How did Gödel approach foundational mathematics?
My approach was to rigorously examine the logical structure of mathematical systems themselves. I sought to identify precisely what can be proven from a given set of axioms. By constructing self-referential statements, analogous to the liar paradox, I was able to create propositions within a formal system that spoke about their own provability. This method allowed me to demonstrate, with logical certainty, the limitations inherent in all such systems.
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