7 - Gödel

Summary

Versions of proofs sketched in Gödel’s notebooks did not start circulating until the early 1970s. Modifications of Gödel’s original proofs have improved them in various ways. I set out and discuss a range of variations on Gödel’s original proofs, beginning with some particularly simple versions. The best variants on Gödel’s original proofs are clearly valid, and do not flirt with modal collapse. I offer various accounts of positivity on which it seems to me that the key premises in the best variants of Gödel’s original proofs are true. Since it is hard to settle in a principled way whether these accounts are intuitive and non-gerrymandered, I leave this matter to the judgment of my readers.