I agree that the post isn’t a definition of what computation is—but I don’t need to be able to define fire to be able to point out something that definitely isn’t on fire! So I don’t really understand your claim. I agree that it’s objectively hard to interpret computation, but it’s not at all hard to interpret the fact that the integers are less complex and doing less complex computation than, say, an exponential-time Turing machine—and given the specific arguments being made, neither is a wall or a bag of popcorn. Which, as I just responded to the linked comment, was how I understood the position being taken by Searle, Putnam, and Johnson. (And even this ignores that one implication of the difference in complexity is that the wall / bag of popcorn / whatever is not mappable to arbitrary computations, since the number of steps required for a computation may not be finite!)
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 agree that this wasn’t intended as an introduction to the topic. For that, I will once again recommend Scott Aaronson’s excellent mini-book explaining computational complexity to philosophers.
I agree that the post isn’t a definition of what computation is—but I don’t need to be able to define fire to be able to point out something that definitely isn’t on fire! So I don’t really understand your claim. I agree that it’s objectively hard to interpret computation, but it’s not at all hard to interpret the fact that the integers are less complex and doing less complex computation than, say, an exponential-time Turing machine—and given the specific arguments being made, neither is a wall or a bag of popcorn. Which, as I just responded to the linked comment, was how I understood the position being taken by Searle, Putnam, and Johnson. (And even this ignores that one implication of the difference in complexity is that the wall / bag of popcorn / whatever is not mappable to arbitrary computations, since the number of steps required for a computation may not be finite!)
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!