How could you recognize a halting oracle if you saw one?
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Replying to @ReferentOfSelf
You can't, since there are infinitely many things to check. In fact, you can't even expose all the fake oracles as fake.
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Replying to @ModelOfTheory
what even is a halting oracle then if we can't in principle experience one? They seem to be formally useful...
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Replying to @ReferentOfSelf @ModelOfTheory
in particular, there is Post's theorem, and sentences with more than one type of quantifier seem meaningful
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Replying to @ReferentOfSelf
There is a vast difference between meaningful and computable.
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Replying to @ModelOfTheory @ReferentOfSelf
And keep in mind that you asked how to perform an unreasonably difficult task.
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Replying to @ModelOfTheory @ReferentOfSelf
How could you recognize an infinite string of "1"s if you saw one? You can't, because there could always be a 0 later.
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In Cantor space, singleton sets are not open, and hence cannot be effectively open.
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