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Eliezer Yudkowsky which is not supposed to be publicly available (which includes public statements by Eliezer that have been retracted).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.
The existence of the real number line is one thing. The existence of an uncountable ordinal is another. When you consider the hierarchies of uncomputable ordinals to their various Turing degrees that are numbered among the countable ordinals, and that which countable ordinals you can constructively well-order strongly corresponds to the strength of your proof theory and which Turing machines you believe to halt, and when you combine this with the Burali-Forti paradox saying that the predicate "well-ordered" cannot be self-applicable, even though any given collection of well-orderings can be well-ordered...
...I just have trouble believing that there's actually any such thing as an uncountable ordinal out there, because it implies an absolute well-ordering of all the countable well-orderings; it seems to have a superlogical character to it.
Set theory is just a made up bunch of puzzle pieces (axioms) and some rules on how to fit them together (logic) so it's weird to hear you lot talking about "existence" of a set with some property P as something other than whether or not the statement "exists X, P(X)" has a proof or not. I thought Hilbert's finitist approach should have slain Platonism long ago.