In which I attempt to answer the question "What even is a number?" for a friend. https://notebook.drmaciver.com/posts/2019-02-18-08:58.html …
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Presberger arithmetic can be proven correct in a more powerful system then Presberger arithmetic. Peano arithmetic can be proven sound in ZF or much more simply proven consistent by induction on the wellfoundedness of epsilon-zero. I see little moral difference.
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I agree! The footnote is intended as satire, ridiculing logicism as an account of mathematical foundations.
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