I found this chapter a bit hard to parse as a whole—there were a bunch of individual arguments against modesty, but I didn’t come away feeling their interconnectedness. This might just be a personal quirk, and I will read it again, because I really appreciated many of the different sections e.g. the specific examples of when to actually Auman (with Salamon and Bostrom) that helped me understand how to use the agreement theorem. I also really liked the recommendation to spend most of your time on the object level, a little time on the meta, and much less on the meta-meta. As usual the writing quality is also really high, and so for these reasons I’ve promoted it to Featured.
I actually wasn’t much of a fan of the reductios section—I feel an intuition that I expect mathematicians who only accept constructivist proofs feel, in that I have a gut level feel of ‘wastefulness’ in spending time thinking about epistemology that isn’t about following good reasoning, but is just about finding technical disproofs of possible reasoning moves, that don’t inform why the arguments for the epistemic move are false.
I found this chapter a bit hard to parse as a whole—there were a bunch of individual arguments against modesty, but I didn’t come away feeling their interconnectedness. This might just be a personal quirk, and I will read it again, because I really appreciated many of the different sections e.g. the specific examples of when to actually Auman (with Salamon and Bostrom) that helped me understand how to use the agreement theorem. I also really liked the recommendation to spend most of your time on the object level, a little time on the meta, and much less on the meta-meta. As usual the writing quality is also really high, and so for these reasons I’ve promoted it to Featured.
I actually wasn’t much of a fan of the reductios section—I feel an intuition that I expect mathematicians who only accept constructivist proofs feel, in that I have a gut level feel of ‘wastefulness’ in spending time thinking about epistemology that isn’t about following good reasoning, but is just about finding technical disproofs of possible reasoning moves, that don’t inform why the arguments for the epistemic move are false.