Post #2022530
2026-05-04 16:00 UTC
> What Turing and Gödel independently proved is that a human observer can (theoretically) always have insights about mathematics and programming that are incomputable. That is, you cannot program or axiomatize or formalize or digitize everything that a mind can do. Period.
that is not what either of them proved. like... at all
Replies (1)
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@yeahiknow3@lemmy.dbzer0.com 2026-05-04 17:42
I study this stuff. You will find what I said in any philosophy of mathematics textbook dealing with the subject. In fact, I am [paraphrasing the Oxford logician](https://a.co/d/00ZImU8a) Joel David Hamkins. You’re welcome to also read [Shapiro’s famous paper](https://www.jstor.org/stable/421032) for a rephrasing. These results have been well understood for half a century, although because the implications are ultimately metaphysical and not mathematical, we can’t be sure of the wider consequences, if any.