3 ms·

For an overview of the debate re: incompleteness and strong AI: https://plato.stanford.edu/entries/goedel-incompleteness/#GdeArgAgaMec https://plato.stanford.ed

• posterboy 7y ago
  Interesting argument further down > That is, in his 1951 Gibbs lecture, Gödel drew the following disjunctive conclusion from the incompleteness theorems: > either … the human mind (even within the realm of pure mathematics) infinitely surpasses the power of any finite machine, or else there exist absolutely unsolvable diophantine problems. >Gödel speaks about this statement as a “mathematically established fact” (Gödel 1951; for more discussion on Gödel's disjunctive claim, see, e.g., Shapiro 1998). According to Gödel, the second alternative > seems to disprove the view that mathematics is only our own creation … that mathematical objects and facts … exist objectively and independently of our mental acts and decisions. > Gödel was nonetheless inclined to deny the possibility of absolutely unsolvable problems, and although he did believe in mathematical Platonism, his reasons for this conviction were different, and he did not maintain that the incompleteness theorems alone establish Platonism. Thus Gödel believed in the first disjunct, that the human mind infinitely surpasses the power of any finite machine. Still, this conclusion of Gödel follows, as Gödel himself clearly explains, only if one denies, as does Gödel, the possibility of humanly unsolvable problems. It is not a necessary consequence of incompleteness theorems. The level of arrogance is remarkable and can only be excused as naive. He's humble enough to reject any relevance of the theorems for sake of the discussion. Fortunately so, because now I don't have to go in on recursiveness, the arithmetic hierarchy and schemas of induction, or what is mechanism--of which I have no precise understanding anyway. But still, from a very basic logical stand point, it seems obvious that the question is sold as the answer. Whether the human mind could answer any and all question, is one of the questions in question. Questionmark.