Gentzen’s consistency proof is more impressive than you expect

I recently said something about the impossibility to prove the consistency of PA, and that Gentzen proved just this in 1936. Because I got critizised quite a bit, and realized that even famous mathematicians get critizized if they dare to mention this, I decided to read the original papers of Gentzen. I was deeply impressed how well explained they are, and how much more perspective they add. But I also realized that they are written in German, and that it will probably be impossible to express the thoughts with the same clarity in English, at least for me. Still

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About gentzen

Logic, Logic, and Logic
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2 Responses to Gentzen’s consistency proof is more impressive than you expect

  1. vznvzn says:

    not aware of any controversy on this. why do “even famous mathematicians get criticized if they dare mention” it?

    • gentzen says:

      I added links to the criticisms of Voevodsky’s position now.

      Linking to the criticism of my statement turned out to be difficult, because the down-votes and comments were removed after I updated my answer. If I remember correctly, the criticism was targeted against my conclusion: “Well, even mathematical proofs depend on general context, implicit assumption and explicit premises.” Especially the part with the “implicit assumptions” was ill received.

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