My thoughts exactly. Goedel is just basically "set of all sets that don't contain themselves ... does it contain itself or not?" applied to 'provability'.
It gives you no more profound insight than "you can eff yourself with recursion if you aren't super careful" which is obvious for any beginner programmer who encounters recursion and tries to write whatever he likes in recursive function.
I guess this might have been surprise for mathematicians who always thought they have all infinites at their disposal and thus are completely unrestricted and brushed self-referential paradoxes under the rug as curiosities until Godel showed they can be constructed about things mathematicians care about like provability.
I believe you can make a consistent fully provable axiomatic system by excluding statements that are not provable from your system, as meaningless.
You don't consider whether "number 5 contains itself" is true because it's nonsensical. "This statement is unprovable" can be considered similarily nonsensical not because it wrongly combines math concepts but because it's a self-referential paradox and we choose to not allow that.
It gives you no more profound insight than "you can eff yourself with recursion if you aren't super careful" which is obvious for any beginner programmer who encounters recursion and tries to write whatever he likes in recursive function.
I guess this might have been surprise for mathematicians who always thought they have all infinites at their disposal and thus are completely unrestricted and brushed self-referential paradoxes under the rug as curiosities until Godel showed they can be constructed about things mathematicians care about like provability.
I believe you can make a consistent fully provable axiomatic system by excluding statements that are not provable from your system, as meaningless.
You don't consider whether "number 5 contains itself" is true because it's nonsensical. "This statement is unprovable" can be considered similarily nonsensical not because it wrongly combines math concepts but because it's a self-referential paradox and we choose to not allow that.