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

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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