On 5/23/2020 4:42 AM, Bruno Marchal wrote:
Well, those are theorem provable in very weak theories. It is more a question of grasping the proof than subscribing to a philosophical idea. That arithmetic executes all programs is a theorem similar to Euclid’s theorem that there is no biggest prima numbers. It is more a fact, than an idea which could be debated. I insist on this as I realise this is less known by the general scientists than 20 years ago. We knew this implicitly since Gödel 1931, and explicitly since Church, Turing and Kleene 1936.
Recently you have said that your theory is consistent with finitism, even ultrafinitism. But the idea that arithemtic exectues all programs certainly requires infinities.
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