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>> (For example, both these explanations neatly omit the fact that
>> Godel's theorum only applies to "sufficiently powerful systems".)
>
> Yes, except "sufficiently powerful" includes "anything that can do
> integer arithmetic." And Godel indeed does apply to insufficiently
> powerful systems because they can't, by definition, prove everything
> that is true.
I can't remember which article it was, but I was reading earlier today
about some system or other, and there was a remark about "there exists
an algorithm which can prove or disprove any possible statement in this
language. This does not contradict Godel since this language is
insufficiently powerful." (No, I can't remember what the language was...)
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