Nineteenth Century Philosophy

Philosophy of Mathematics and Logic

How did non-Euclidian geometry affect other fields?

The relationship between space and geometry changed forever in people’s minds, thanks to non-Euclidian geometry. The question arose of whether space itself was curved. This made the whole of geometry seem hypothetical and led some to question the possibility of a priori knowledge. That is, if space is not necessarily Euclidian and there are other unknown geometries of space, then what does it mean to say that we have “a priori knowledge of space?” Also, the idea of the curvature of space was conducive to Albert Einstein’s theory of relativity, thus influencing physics and our concept of the universe.


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