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dlthomas comments on What independence between ZFC and P vs NP would imply - Less Wrong Discussion
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Yes, but they can confirm that some machines will halt, without observing that they have halted, which seemed to be what was asked for. Any such approach must of course say "I don't know" (or itself fail to halt) in some cases.
My apologies, I was imprecise in my original comment. I was trying to get at the fact that "whether Turing machine M halts" is not actually a concrete question, as had been claimed above (I was assuming that the reason it was presumed to be concrete is because you can just watch the machine and it either halts or doesn't, and my point was that you can't actually just watch a machine to see if it will halt).