Not long ago, I added a tag to LessWrong for the problem of the criterion. Shortly after that its text received an edit claiming it is an open problem. However, I think the problem of the criterion is not really an open problem. Here's why.
Here on LessWrong we say open problems are "the things in a field that haven't yet been figured out". On Wikipedia, an open problem is described as "a known problem which can be accurately stated, and which is assumed to have an objective and verifiable solution, but which has not yet been solved (i.e., no solution for it is known)." By either of these standards, does the problem of the criterion qualify as an open problem?
If our standard is "has it been figured out?", I'd say yes. I think not everyone likes what was figured out, which is a reason to make a bid to claim the problem is open, but not liking the answer should be insufficient reason to make such a claim. After all, I don't exactly like that the solution to the halting problem is that we can't create a general program that can determine if an arbitrary program halts, but so be it, that's the universe we find ourselves in, let's move on. So I think it is with the problem of the criterion: yeah, kinda sucks the kind of truth we can achieve when we restrict ourselves to mathematical thinking can't be achieved everywhere, but that's how the world is, so I guess we'll figure out how to live with it because we already are.
What about if we use Wikipedia's definition of an open problem? The problem of the criterion is certainly "a known problem which can be accurately stated". Is it "assumed to have an objective and verifiable solution"? The whole point of my and other's analysis of the problem is to show that this assumption is unfounded in some way and that no objective and verifiable solution can be found because the question is fundamentally flawed by asking for something impossible. In this way it seems similar to the "complete and consistent problem" or the "momentum and position problem": Gödel's incompleteness theorems and Heisenberg's uncertainty principle respectively show these are problems that don't have "objective and verifiable solutions". In this same way, I and others claim the problem of the criterion is "solved" because we've shown that solving it is impossible.
This is small issue, so why have I bothered to take the time to talk about it? Because I think letting something like calling the problem of the criterion an "open problem" slip by is on par with, say, letting belief in astrology as a causal force slip by: it's bad epistemic hygiene to leave this kind of thing lying around in your mind or in a community and provides a door through which more stuff can enter. So although this may seem a minor point, it's a point worth clarifying in my ongoing project to upgrade the epistemology of the LessWrong community.
If you click through to the problem of the criterion tag page on the date of publication (2022-01-06) you'll notice it still contains the open problem claim. Rather than unilaterally making this edit, I'm publishing this post to see what the response is. Since there's some existing disagreement (I wouldn't call it an open problem and at least one fellow LessWronger would), it's reasonable that I may be mistaken and should at least check with others first. So if you disagree, make the case below and see if you can convince me! Somewhere out of any conversation I hope will fall some compelling evidence that it's worth changing or leaving as is.