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An Obscure Mathematical Theory and the Consciousness Debate in AI

15 points by Anon84 7y ago

eukaryote31 7y ago
Nitpicks: there are lots of grammatical errors, egregiously out-of-place usage of emojis and emoticons, and it could be argued that Gödel's incompleteness theorem is hardly "obscure."
- airstrike 7y ago
  I wouldn't really call these nitpicks. No offense to the author, but this is one of the worst articles I've read in a while... > The previous part of this essay introduced a framework pioneered by known physicist Dr. Michio Kaku to evaluate consciousness in four different levels. In Dr. Kaku’s theory, Level 0 consciousness describes organisms such as plants that evaluate their reality based on a handful of parameters such as temperature. Reptiles and insects exhibit Level 1 consciousness as they create models of the world using new parameters including space. Level 2 consciousness involves creating models of the world based on emotions and the relationship to other species. Mammals are the main group associated with Level 2 consciousness. Finally, we have humans that can be classified at Level 3 consciousness based on models of the world that involve simulations of the future. This entire excerpt could be removed and the article would only be improved. He's just restating the past couple paragraphs! I spent far too long reading before the author made his points and ultimately I just decided to give up half way through
vga805 7y ago
For an overview of the debate re: incompleteness and strong AI: https://plato.stanford.edu/entries/goedel-incompleteness/#GdeArgAgaMec https://plato.stanford.edu/entries/goedel-incompleteness/#Gd...
- 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.
arafa 7y ago
Not the first time Goedel's Incompleteness theorem has been related to consciousness. It's a running theme in Douglas Hofstadter's work, especially in Goedel, Escher, Bach. I think Hofstadter's answer to this question would be: To what extent is AI engaging in and using self-reference? That's the degree of consciousness it has. https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach https://en.wikipedia.org/wiki/I_Am_a_Strange_Loop https://en.wikipedia.org/wiki/I_Am_a_Strange_Loop
ilaksh 7y ago
I think this is a pretty good discussion: https://youtu.be/piHkfmeU7Wo https://youtu.be/piHkfmeU7Wo Christof Koch: Consciousness | MIT Artificial Intelligence (AI) Podcast

15 points by Anon84 7y ago

Nitpicks: there are lots of grammatical errors, egregiously out-of-place usage of emojis and emoticons, and it could be argued that Gödel's incompleteness theorem is hardly "obscure."

airstrike 7y ago
I wouldn't really call these nitpicks. No offense to the author, but this is one of the worst articles I've read in a while... > The previous part of this essay introduced a framework pioneered by known physicist Dr. Michio Kaku to evaluate consciousness in four different levels. In Dr. Kaku’s theory, Level 0 consciousness describes organisms such as plants that evaluate their reality based on a handful of parameters such as temperature. Reptiles and insects exhibit Level 1 consciousness as they create models of the world using new parameters including space. Level 2 consciousness involves creating models of the world based on emotions and the relationship to other species. Mammals are the main group associated with Level 2 consciousness. Finally, we have humans that can be classified at Level 3 consciousness based on models of the world that involve simulations of the future. This entire excerpt could be removed and the article would only be improved. He's just restating the past couple paragraphs! I spent far too long reading before the author made his points and ultimately I just decided to give up half way through

vga805 7y ago

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

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.

arafa 7y ago

Not the first time Goedel's Incompleteness theorem has been related to consciousness. It's a running theme in Douglas Hofstadter's work, especially in Goedel, Escher, Bach. I think Hofstadter's answer to this question would be: To what extent is AI engaging in and using self-reference? That's the degree of consciousness it has. https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach https://en.wikipedia.org/wiki/I_Am_a_Strange_Loop https://en.wikipedia.org/wiki/I_Am_a_Strange_Loop

ilaksh 7y ago

I think this is a pretty good discussion: https://youtu.be/piHkfmeU7Wo https://youtu.be/piHkfmeU7Wo Christof Koch: Consciousness | MIT Artificial Intelligence (AI) Podcast