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EL1 2
ANSWERS: 2
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there are elements of mathematics which we can know through instinct, but can never be PROVED using basic principles.
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Mathematician Kurt Godel famously proved that in mathematics, there exist theorems that are undecidable -- that is, which can neither be proven true nor false. So the answser to the question is yes -- in a very deep sense of mathematical logic. In everyday practical terms, most propositions that mathematicians come up with are either proven true or shown false by counterexample.
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