but I don’t need to be able to define fire to be able to point out something that definitely isn’t on fire!
I guess I can see that. I just don’t think that e.g. Mike Johnson would consider his argument refuted based on the post; I think he’d argue that the type of problems illustrated by the popcorn thought experiment are in fact hard (and, according to him, probably unsolvable). And I’d probably still invoke the thought experiment myself, too. Basically I continue to think they make a valid point, hence are not “refuted”. (Maybe I’m being nit-picky? But I think the standards for claiming to have refuted sth should be pretty high.)
Yeah, perhaps refuting is too strong given that the central claim is that we can’t know what is and is not doing computation—which I think is wrong, but requires a more nuanced discussion. However, the narrow claims they made inter-alia were strong enough to refute, specifically by showing that their claims are equivalent to saying the integers are doing arbitrary computation—when making the claim itself requires the computation to take place elsewhere!
I guess I can see that. I just don’t think that e.g. Mike Johnson would consider his argument refuted based on the post; I think he’d argue that the type of problems illustrated by the popcorn thought experiment are in fact hard (and, according to him, probably unsolvable). And I’d probably still invoke the thought experiment myself, too. Basically I continue to think they make a valid point, hence are not “refuted”. (Maybe I’m being nit-picky? But I think the standards for claiming to have refuted sth should be pretty high.)
Yeah, perhaps refuting is too strong given that the central claim is that we can’t know what is and is not doing computation—which I think is wrong, but requires a more nuanced discussion. However, the narrow claims they made inter-alia were strong enough to refute, specifically by showing that their claims are equivalent to saying the integers are doing arbitrary computation—when making the claim itself requires the computation to take place elsewhere!