The foundations of mathematics are unproven Philosopher and logician Kurt Gödel upended our understanding of mathematics and truth. ..... Kurt Gödel showed just how groundless the axioms of mathematics are. Gödel's theorem does not devalue mathematics but reveals that some truths are unprovable. ............... Hilbert hated the fact that the whole of mathematics depended on certain “axioms” that were, themselves, not proven. ......... axioms are the building blocks of mathematics. ......... It’s impossible for math, on its own, to prove its own axioms. ........ More famously, the liar paradox imagines a sentence like, “This sentence is false.” When you examine it closely, it creates a logical circularity. If the sentence is true, then it’s false; but then if it’s false, it’s true. It’s enough to make a robot’s brain explode. ............. Gödel only showed that truth does not always need to be proven. ....... Gödel, himself, thought there were objective truths. His theory only went to show the limitations of mathematics but not that it was flawed in any way. He would have hated what the postmodernists made of his work.
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