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lessdazed comments on Why do people commit mathematical mistakes? What are the mechanisms behind them? - Less Wrong
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Why do people ever reason correctly on mathematical problems? What are the mechanisms behind this seemingly miraculous kludge?
-Leo Tolstoy, Anna Karenina
Robin Hanson elaborates.
the more you investigate the foundations of mathematics the more miraculous "obvious" inference jumps will become.
Really? How so?
No matter how well you atomize a proof there remains inferential gaps that gets filled by humans agreeing that something is obvious. Some are considered axiomatic, many aren't.
... That's basically what many theists object to Yudkowsky's sequences. "There are inferential gaps".
I don't remember the exact quote or source, but I once read something along the lines of "humans don't prove anything, we just decide which side of the argument we will hold to a higher standard of proof."
Motivated Continuing and Motivated Stopping? But accusing someone of that would be incurring in the Genetic Fallacy...