According to artificial intelligence researcher Joscha Bach, only classical mathematics is affected by Gödel’s incompleteness theorem however not computation where calculations are performed in a step-wise and thus time-dependent manner.
In the YouTube video “Donald Hoffman Λ Joscha Bach on Consciousness, Free Will, and Gödel“, Bach explains that classical (= “stateless”) mathematics is a time-independent way of performing all necessary operations at once, so that e.g. pi is considered a value. Whilst in computation which is only progressing in a step-by-step (state-to-state) fashion pi just becomes a function that allows one to know more and more digits of pi by further iterating through the algorithm – something like the last digit of pi can never be reached.
Now, Bach holds that unlike computation, part of mathematics is based on erroneous assumptions (like that one of infinity) which is why new axioms will have to be added to fix the issues Gödel discovered:
“so basically what Gödel and Turing have shown is that stateless mathematics doesn't work and the opposite is true there is no deeper notion of truth than proof … Gödel has not discovered that mathematics cannot reach truth but that truth is no more than the result of a sequence of steps that is compressing a statement to axioms losslessly”
Could you please let me know your thoughts about this? Do you agree or disagree, and why?
Thank you in advance.