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What does it mean, "to apply mathematics?" Even if mathematics could 'speak" with phenomena immediately and directly, it would be of no help, for this would mean that everything could be expressed in mathematical terms and that mathematical structures were an exact reflection of shapes carved in space and forever fixed in time. We would grasp the ideal functioning of every phenomenon, and our power over things would be infinite. But it does not take an epistemologist or an historian of science to realize that nothing could be further from the truth. A veil hangs between mathematics and things, in the case of most of the sciences, a thick veil. Over millennia, this veil has become more transparent, first in astronomy and then in optics, and more recently in mechanics and the other disciplines of physics. But despite this veil, there have always been applications of mathematics that force us to learn about phenomena and things in terms of mathematics. Clearly, as the applications grew in number and impact, so our question claimed the attention of philosophers, until — starting from the second half of the eighteenth century — it became the very heart of modern philosophy.

DOI: 10.1007/978-94-017-2658-0_20

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