Most mathematicians could not state the axioms of ZFC from memory. My suspicion is that AC skepticism is highest among mathematicians who can.
I don't see why this is even relevant, but for what it's worth, I don't particularly share this suspicion: I would expect those who know the axioms from memory to be more philosophically sophisticated (i.e. non-Platonist), and to be more likely to be familiar with technical results such as Gödel's theorem that ZFC is as consistent as ZF.
My own impression is that professed "AC skepticism" (scarequotes because I think it's a not-even-wrong confusion) is most correlated not with interest in logic and foundations, but with working in finitary, discrete, or algebraic areas of mathematics where AC isn't much used.
One piece of evidence that AC skepticism is not low-status is that papers and textbooks will often emphasize when a proof uses AC, or when a result is equivalent to AC. People find such things interesting.
The fact that people find such things interesting is at best extremely weak evidence for the proposition that constructivism and related positions are mainstream. (After all, I find such things interesting!)
As I pointed out in the comment linked to above, there is a difference between dinner-party acknowledgement of constructivism (which is widespread) and actually taking it seriously enough to worry about whether one's results are correct (which would be considered eccentric).
If AC skepticism were not low-status, you would expect to find papers and textbooks actively rejecting AC results, rather than merely mentioning in a remark or footnote that AC is involved. (Such footnotes are for use at dinner parties.)
And also, texts just as frequently do not bother to make apologies of the sort you allude to. A fairly random example I recently noticed was on p.98 of Algebraic Geometry by Hartshorne, where Zorn's Lemma is used without any more apology than an exclamation point at the end of the (parenthetical) sentence.
But what do status considerations have to do with whether Yudkowsky's beliefs and hunches are justified?
It tends to irritate me when people get something wrong which they could easily have gotten right by using a standard human heuristic (such as the "status heuristic", noticing what the prestigious position is).
If AC skepticism were not low-status, you would expect to find papers and textbooks actively rejecting AC results, rather than merely mentioning in a remark or footnote that AC is involved. (Such footnotes are for use at dinner parties.)
Not entirely. If the only known proof for a result assumes choice, then a proof that doesn't use choice will almost certainly be publishable.
...And also, texts just as frequently do not bother to make apologies of the sort you allude to. A fairly random example I recently noticed was on p.98 of Algebraic Geometry by Hart
Update: Discussion has moved on to a new thread.
The hiatus is over with today's publication of chapter 73, and the previous thread is approaching the 500-comment threshold, so let's start a new Harry Potter and the Methods of Rationality discussion thread. This is the place to discuss Eliezer Yudkowsky's Harry Potter fanfic and anything related to it.
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: one, two, three, four, five, six, seven. The fanfiction.net author page is the central location for information about updates and links to HPMOR-related goodies, and AdeleneDawner has kept an archive of Author's Notes.
As a reminder, it's often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: