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Metaphysics

Mathematical Knowledge: A Dilemma

Rui Vieira thinks of a number.

What exactly are the objects of mathematics, and how do they relate to our knowledge of them? Since Plato (427 BC–347 BC) such questions have been central to the philosophy of mathematics. Plato realized that mathematics seems to involve perfect circles, triangles, and so on. But as Plato also noticed, there are no perfect circles or triangles to be found in the world, only imperfect approximations. Imagine a polygon [shape] with an ever-increasing number of equal sides. As the number of sides approaches infinity, the polygon will become a circle.

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