It appears that it isn't impossible to prove the Peano axioms consistent...if your definition of 'prove' is loose enough. Pebbles all the way down, man. https://en.wikipedia.org/wiki/Peano_axioms#Consistency …
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Yup. It’s actually surprising how much of math is “essentially contested”, i.e. people disagree and there’s no way of resolving the disagreement rationally. There was a great post recently about natural-seeming questions that are independent of ZF and not obviously = AC or CH.
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I'm not sold on the idea that outsourcing the task of recognizing pebbles as objects to an artifact (brain or computer) suddenly makes this "circumrational". You can make rational reasoning which artifact is better for the support task.
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For starters, you vastly underestimate the amount of free time I have.
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I hereby propose your book to be called "How to human".
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"It’s not that the shepherd’s bucket or pebbles are different from the fair-goer’s. It’s that he’s doing ongoing work to make them correspond with sheep..." Linking peddles to sheep seems to reflect the ability to think in metaphors.
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Counting, the most basic rational procedure, depends on non-rational skills. Simple illustration of a major theme of my meta-rationality book.
(How would you count the pebbles in this bucket?)