Yudkowsky has written about it:

(...) In standard metaethical terms, we have managed to rescue 'moral cognitivism' (statements about rightness have truth-values) and 'moral realism' (there is a fact of the matter out there about how right something is). We have not however managed to rescue the pretheoretic intuition underlying 'moral internalism' (...)

Replace in the post "morality" with "rationality" and you get a reductio ad absurdum.

I made basically the same proposal here, but phrased as a task of translating between a long alien message and human languages: https://www.lesswrong.com/posts/J3zA3T9RTLkKYNgjw/is-llm-translation-without-rosetta-stone-possible See also the comments, which contain a reference to a paper with a related approach on unsupervised machine translation. Also this comment echoes your post:

I think this is a really interesting question since it seems like it should neatly split the "LLMs are just next token predictors" crows from the "LLMs actually display understanding" crowd.

Arguably, "basic logical principles" are those that are true in natural language. Otherwise nothing stops us from considering absurd logical systems where "true and true" is false, or the like. Likewise, "one plus one is two" seems to be a "basic mathematical principle" in natural language. Any axiomatization which produces "one plus one is three" can be dismissed on grounds of contradicting the meanings of terms like "one" or "plus" in natural language.

The trouble with set theory is that, unlike logic or arithmetic, it often doesn't involve strong intuitions from natural language. Sets are a fairly artificial concept compared to natural language collections (empty sets, for example, can produce arbitrary nestings), especially when it comes to infinite sets.

Interesting, I really hope TMS gains more acceptance. By the way, according to studies, ECT (the precursor of TMS) is even more effective, though it does have more side effects, due to the required anesthesia, and it is gatekept even more strongly. In my youth I suffered from depression for several years, and all of this likely would have been avoidable with a few ECT sessions (TMS wasn't a thing yet), if it wasn't for the medical system's irrational bias in favor of exclusively using SSRIs and CBT. I think this happens because most medical staff have no idea how terrible depression can be, so they don't get the sense of urgency they'd get from more visible diseases.

Guys, for this specific case you really have to say what OS you are using. Otherwise you might be totally talking past each other.

(Font-size didn't change on any OS, but the font itself changed from Calibri to Gill Sans on Windows. Gill Sans has a slightly smaller x-height so probably looks a bit smaller.)

I tested it on Android, it's the same for both Firefox and Chrome. The font looks significantly smaller than the old font, likely due to the smaller x-height you mentioned. Could the font size of the comments be increased a bit so that it appears visually about as large as the old one? Currently I find it too small to read comfortably. (Subjective font size is often different from the standard font size measure. E.g. Verdana appears a lot larger than Arial at the same standard "size".)

(A general note: some people are short sighted and wear glasses, and the more short-sighted you are, the stronger the glasses contract your field of view to a smaller area. So things that may appear as an acceptable size for people who aren't particularly short-sighted, may appear too small for more short-sighted people.)

Did the font size in comments change? It does seem quite small now...

Of course for a "real" prisoners dilemma any form of coordination is ruled out from the start. But in real world instances, coordination can sometimes be introduced into systems that previously were prisoner's dilemmas. That's what I mean with "solving" a prisoner's dilemma. Making the dilemma go away.

The thing I'm pointing out here is that "coordination" is a very unspecific term, and one concrete form of coordination is being able to vote for cooperation. (Example: voting on a climate change bill instead of trying to minimize your personal carbon footprint, which would make you personally significantly worse of with hardly any benefit on the whole, which is why you would defect but vote on cooperate.) I think voting is usually not appreciated as a method of coordination, only as a method of choosing the most popular policy/party, which doesn't need to involve solving a prisoner's dilemma.

Some issues that seem to be controversial are really taboo, or arise due to an underlying taboo. For this case I have two general recommendations here.

Related to this: Some opinions may be often expressed because of virtue signalling; e.g. because the opposite is taboo, or for other reasons. Hearing such opinions doesn't provide significant testimonial evidence for their truth, since people don't hold them because of evidence they encountered, but because they feel virtuous. Though it is not easy to recognize why particular opinions are being expressed, whether they are motivated by signalling or not.

Solutions to a prisoner's dilemma are typically assumed to involve "coordination" in some sense. But what kinds of mechanism are appropriate examples for coordination? For an N-person prisoner's dilemma, one form of coordination is implementing voting. Say, everyone is forced to cooperate when the majority votes "cooperate". Nobody has a selfish interest to cooperate, but everyone has a selfish interest to vote for "cooperate".

This is interesting because economists often see voting as irrational for decision theoretic reasons. But from the game theoretic perspective above, it appears to be rational. This is probably not a new insight, but I haven't seen voting being portrayed as a type of solution to N-person prisoner's dilemmas.