Any examples of programs which, as of our understanding today, have roughly 1:1 odds of halting? (No random numbers allowed duh)
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Instantiating the halting prob. can be how you *prove* undecidability in probs of interest for other reasons; I've seen that.
in those cases I always feel let down because the halting problem usually isn't a "pragmatic" usage of a system
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yes, not all sentences in first-order logic are decidable, but I'm not interested in using any old sentence, just useful ones
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This line of reasoning seems wrong to me. Do you have reason to think you're interested in a subclass that's decidable?
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One practical example is that you cannot write a truly optimal compiler. https://en.wikipedia.org/wiki/Full_employment_theorem …
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Although you may think that cases to worry about are rather pathological.
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