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Geometrical finiteness and numerical finiteness relate to our mundane, very real, experiences. This is why we find it difficult to digest mathematical entities such as a singularity (both finite and infinite, in some respects). We prefer the fiction of finiteness (temporal, spatial, logical) ? over the reality of the infinite...
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Antinomies made it necessary to reject the principle of the excluded middle ("yes" or "no" and nothing in between). One of his antinomies "proved" that the world was not infinite, nor was it finite. The antinomies were disputed (Kant's answers were not the ONLY ways to tackle them). But one contribution stuck : the world is not a perfect whole...
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