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I don't understand how Gödel showed limits of AI, or even addressed AI in its modern incarnation, which has little to do with logic. Perhaps some more knowledge

I don't understand how Gödel showed limits of AI, or even addressed AI in its modern incarnation, which has little to do with logic. Perhaps some more knowledgeable reader can elucidate?

YeGoblynQueenne 5y ago
Without getting too technical, if AI must run on a computer, and there are programs that computers cannot compute, then there are limits to what AI can compute, or in other words think (because it's an AI; so to think, it computes). As a very crude example of this kind of limitation, I'm sure I've read a hundred Sci-Fi stories where the humans defeat the AI by posing to it an unsolvable problem, usually a variation of the "liar's paradox", e.g. "this statement is false" (which btw is used by Gödel in his proof). So a human traipses over to the superintelligent AI and blurts "I always lie". Then the AI spends an aeon processing the sentence and then blows up. Even worse, intelligence itself may turn out to be an uncomputable program that cannot be executed on a computer. In that case- no AI.
- visarga 5y ago
  The scenarios you described are not realistic. There's no AI getting stuck into a loop by a tricky question, not even GPT-3. Any solution would take into consideration its computation cost. AlphaGO for example would evaluate 50K board states per move, it won't go into a 3^361 recursion. In general when the problem is so hard evolutionary methods are suitable. They naturally blend the notion of cost with that of search and cope better with deceptive objectives.
  - deleted 5y ago
    [deleted]
  - YeGoblynQueenne 5y ago
    Your turn of phrase "there's no AI getting stuck..." has me stuck. Are you assuming that there exist "AIs", as in artificially intelligent entities, like the kind imagined by science fiction writers and (some) AI researchers, alike? To clarify, there are no such systems. "AI" is the name of a research field, not any ability that characterises a class of systems currently known. This suffices to explain why there is, indeed "no AI getting stuck inot a loop by a tricky question". Because there is "no AI" at all, certainly not of the kind that can understand a "tricky question" sufficiently well to stumble on the paradox inside it. For example, GPT-3 has no ability to process "this sentence is false" in such a way as to decide its truth. AlphaGo is not capable of processing language at all, it is only capable of playing board games and it isn't even capable of playing board games by reasoning, only by search. AlphaGo searches a game tree structured as a directed graph, without loops so it's hard to see how it could get stuck on recursive paradoxes anyway. In general, such systems as exist today do not have the mathematical properties of the formal systems described by Gödel, Church and Turing. They don't even have memories. So they are, let's say immune to incompleteness, because they're not even incomplete.
- simiones 5y ago
  It's important though to note that we know of no problem so far that a human mind can solve that couldn't be solved by a Turing Machine. Godel's incompleteness theorems may very well apply to human minds as well, and so far this seems more likely than not (though a lot of human thinking is actually inconsistent, so perhaps it falls to the other side of the incomplete/inconsistent "choice" than formal systems).
  - YeGoblynQueenne 5y ago
    Well... maybe human minds are themselves as limited as Turing machines? In that case we may never be able to create a machine that can overcome our, and Turing machines', limitations.
    - simiones 5y ago
      That is exactly what I personally believe.
acuozzo 5y ago
If your AI uses a classical computer, then everything it's doing is reducible to the Boolean algebra of its component logic gates. All of the training you've done on the GPU; all of the coordination done by the CPU; everything… it's all one (absurdly long) boolean expression. Like all algebraic structures, Boolean algebra is built from an initial set of axioms. Under Gödel's incompleteness theorem, it is therefore true that if Boolean algebra isn't inherently broken (inconsistent), then we can craft questions that cannot be answered using Boolean algebra alone, but this is all your classical computer is capable of doing! Now, if you're training AI using an analog system or a non-classical computer such as a quantum computer, then this opens up a totally different discussion.
- chakhs 5y ago
  Isn't his theorem proving that any mathematical system will be either incomplete or inconsistent ? And quantum computing is still a mathematical system so the same applies ?
  - acuozzo 5y ago
    Yes, but I didn't cite QC as an exception to the rule. I only mentioned it because it's governed by a different set of axioms and would result in a different discussion.
- visarga 5y ago
  > we can craft questions that cannot be answered using Boolean algebra alone Sure, that's trivial, the travelling salesman problem for example can't be solved exactly, but approximative methods come very close. Given that brains are pattern recognition machines generating probabilities we're already in the approximative regime. Nothing is certain, even science has its revisions. So does it matter if we can only approximate? For living things the main thing that matters is life, self reproduction, not exactness. As long as they reproduce they are still valid, with all imperfections and approximations. I think the only questions that matter are those related to life, there are plenty of uncomputable things outside self reproduction. This is for biological agents, an AI would be using evolutionary methods to reproduce their digital genes instead.

I don't understand how Gödel showed limits of AI, or even addressed AI in its modern incarnation, which has little to do with logic. Perhaps some more knowledgeable reader can elucidate?

YeGoblynQueenne 5y ago

Without getting too technical, if AI must run on a computer, and there are programs that computers cannot compute, then there are limits to what AI can compute, or in other words think (because it's an AI; so to think, it computes). As a very crude example of this kind of limitation, I'm sure I've read a hundred Sci-Fi stories where the humans defeat the AI by posing to it an unsolvable problem, usually a variation of the "liar's paradox", e.g. "this statement is false" (which btw is used by Gödel in his proof). So a human traipses over to the superintelligent AI and blurts "I always lie". Then the AI spends an aeon processing the sentence and then blows up. Even worse, intelligence itself may turn out to be an uncomputable program that cannot be executed on a computer. In that case- no AI.

visarga 5y ago
The scenarios you described are not realistic. There's no AI getting stuck into a loop by a tricky question, not even GPT-3. Any solution would take into consideration its computation cost. AlphaGO for example would evaluate 50K board states per move, it won't go into a 3^361 recursion. In general when the problem is so hard evolutionary methods are suitable. They naturally blend the notion of cost with that of search and cope better with deceptive objectives.
- deleted 5y ago
  [deleted]
- YeGoblynQueenne 5y ago
  Your turn of phrase "there's no AI getting stuck..." has me stuck. Are you assuming that there exist "AIs", as in artificially intelligent entities, like the kind imagined by science fiction writers and (some) AI researchers, alike? To clarify, there are no such systems. "AI" is the name of a research field, not any ability that characterises a class of systems currently known. This suffices to explain why there is, indeed "no AI getting stuck inot a loop by a tricky question". Because there is "no AI" at all, certainly not of the kind that can understand a "tricky question" sufficiently well to stumble on the paradox inside it. For example, GPT-3 has no ability to process "this sentence is false" in such a way as to decide its truth. AlphaGo is not capable of processing language at all, it is only capable of playing board games and it isn't even capable of playing board games by reasoning, only by search. AlphaGo searches a game tree structured as a directed graph, without loops so it's hard to see how it could get stuck on recursive paradoxes anyway. In general, such systems as exist today do not have the mathematical properties of the formal systems described by Gödel, Church and Turing. They don't even have memories. So they are, let's say immune to incompleteness, because they're not even incomplete.
simiones 5y ago
It's important though to note that we know of no problem so far that a human mind can solve that couldn't be solved by a Turing Machine. Godel's incompleteness theorems may very well apply to human minds as well, and so far this seems more likely than not (though a lot of human thinking is actually inconsistent, so perhaps it falls to the other side of the incomplete/inconsistent "choice" than formal systems).
- YeGoblynQueenne 5y ago
  Well... maybe human minds are themselves as limited as Turing machines? In that case we may never be able to create a machine that can overcome our, and Turing machines', limitations.
  - simiones 5y ago
    That is exactly what I personally believe.

acuozzo 5y ago

If your AI uses a classical computer, then everything it's doing is reducible to the Boolean algebra of its component logic gates. All of the training you've done on the GPU; all of the coordination done by the CPU; everything… it's all one (absurdly long) boolean expression. Like all algebraic structures, Boolean algebra is built from an initial set of axioms. Under Gödel's incompleteness theorem, it is therefore true that if Boolean algebra isn't inherently broken (inconsistent), then we can craft questions that cannot be answered using Boolean algebra alone, but this is all your classical computer is capable of doing! Now, if you're training AI using an analog system or a non-classical computer such as a quantum computer, then this opens up a totally different discussion.

chakhs 5y ago
Isn't his theorem proving that any mathematical system will be either incomplete or inconsistent ? And quantum computing is still a mathematical system so the same applies ?
- acuozzo 5y ago
  Yes, but I didn't cite QC as an exception to the rule. I only mentioned it because it's governed by a different set of axioms and would result in a different discussion.
visarga 5y ago
> we can craft questions that cannot be answered using Boolean algebra alone Sure, that's trivial, the travelling salesman problem for example can't be solved exactly, but approximative methods come very close. Given that brains are pattern recognition machines generating probabilities we're already in the approximative regime. Nothing is certain, even science has its revisions. So does it matter if we can only approximate? For living things the main thing that matters is life, self reproduction, not exactness. As long as they reproduce they are still valid, with all imperfections and approximations. I think the only questions that matter are those related to life, there are plenty of uncomputable things outside self reproduction. This is for biological agents, an AI would be using evolutionary methods to reproduce their digital genes instead.