Eli5: can someone explain to me the difference between what godels system and the Turing machine proved? Aren’t they both basically just proving that x can’t equal (x≠x)

Question

Eli5: can someone explain to me the difference between what godels system and the Turing machine proved? Aren’t they both basically just proving that x can’t equal (x≠x)

In: Mathematics

Answer 1

My first attempt eli5ing so here goes

So before godel the hypothesis was that

The universe is made up of well defined rules and once you enumerate the rules you can automate them to be performed by machines and that these machines can perform the tasks as good as humans.

Turing’s hypothesis lays down the tenets for what makes a machine indistinguishable from a human.

Godel’s incompletenes theorem disproves that everything can be enumerated.