it would include gravitation along with electromagnetic, weak, and strong interactions. Einstein’s geometrization of gravitation can be continued into a purely mathematical theory of it following Euclid’s realization for geometry to be exhaustively built in a deductive and axiomatic way as well as Riemann’s parametrization of all the class of Euclidean and non-Euclidean geometries by “space curvature”, then being generalized to Minkowski space as the operators on pseudo-Riemannian space as the Einstein field equation means gravitation. The transition from mathematical gravitation to logical one can rely on the historical lesson of the pair of Lobachevski’s and Riemann’s approaches now “reversely”, i.e., from the latter to the former. Logical gravitation is linkable to Hegel’s dialectical logic and ontological dialectics abandoning their interpretations as a new zero logic substituting classical propionyl logic. The approach of ontomathematics generalizing that of ontology, traceable even to Aristotle’s reformation of Plato’s doctrine, needs Hegel’s doctrine to be formalized as a first-order logic naturally containing Boolean algebra, isomorphic to both classical propositional logic and set theory being the class of all first-order logics, as a sub-logic along with Peano arithmetic as another sub-logic. The first-order logic at issue is called Hilbert arithmetic and elaborated in detail in other papers. It allows for both self-foundation of mathematics to be internally proved as complete and furthermore, quantum mechanics reinterpreted as quantum information to be included by the qubit Hilbert space interpretable in turn as a dual and physical counterpart of Hilbert arithmetic in a narrow sense, that is, both counterparts constitute Hilbert arithmetic in a wide sense, being mathematical and physical simultaneously and thus overcoming the Cartesian dualism of “body” gapped from “mind” by an abyss. Then, the proper philosophical interpretation of gravitation to be the fundamental ontomathematical force or interaction overcomes the ridiculous belief of the Big Bang wrongly alleged to be a scientific theory. Ontomathematical gravitation suggests an omnipresent and omnitemporal medium of “God’s” creation “ex nihilo” following only the natural necessity of quantum-information conservation particularly and locally manifested as energy conservation. (shrink)

Arguments for the effectiveness, and even the indispensability, of mathematics in scientific explanation rely on the claim that mathematics is an effective or even a necessary component in successful scientific predictions and explanations. Well-known accounts of successful mathematical explanation in physical science appeals to scientists’ ability to solve equations directly in key domains. But there are spectacular physical theories, including general relativity and fluid dynamics, in which the equations of the theory cannot be solved directly in target domains, and yet (...) scientists and mathematicians do effective work there (McLarty 2023, Elder 2023). Building on extant accounts of structural scientific explanation (Bokulich 2011, Leng 2021), I argue that philosophical accounts of the role of equations in scientific explanation need not rely on scientists’ ability to solve equations independently of their understanding of the empirical or experimental context. For instance, the process of formulating solutions to equations can involve significant appeal to information about experimental contexts (Curiel 2010) or of physically similar systems (Sterrett 2023). Working from a close analysis of work in fluid mechanics by Martin Bazant and Keith Moffatt (2005), I propose an account of heuristic structural explanation in mathematics (Einstein 1921, Pincock 2021), which explains how physical explanations can be constructed even in domains where basic equations cannot be solved directly. (shrink)

To many contemporary scholars, Émile Meyerson is a footnote in an obscure history: early twentieth-century French philosophy of science. While the traditions of épistémologie are beginning to enjoy the scrutiny they deserve, Meyerson’s role remains overlooked. This article provides an overview of Meyerson’s philosophical project to help sow the seeds for a more systematic recuperation of its legacy. By orienting his work historically, I elucidate the nature of Meyerson’s critique of positivism, his distinctive method, and the implications these have for (...) the relation between science and philosophy. In particular, I show that for Meyerson positivisme refers not only to the doctrine of Auguste Comte but to a general philosophical tendency. Inseparable from Meyerson’s critique of this tendency is his implementation of a new methodology—épistémologie—according to which reason must be understood through the historical development of science. Épistémologie reveals that positivism not only is an incomplete account of science but is detrimental to its progress. Accordingly, Meyerson hopes to secure science’s right to function according to its own immanent principles, thereby providing prolegomena to all future metaphysics through a historical determination of the nature and limits of human reason. (shrink)

The modern mathematical theory of dynamical systems proposes a new model of mechanical motion. In this model the deterministic unstable systems can behave in a statistical manner. Both kinds of motion are inseparably connected, they depend on the point of view and researcher's approach to the system. This mathematical fact solves in a new way the old problem of statistical laws in the world which is essentially deterministic. The classical opposition: deterministic‐statistical, disappears in random dynamics. The main thesis of the (...) paper is that the new theory of motion is a revolution in the research programme of classical mechanics. It is the revolution brought about by the development of mathematics. (shrink)

We discuss Einstein’s knowledge of projective geometry. We show that two pages of Einstein’s Scratch Notebook from around 1912 with geometrical sketches can directly be associated with similar sketches in manuscript pages dating from his Princeton years. By this correspondence, we show that the sketches are all related to a common theme, the discussion of involution in a projective geometry setting with particular emphasis on the infinite point. We offer a conjecture as to the probable purpose of these geometric considerations.

Gerald Holton has famously described Einstein’s career as a philosophical “pilgrimage”. Starting on “the historic ground” of Machian positivism and phenomenalism, following the completion of general relativity in late 1915, Einstein’s philosophy endured (a) a speculative turn: physical theorizing appears as ultimately a “pure mathematical construction” guided by faith in the simplicity of nature and (b) a realistic turn: science is “nothing more than a refinement ”of the everyday belief in the existence of mind-independent physical reality. Nevertheless, Einstein’s mathematical constructivism (...) that supports his unified field theory program appears to be, at first sight, hardly compatible with the common sense realism with which he countered quantum theory. Thus, literature on Einstein’s philosophy of science has often struggled in finding the thread between ostensibly conflicting philosophical pronouncements. This paper supports the claim that Einstein’s dialog with Émile Meyerson from the mid 1920s till the early 1930s might be a neglected source to solve this riddle. According to Einstein, Meyerson shared (a) his belief in the independent existence of an external world and (b) his conviction that the latter can be grasped only by speculative means. Einstein could present his search for a unified field theory as a metaphysical-realistic program opposed to the positivistic-operationalist spirit of quantum mechanics. (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)

Despite the praise his writing garnered during his lifetime, e.g., from readers such as Einstein and de Broglie, Émile Meyerson has been largely forgotten. The rich tradition of French épistémologie has recently been taken up in some Anglo-American scholarship, but Meyerson—who popularized the term épistémologie through his historical method of analyzing science, and criticized positivism long before Quine and Kuhn—remains overlooked. If Meyerson is remembered at all, it is as a historian of classical science. This paper attempts to rectify both (...) states of affairs by explicating one of Meyerson׳s last and untranslated works, Réel et déterminisme dans la théorie quantique, an opuscule on quantum physics.I provide an overview of Meyerson׳s philosophy, his critique of Max Planck׳s interpretation of quantum physics, and then outline and evaluate Meyerson׳s neo-Kantian alternative. I then compare and contrast this interpretation with Cassirer׳s neo-Kantian program. Finally I show that, while Meyerson believes the revolutionary new physics requires "profoundly" modifying our conception of reality, ultimately, he thinks, it secures the legitimacy of his thesis: that science seeks explanations in the form of what he calls "identification." I hope my research will enable a more general and systematic engagement with Meyerson׳s work, especially with a view to assessing its viability as a philosophical method today. (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)

(1987). Einstein's brand of verificationism. International Studies in the Philosophy of Science: Vol. 2, No. 1, pp. 33-54. doi: 10.1080/02698598708573301.