Geometrical conventionalism and the Theory of Relativity: can we know the true geometry of space?




Mueller, Paul Jacob

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The central question which will be addressed in this paper is: can we know the true geometry of space? My answer will be in the negative, but not first without heavy qualification. The thesis concerns the notion of truth in mathematical science, i.e. physical science for which mathematics (particularly geometry) is integral, and will ask whether we can know with certainty, or via some empirical test, which geometry is an accurate description of the actual universe. It will be a fairly historical approach, but hopefully not entirely so. We will begin with a 17th century debate on the nature of space between Newton and Leibniz and how Kant proposed to resolve the debate, and then move on to the views of the late 19th century mathematician Poincaré, but we will end with Einstein's Theory of Relativity - a theory which uses a very different geometry to which most of us are perhaps accustomed. In general, the goal will be to better understand the nature of geometry and its role in scientific theory; specifically, however, it will be an attempt to answer, in the negative, the central question before us.



geometry, space, Einstein, Albert