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I feel like this kind of attitude belies that everyone has a different idea of obvious, and that this kind of self-assured confidence is what froze geometry until about 100 years ago.

Realizing that axioms were switches to be turned on and off to generate new structures that may or may not be useful was an important step to abandoning the most obvious and intuitive truths of geometry. Thus geometry has no concept of true outside of axioms, and true simply means internally coherent. Outside of formalization, "obviously true" is the hindrance of confidence.




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