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:
You do not need to rot13 anything about HP:MoR or the original Harry Potter series unless you are posting insider information from Eliezer Yudkowsky which is not supposed to be publicly available (which includes public statements by Eliezer that have been retracted).
If there is evidence for X in MOR and/or canon then it's fine to post about X without rot13, even if you also have heard privately from Eliezer that X is true. But you should not post that "Eliezer said X is true" unless you use rot13.
I think we may have something of a clash of backgrounds here. The reason I'm inclined to take the real continuum seriously is that there are numerous physical quantities that seem to be made of real or complex numbers. The reason I take mathematical induction seriously is that it looks like you might always be able to add one minute to the total number of minutes passed. The reason I take second-order logic seriously is that it lets me pin down a single mathematical referent that I'm comparing to the realities of space and time.
The reason I'm not inclined to take the least uncountable ordinal seriously is because, occupying as it does a position above the Church-Kleene ordinal and all possible hypercomputational generalizations thereof, it feels like talking about the collection of all collections - the supremum of an indefinitely extensible quality that shouldn't have a supremum any more than I could talk about a mathematical object that is the supremum of all the models a first-order set theory can have. If set theory makes the apparent continuum from physics collide with this first uncountable ordinal, my inclination is to distrust set theory.
How can you say this after having read this thread?
If you believe in second-order model theory, then you believe in set theory. (However, by limiting it to second order over the natural numbers, without going on to third order, you are not obligated to believe in uncountable ordinals.)
ETA: It is very imprecise to compare second-order model theory and set theory like this. Already model theory ... (read more)