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> all computational systems are axiomatic systems Whatever gave you that idea?
by 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 agoIf programs are not axiomatic systems, then they cannot learn, period. Only ones that have consistent axioms have a hope of learning, and even then it is severely limited.
- yters 9y agoInconsistent axioms can provide a valid proof of Kolmogorov complexity, but not a sound one. Thinking a false statement is true is not learning.