However, when arguing about what philosophically sophisticated people are going to think, we're both naturally inclined to think that they'll agree with ourselves, so our impressions about that prove nothing.
I'm not sure about that. You and komponisto seem to be using 'philosophically sophisticated' to contrast with Platonism.
Yes, which agrees with my complaint quoted above. Neither of us is a Platonist, so we both assume that philosophically sophisticated people won't be Platonists, although we derive different things thereafter.
showing of your intelligence by providing convincing arguments for a position that violates common sense. In this case arguing that mathematical statements don't have inherent truth value.
I'm certainly not trying to show off my intelligence. I just think that the idea of inherent truth value for abstract statements about completed infinities violates common sense!
I just think that the idea of inherent truth value for abstract statements about completed infinities violates common sense!
If that's so, what accounts for your intuition that ZF and other systems for reasoning about completed infinities are consistent?
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: