Weyl, Hermann (1885–1955)

Author(s):  
T.A. Ryckman

A leading mathematician of the twentieth century, Weyl made fundamental contributions to theoretical physics, to philosophy of mathematics, and to philosophy of science. Weyl wrote authoritative works on the theory of relativity and quantum mechanics, as well as a classic philosophical examination of mathematics and science. He was briefly a follower of Brouwer’s intuitionism in philosophy of mathematics. Upon moving closer to Hilbert’s finitism, he articulated a conception of mathematics and physics as related species of ‘symbolic construction’.

Author(s):  
David J. Stump

Although primarily a mathematician, Henri Poincaré wrote and lectured extensively on astronomy, theoretical physics, philosophy of science and philosophy of mathematics at the turn of the century. In philosophy, Poincaré is famous for the conventionalist thesis that we may choose either Euclidean or non-Euclidean geometry in physics, claiming that space is neither Euclidean nor non-Euclidean and that geometry is neither true nor false. However, Poincaré’s conventionalism was not global, as some have claimed. Poincaré held that only geometry and perhaps a few principles of mechanics are conventional, and argued that science does discover truth, despite a conventional element. Poincaré followed new developments in mathematics and physics closely and was involved in discussion of the foundations of mathematics and in the development of the theory of relativity. He was an important transitional figure in both of these areas, sometimes seeming ahead of his time and sometimes seeming very traditional. Perhaps because of the breadth of his views or because of the way in which philosophers focused on issues or small pieces of his work rather than on accurate history, interpretations of Poincaré vary greatly. Frequently cited by the logical positivists as a precursor, and widely discussed in the philosophy of science and the philosophy of mathematics, Poincaré’s writings have had a strong impact on English-language philosophy.


Author(s):  
Mary Tiles

One indication of the originality of Bachelard’s work is that he was famous for his writings both in the philosophy of science and on the poetic imagination. His work demonstrates his belief that the life of the masculine, work-day consciousness (animus), striving towards scientific objectivity through reasoning and the rectification of concepts, must be complemented by the life of a nocturnal, feminine consciousness (anima), seeking an expanded poetic subjectivity, as, in reverie, it creates the imaginary. In common with other scientist-philosophers writing in the first half of the twentieth century, Bachelard reflected on the upheavals wrought by the introduction of relativity theory and quantum mechanics. The views at which he arrived were, however, unlike those of his contemporaries; he argued that the new science required a new, non-Cartesian epistemology, one which accommodated discontinuities (epistemological breaks) in the development of science. It was only after he had established himself as one of France’s leading philosophers of science, by succeeding Abel Rey in the chair of history and philosophy of science at the Sorbonne, that Bachelard began to publish works on the poetic imagination. Here his trenchantly anti-theoretical stance was provocative. He rejected the role of literary critic and criticized literary criticism, focusing instead on reading images and on the creative imagination.


Author(s):  
Gary Gutting

A distinctively French tradition in the philosophy of science began with Descartes, continued through the Enlightenment in works such as D’Alembert’s Discours préliminaire and the Encyclopédie, and flowered in the ninteenth and the early twentieth century with the work of Comte, Duhem, Meyerson and Poincaré. Throughout the twentieth century, the dominant fashions in French philosophy derived more and more from German influences, especially idealism and phenomenology (Hegel to Heidegger). But amidst these developments, there persisted an essentially autonomous tradition of French philosophy of science that offered an indigenous alternative to the Germanic imports. Here the key figure was Gaston Bachelard (1884–1962), for many years professor at the Sorbonne and director of the Institut d’Histoire des Sciences et des Techniques. His work was continued and modified by Georges Canguilhem (1904–95), his successor at the Institute, who himself was an important influence on philosophers such as Louis Althusser, Michel Foucault and Michel Serres. Jean Cavaillès’ critique of Husserl’s philosophy of mathematics and his effort to develop a neo-Hegelian alternative to it had deep affinities with Bachelard’s work and was also an important influence on Canguilhem. The most important general features of twentieth-century French philosophy of science appear if we contrast it with its two major rivals: existential phenomenology and logical positivism. Existential phenomenology is a ‘philosophy of the subject’, maintaining that ultimate truth resides in the immediacy of lived experience. Bachelard and his followers, by contrast, proposed a ‘philosophy of the concept’, for which experiential immediacy is subordinate to and corrected by concepts produced by rational reflection. This process of rational reflection is, moreover, embodied in science, which is not, as existential phenomenology maintains, a derivative and incomplete form of knowing, but the very paradigm of knowledge. In giving science a privileged epistemic position, the French philosophers of science are like the logical positivists. But, unlike the positivists, they treat science as essentially historical, irreducible in either method or content to the rigour of a formal system. They also opposed the positivists’ effort to find the foundations of scientific knowledge in sense experience, maintaining that there are no simply given data and that all experience is informed by conceptual interpretation.


Philosophy ◽  
2014 ◽  
Author(s):  
Brendan Larvor ◽  
Colin Jakob Rittberg

Imre Lakatos (b. 1922–d. 1974) was a philosopher of mathematics and science. Having left Hungary in 1956, he made his first appearance on the international stage with a series of four papers during 1963 and 1964 in the British Journal for the Philosophy of Science, later published together posthumously in Proofs and Refutations (1976), in which he discusses the formation of mathematical concepts by proof-analysis. This radical break with classical approaches to the philosophy of mathematics attracted sufficient interest that Kitcher and Aspray deem Lakatos to have started a new and “maverick” tradition in the field (“An Opinionated Introduction,” in History and Philosophy of Modern Mathematics, 1988). By 1959, Lakatos had become an assistant lecturer in the Department of Philosophy, Logic and Scientific Method at the London School of Economics and Political Science. This department was still under the direction of its founder, Karl Popper, and Lakatos’s evolving and ultimately antagonistic relations with Popper and the Popperians conditioned much of his work. The chief part of this work was a series of influential papers on the philosophy of science. These are included in the two books of his work that two of his former students, John Worrall and Gregory Currie, published after his death (Lakatos 1978a and Lakatos 1978b, cited under Posthumously Published). In 1974, Lakatos died of a heart attack, leaving his projects in philosophy of science and mathematics incomplete.


2002 ◽  
Vol 50 ◽  
pp. 277-292 ◽  
Author(s):  
Simon Saunders

But this picture of a ‘block universe’, composed of a timeless web of ‘world-lines’ in a four-dimensional space, however strongly suggested by the theory of relativity, is a piece of gratuitous metaphysics. Since the concept of change, of something happening, is an inseparable component of the common-sense concept of time and a necessary component of the scientist's view of reality, it is quite out of the question that theoretical physics should require us to hold the Eleatic view that nothing happens in ‘the objective world’. Here, as so often in the philosophy of science, a useful limitation in the form of representation is mistaken for a deficiency of the universe (Black, 1962).


1976 ◽  
Vol 21 (4) ◽  
pp. 385-392 ◽  
Author(s):  
J. R. Giles ◽  
Jennifer Seberry Wallis

George Szekeres was born in Budapest on 29th May, 1911 the second of three sons to wealthy Jewish parents. As a youth he was shy and retiring, but early it become clear that his gifts lay in the direction of science and mathematics. At high school George was greatly influenced by his teacher in mathematics and physics, K. (Charles) Novobátzky, who worked actively in the theory of relativity and was in 1945 to become a professor of theoretical physics at the University of Budapest. Small wonder that George's first great mathematical interest was relativity. The other major formative influence at high school was the journal ‘Koözeépiskolai Matematikai és Fizikai Lapok’. The names of problem solver were published with each solution and with the completion of the year's volume, photographs of the main contributors were reproduced.


2020 ◽  
Vol 57 (4) ◽  
pp. 128-132
Author(s):  
Andrey Yu. Sevalnikov ◽  

The article is devoted to the problem of time in modern science, where in recent years there have been major changes related to the latest discoveries in the field of the foundations of quantum theory. The author refers to works of K.-F. von Weizsacker (which works are not well-known in Russian-speaking field). Weizsacker deploys a large-scale program of building modern physics, while starting (not only as a physicist, but also a professional philosopher) with questions of philosophical interpretation of postulates of modern physics, especially quantum mechanics. His key thesis is that time in physics is fundamentally distinct, which represents the whole physics as an integral scientific discipline. Weizsacker comes from physical and philosophical reflections, that give a special value to his work. Analyzing the conclusions of theoretical physics, namely the issues of substantiation of statistical mechanics, thermodynamics, and, above all, quantum mechanics, Weizsacker comes to the key idea of the structure of time in the substantiation of physical theory. The author in this conclusion disagrees with the opinion of most modern physicists that time has a subjective character, and the modus of the past, present and future reflects its essential character. The allocation of the time structure requires special logic. Such a logic is temporal and quantum. Starting from temporal logic, introducing the concept of possibility and probability, he comes to the substantiation of quantum mechanics. Being modal logic, it is based on the concept of possibility and probability. Key concept for Weizsacker is a binary alternative (Uralternative), closely related to the principle of superposition in quantum mechanics. By introducing the concept of certain alternatives, essentially actualized alternatives, Weizsacker shows how one can get the theory of relativity with its space-time structure. Further, he shows that based on its structure, you can get the theory of relativity. The space-time structure in this case is secondary, relational, as understood by Leibniz, Mach, and Einstein.


Author(s):  
Leemon B. McHenry

What kinds of things are events? Battles, explosions, accidents, crashes, rock concerts would be typical examples of events and these would be reinforced in the way we speak about the world. Events or actions function linguistically as verbs and adverbs. Philosophers following Aristotle have claimed that events are dependent on substances such as physical objects and persons. But with the advances of modern physics, some philosophers and physicists have argued that events are the basic entities of reality and what we perceive as physical bodies are just very long events spread out in space-time. In other words, everything turns out to be events. This view, no doubt, radically revises our ordinary common sense view of reality, but as our event theorists argue common sense is out of touch with advancing science. In The Event Universe: The Revisionary Metaphysics of Alfred North Whitehead, Leemon McHenry argues that Whitehead's metaphysics provides a more adequate basis for achieving a unification of physical theory than a traditional substance metaphysics. He investigates the influence of Maxwell's electromagnetic field, Einstein's theory of relativity and quantum mechanics on the development of the ontology of events and compares Whitehead’s theory to his contemporaries, C. D. Broad and Bertrand Russell, as well as another key proponent of this theory, W. V. Quine. In this manner, McHenry defends the naturalized and speculative approach to metaphysics as opposed to analytical and linguistic methods that arose in the 20th century.


2019 ◽  
Author(s):  
Vitaly Kuyukov

Quantum tunneling of noncommutative geometry gives the definition of time in the form of holography, that is, in the form of a closed surface integral. Ultimately, the holography of time shows the dualism between quantum mechanics and the general theory of relativity.


2021 ◽  
Vol 64 (3) ◽  
pp. 15-17
Author(s):  
Don Monroe

A theorem about computations that exploit quantum mechanics challenges longstanding ideas in mathematics and physics.


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