Nature's drawing: problems and resolutions in the mathematization of motion (original) (raw)
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The mathematical nature of modern science is an outcome of a contingent historical process, whose most critical stages occurred in the seventeenth century. 'The mathematization of nature' (Koyré 1957, From the closed world to the infinite universe, 5) is commonly hailed as the great achievement of the 'scientific revolution', but for the agents affecting this development it was not a clear insight into the structure of the universe or into the proper way of studying it. Rather, it was a deliberate project of great intellectual promise, but fraught with excruciating technical challenges and unsettling epistemological conundrums. These required a radical change in the relations between mathematics, order and physical phenomena and the development of new practices of tracing and analyzing motion. This essay presents a series of discrete moments in this process. For mediaeval and Renaissance philosophers, mathematicians and painters, physical motion was the paradigm of change, hence of disorder, and ipso facto available to mathematical analysis only as idealized abstraction. Kepler and Galileo boldly reverted the traditional presumptions: for them, mathematical harmonies were embedded in creation; motion was the carrier of order; and the objects of mathematics were mathematical curves drawn by nature itself. Mathematics could thus be assigned an explanatory role in natural philosophy, capturing a new metaphysical entity: pure motion. Successive generations of natural philosophers from Descartes to Huygens and Hooke gradually relegated the need to legitimize the application of mathematics to natural phenomena and the blurring of natural and artificial this application relied Synthese on. Newton finally erased the distinction between nature's and artificial mathematics altogether, equating all of geometry with mechanical practice.
The Roles of Mathematics in the History of Science: The Mathematization Thesis
Transversal: International Journal for the Historiography of Science
In this paper, we present an analysis of the evolution of the history of science as a discipline focusing on the role of the mathematization of nature as a historiographical perspective. Our study is centered in the mathematization thesis, which considers the rise of a mathematical approach of nature in the 17th century as being the most relevant event for scientific development. We begin discussing Edmund Husserl whose work, despite being mainly philosophical, is relevant for having affected the emergence of the narrative of the mathematization of nature and due to its influence on Alexandre Koyré. Next, we explore Koyré, Dijksterhuis, and Burtt’s works, the historians from the 20th century responsible for the elaboration of the main narratives about the Scientific Revolution that put the mathematization of science as the protagonist of the new science. Then, we examine the reframing of the mathematization thesis with the narrative of two traditions developed by Thomas S. Kuhn and ...
Transversal: International Journal for the Historiography of Science, 2020
In this paper, we present an analysis of the evolution of the history of science as a discipline focusing on the role of the mathematization of nature as a historiographical perspective. Our study is centered in the mathematization thesis, which considers the rise of a mathematical approach of nature in the 17 th century as being the most relevant event for scientific development. We begin discussing Edmund Husserl whose work, despite being mainly philosophical, is relevant for having affected the emergence of the narrative of the mathematization of nature and due to its influence on Alexandre Koyré. Next, we explore Koyré, Dijksterhuis, and Burtt's works, the historians from the 20 th century responsible for the elaboration of the main narratives about the Scientific Revolution that put the mathematization of science as the protagonist of the new science. Then, we examine the reframing of the mathematization thesis with the narrative of two traditions developed by Thomas S. Kuhn and Richard Westfall, in which the mathematization of nature shares space with other developments taken as equally relevant. We conclude presenting contemporary critical perspectives on the mathematization thesis and its capacity for synthesizing scientific development.
How the World Became Mathematical
My title, of course, is an exaggeration. The world no more became mathematical in the seventeenth century than it became ironic in the nineteenth. Either it was mathematical all along, and seventeenth-century philosophers discovered it was, or, if it wasn't, it could not have been made so by a few books. What became mathematical was physics, and whether that has any bearing on the furniture of the universe is one topic of this paper. Garber says, and I tend to agree, that for Descartes bodies are the things of geometry made real ( Ref). That is a claim about the world: what God created, and what we know in physics, is nothing other than res extensa and its modes. Others, including Marion after Heidegger, hold that in modern science, here represented at its origins by Descartes, representation displaces beings: the knower no longer confronts Being or beings but rather a system of signs, a "code" as Marion calls it, to which the knower stands in the relation of subject to object. The Meditations, or perhaps even the Regulae, are the first step toward the transcendental idealism of Kant.
Tracing the Precept of Motion from the Ancient to the Scientific Revolution
International Journal of Mechanical and Production Engineering Research and Development, 2020
Philosophers since times immemorial have endeavoured to comprehend the reality of nature and within it the primacy of "motion". An attempt in this enquiry is being made, to sieve through the corpus of thought, relating to the ontology of motion through primary and secondary data. The article traces the systematic attempt over the ages to cogitate on and formulate the concept of motion, beginning with the ancient mechanistic view, and culminating in Newton's work. In this exposition we scrutinize the shift from positivism, to what Husserl called idealization to account for the scientific theories of motion. In Newton's own words, "Since the ancients esteemed the science of mechanics of greatest importance in the investigation of natural things, and the moderns rejecting substantial forms and occult qualities, have endeavoured to subject the phenomenon of nature to the laws of mathematics, as far as it relates to philosophy" (Newton,1952 ,p.1). In the spirit of a larger inquiry, we have tried to identify whether any of the thought processes emerging out with the onset of the Scientific Revolution could be gleaned in any of the preceding historical moments of intellectual investigation.
Historico-Philosophical Aspects of Mathematisation of Nature in Modern Science
Discourse
Introduction. The paper deals with the philosophical problems of the mathematisation of nature in modern science.Methodology and sources. The analysis is based on the issues in modern science viewed through the prism of the critique of the mathematisation of nature in phenomenological philosophy.Results and discussion. It is argued that the radical mathematisation of nature devoid of any references to the source of its contingent facticity in humanity, leads to the diminution of humanity and concealment of the primary medium of existence, that is the life world. Phenomenology shows how the life-word can be articulated through contrasting it to “nature” constructed scientifically. It is the analysis of the scientific universe as mental creation that can help to uncover the life-world when “nature” (as scientifically constructed and abstracted from the life-world), is itself subjected to a kind of deconstruction which leads us back to the life-world of the next, so to speak, reflected...
“A Certain Correspondence”: The Unification of Motion from Galileo to Huygens
In this work, I focus on one of Galileo's concepts which was neither mathematically nor empirically derived, but instead based on a fundamental intuition regarding the nature of motion: that all mechanical phenomena can be treated in the same way, using the same mathematical and conceptual apparatus. This was Galileo's concept of 'correspondence', and I follow it from its origins at the turn of the 17th century through Thomas Harriot, Marin Mersenne and ultimately to Christiaan Huygens. At the centre of the concept of correspondence was that phenomena which looked similar really were the same; they were separate instances of the same fundamental processes. Hanging chains and projectile trajectories did not form the same curve by coincidence; they formed the same curve because both were produced by the same competition between vertical and horizontal tendencies. Correspondences were one of the major motivating and legitimising factors behind both Galileo and Huygens' desire to treat all of nature mathematically. This conceptual structure justified their treatment of all of mechanics as mathematically the same. Harriot and Mersenne's roles in this story are to show how contemporaries of Galileo could approach the same topic in drastically different ways. Unlike Huygens, neither Harriot nor Mersenne understood the concept of correspondences. While Galileo and Huygens relied crucially on correspondences to understand natural phenomena, both Harriot and Mersenne were able to achieve many important results in mechanics without it. This work is the biography of a concept; one that is contingent, constructed, frequently fruitful but not a historical or scientific necessity.