Re:Minds, Machines and Gödel (1961)
by pdonis on Monday March 02, 2020 @12:41PM
(#22466668)
> The article is asking whether the formal system in question can fully explain human intelligence.
No, it's asking whether any formal system whatever can fully explain human intelligence. And it gives the wrong answer; see below.
> Which we all agree it can’t.
No, we don't, because the article misrepresents what "fully explain" means. The article assumes that, for a formal system to "fully explain" something, it must produce proofs of all sentences that that something could produce. But that condition is too strong. All the formal system needs to do is produce, by hook or by crook, the same outputs as the something (a human, or whatever) does. It doesn't have to produce proofs of all those outputs as theorems. Humans certainly don't produce formal proofs of all the things we claim we can intuitively see are true.
No, it's asking whether any formal system whatever can fully explain human intelligence. And it gives the wrong answer; see below.
> Which we all agree it can’t.
No, we don't, because the article misrepresents what "fully explain" means. The article assumes that, for a formal system to "fully explain" something, it must produce proofs of all sentences that that something could produce. But that condition is too strong. All the formal system needs to do is produce, by hook or by crook, the same outputs as the something (a human, or whatever) does. It doesn't have to produce proofs of all those outputs as theorems. Humans certainly don't produce formal proofs of all the things we claim we can intuitively see are true.