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Inverse View
It is not the case that Scientific knowledge of space is of a different kind from our knowledge of geometry.
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Reasons For
2 perspectives
Reason for 1 of 2
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1.
Einstein's general relativity demonstrated that physical geometry is empirically revisable, collapsing the analytic/synthetic distinction Kant relied upon.
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2.
If spatial structure is discovered through physical theorizing rather than pure intuition, scientific and geometrical knowledge share the same empirical foundation.
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Reason for 2 of 2
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1.
Reichenbach and the logical empiricists showed that geometric axioms function as coordinating principles whose truth is fixed by physical convention, not pure reason.
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2.
When geometry is conventional and empirically constrained, no principled epistemic difference separates it from other scientific knowledge about space.
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Reasons Against
1 perspective
Reason against
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1.
Sensitive knowledge of corresponding objects can never achieve the same degree of certainty as geometrical knowledge.
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2.
Our knowledge of space derives from our knowledge of objects.
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