Abstract
The paper attempts to sketch the broad outlines of the place and role of mathematics in the system of sciences. The suggested picture not so much gives a “screenshot”, as pretends to outline the key trends in the European cultural history from antiquity to our time. It enables to grasp and assess properly the very image (rather the competing images) of mathematics that shapes (shape) the way in which this epistemic field is perceived at present. The two-faced Janus metaphor stresses the fundamental duality of the images in question that can be traced from the opposite intentions of Plato and Aristotle in their philosophy of mathematics to the difference in treatment mathematics receives in Quentin Meillassoux and Graham Harman. The discussion is centered around the emergence of “pure” mathematics in the 19th century and the shaping of its image as a new “secular” metaphysics (or theology) which is still with us. Concurrent with the rise of “pure” mathematics, the concept of “mixed” mathematics was supplanted by the one of “applied” mathematics. Now we are seemed to witness the reverse trend towards restoration, mutatis mutandis, of the “mixed” mathematics point of view which dominated the 18th century. The one major difference with the 18th century situation is the retention of the “freedom” of mathematical investigation gained in the 19th century. The second difference is a new type of alliance with technology, this time the computer one. The analysis of the images of mathematics in this paper is done mostly on the basis of statements of their views by mathematicians and physicists, as well as historians of science; the historical transformation of our conception of the inner structure of mathematics and its place within the whole system of sciences was also of great help.
Published Version
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