There can never be surprises in logic.
With my full philosophical rucksack I can only climb slowly up the mountain of mathematics.
Mathematics is a logical method. . . . Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.
Logic takes care of itself; all we have to do is to look and see how it does it.
We could present spatially an atomic fact which contradicted the laws of physics, but not one which contradicted the laws of geometry.
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