It's not necessarily an either/or situation. Maybe this universe has started a few billions of years ago in a Boltzmann-like event, but since then it evolves, uhm, just like we think it does.
The analogy of the monkeys with typewriters is misleading. The laws of physics are local: what happens next does depend on what happens now; that's unlike the monkey with the typewriter where the following letter is completely independent on the previous part of the book. If some random process would create a brain, in a body, in a room, then even if the room is immediately destroyed at the speed of light, still, during those few microseconds until the destruction reaches the brain, the brain would operate logically.
On the other hand, random processes creating the brain in the body in the room are much less likely than random processes creating only the brain, or only parts of the brain. So this requires some more though, and I am too tired now to make it.
But my point is that if you are randomly created exactly in this moment, you don't have a reason to trust your reason... but if you were created a while ago, and your reason had some time to work, that's not the same situation. In the extreme situation, if the universe was created randomly billions of years ago and then we have evolved lawfully, that's business as usual: the details of random creation of the universe long ago should not be relevant for our reasoning about our reason now.
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[Please read the OP before voting. Special voting rules apply.]
Feminism is a good thing. Privilege is real. Scott Alexander is extremely uncharitable towards feminism over at SSC.
Do you mind telling me how you think he's being uncharitable? I agree mostly with your first two statements. (If you don't want to put it on this public forum because hot debated topic etc I'd appreciate it if you could PM; I won't take you down the 'let's argue feminism' rabbit-hole.)
(I've always wondered if there was a way to rebut him, but I don't know enough of the relevant sciences to try and construct an argument myself, except in syllogistic form. And even then, it seems his statements on feminists are correct.)