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Doesn't Chaitin's incompleteness theorem mean AI cannot learn? All axiomatic systems have a fairly low threshold past which they cannot identify random bitstri
by yters 9y ago
Doesn't Chaitin's incompleteness theorem mean AI cannot learn? All axiomatic systems have a fairly low threshold past which they cannot identify random bitstrings, and all computational systems are axiomatic systems.
- unlikelymordant 9y agoIf true, wouldn't that imply humans can't learn?
- majewsky 9y agoThere is always the possibility that the human mind is more than the collective behavior of a bunch of neurons. It is conceivable that part of the human mind occupies some sort of astral plane like many people believe. I'm not saying that it is. Science does not concern themselves with such theories (yet) because of Alder's Razor ("what cannot be settled by experiment is not worth debating") [1]. [1] https://en.m.wikipedia.org/wiki/Mike_Alder https://en.m.wikipedia.org/wiki/Mike_Alder
- yters 9y agoIf AI cannot learn and humans can, then this is experimental confirmation that humans are not AI, and the matter is settled. Therefore, the issue is worth debating. I submit that AI cannot learn, per my previous comment. Furthermore, I submit that humans can learn, evidence being school, science and math. Ergo, humans are not AI. Matter settled, debate over.
- majewsky 9y agoNot at all. 1. Current AI is a miniscule subset of the set of all AI, so you need to argue why the observation generalizes to all possible AI. 2. The statement "AI cannot learn" is too ambiguous because you fail to define "learn".
- yters 9y ago1. My statement applies to any computational approach to AI. If AI is possible it needs a halting oracle. 2. Learning is being able to recognize ever increasing levels of complexity. All axiomatic systems have a complexity recognition limit.
- yters 9y agoDown votes without counter argument means I'm right and you can't handle it.
- ScottBurson 9y ago> all computational systems are axiomatic systems Whatever gave you that idea?
- yters 9y agoThey cannot be more capable of proving Kolmogorov complexity than an axiomatic system.
- yters 9y agoAlso the Curry-Howard correspondence.
- red75prime 9y agoCitation from https://en.wikibooks.org/wiki/Haskell/The_Curry%E2%80%93Howard_isomorphism https://en.wikibooks.org/wiki/Haskell/The_Curry%E2%80%93Howa... "[...] we can prove any theorem using Haskell types because every type is inhabited. Therefore, Haskell's type system actually corresponds to an inconsistent logic system." Thus Haskell programs in general don't correspond to a consistent axiomatic system, which provides counterexample to your statement. Rebuttal complete.
- yters 9y agoInconsistent systems cannot prove Kolmogorov complexity limits. What's your point?
- red75prime 9y agoInconsistent axiomatic systems can prove anything. Thus either Haskell programs can prove the limits (and prove the opposite statement, as they are inconsistent) or they aren't axiomatic system as you mean it. Both possibilities contradict your statement: > Chaitin's incompleteness theorem mean AI cannot learn
- yters 9y ago
- cassowary 9y agoIf this is true it isn't apparent to me. You're stating it as if it's received wisdom. Could you clarify?
- yters 9y agoIt is not received wisdom. My argument is human learning entails recognizing an ever increasing amount of complexity, given infinite time, resources and motivation we can learn forever. But all axiomatic systems have a complexity limit, per Chaitin's incompleteness theorem, so cannot learn forever. Neither can a system add to its axioms. Therefore, human learning is beyond anything an axiomatic systems can do.