Logic Matters 2008-07-29

Logic's Lost Genius again

The last appendix to Eckart Menzler-Trott's book on Gödel is a thirty-six page essay "From Hilbert's Programme to Gentzen's Programme" by Jan von Plato. As you'd expect from this author, this is accurate and useful, as far as it goes. But actually, although it would have made a long book even longer, it would have been rather good to have fifteen rather than five pages on the key results about the consistency of arithmetic. For von Plato's discussion is a bit frustratingly short of details about the proof-strategies of Gentzen's four proofs. Students who aren't planning to do a heavy-duty course on proof-theory will find it difficult to pick up quite enough about the basics of what is going on in the proofs to satisfy their intellectual curiosity. (All the same, like Smorynski's piece, this essay will be well worth ...

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