Why is non-Euclidean geometry, as encountered in relativity theory, always used as the prime counterexample to rationalism – and regarded as pretty much decisive?
The parallel postulate was controversial from the start and Euclid himself avoided invoking it whenever possible; so it seems far from being a victim of a psychological illusion, the insight of the early geometers into the structure of space was so reliable, that they got – except this one issue – everything right and even correctly singled out the “later refuted”1 axiom as “problematic”.
Is the strong association of rationalism with Kant (who thought – or at least so it is claimed – that space for us could only be Euclidean) the reason behind this?
1 sloppily phrased, of course. Also, afaik there is no way to directly show the non-Euclidean nature of space. It follows from an appeal to the simplicity of the theory, that non-Euclidean geometry is to be preferred and therefore correctly describes space. Which ironically seems a pretty “rationalist” line of argument, too.