> But the inferences of the resulting neural nets is not an algorithm
It is a self-delimiting program. It is an algorithm in the most basic sense of the definition of “partial recursive function” (total in this case) and thus all known results of computability theory and algorithmic information theory apply.
> Formal system is a collection of defined operations
Not at all.
> I don’t think you have to look at humans very hard to see that humans don’t implement any kind of formal system and are not equivalent to Turing machines.
We have zero evidence of this one way or another.
—
I’m looking for loopholes around Gödel’s theorems just as much as everyone else is, but this isn’t it.
It is a self-delimiting program. It is an algorithm in the most basic sense of the definition of “partial recursive function” (total in this case) and thus all known results of computability theory and algorithmic information theory apply.
> Formal system is a collection of defined operations
Not at all.
> I don’t think you have to look at humans very hard to see that humans don’t implement any kind of formal system and are not equivalent to Turing machines.
We have zero evidence of this one way or another.
—
I’m looking for loopholes around Gödel’s theorems just as much as everyone else is, but this isn’t it.