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Do Not Claim Too Much: Second-order Logic and First-order Logic
1999
Philosophia Mathematica
I once heard a story about a museum that claimed to have the skull of Christopher Columbus. In fact, they claimed to have two such skulls, one of Columbus when he was a small boy and one when he was a grown man. Whether there was such a museum or not, the clear moral is that one should not claim too much. The purpose of this paper is to apply the moral to the contrast between first-order logic and second-order logic, as articulated in my Foundations without foundationalism: A case for
doi:10.1093/philmat/7.1.42
fatcat:m2spad6v3rb4hnt6jzpqo4jscy