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The fundamental axioms of mathematics are inconsistent if and only if we can prove that they are consistent.

Because,

(Because, you know, it follows from "logic." (See Second Incompleteness theorem)

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The fundamental axioms of mathematics are inconsistent if and only if we can prove that they are consistent.

Because, you know, it follows from "logic." (See Second Incompleteness theorem)

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The fundamental axioms of mathematics are inconsistent if and only if we can prove that they are consistent. (Second Incompleteness theorem)