And anyways, I suspect the idea that "rationality comes prior to experience" is almost certainly true, albeit in a weak, tho profound, sense. For one, nothing can learn, i.e. form or update beliefs or theories, without a pre-existing algorithm to do so.
> ... That's not the way the 'rationalists' are using it, and what's more, the way they are using it is kinda crude, even if we ignore the fact it displays a kind of illiteracy, or at least, a disinterest in the history of thought, to re-use a really common term in a totally unrelated way.
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> That's also what comes across from the stuff they write. What I've read is clever, well written, well thought out, but also profoundly ignorant of the tradition of thinking about the topics they're interested in. You can't help but be crude if you just try a naive response, without first looking at how other people have addressed the problem at hand. So it comes across as the philosophical equivalent of that guy you met once who's convinced he has invented a new kind of maths without the number zero, because 'zero doesn't exist'. It might have been an interesting debate 2000 years ago, but things have moved on.
The rationalist community is a loose agglomeration of people interested in a bunch of different topics, with the kind of binding focus on forming or acquiring (more) accurate beliefs and acting (more) effectively in the real world. There's an incredibility variety and diversity of interests, backgrounds, and knowledge across a huge number of philosophies, schools, academic disciplines, and intellectual pursuits.
It's interesting that you claim that they "[display] a kind of illiteracy" as it seems clear to me, from reading a lot of the work of the members of the rationalist community, that (a) a lot of those members are perfectly aware of philosophical rationalism; (b) the community doesn't ascribe to anything that anyone terms 'rationalism'; and (c) almost everyone rejects philosophical rationalism as being true or useful.
Among the various members of the community, some of whom don't identify as members too, there's a lot of frequent and deep referencing of academic philosophy, so the claim that the community as a whole is unaware of "how other people have addressed the problem at hand" is just flat wrong. But the rationalist community is more like pre-professional science in that almost everyone is an amateur, there's almost no (formal) gatekeeping. So yes, it's absolutely true that there are many people in or interacting the community that are relatively ignorant of lots of different things like your example of someone convinced that they've invented a new school of mathematics.
And besides all of that, there's a lot of utility, to lots of people, particularly the participants, in debating something that you or academic philosophers might be convinced 'everyone' else has moved on from.