Harry Potter and the Methods of Rationality discussion thread, part 8

Unnamed

14 Harry Potter and the Methods of Rationality discussion thread, part 8

by Unnamed

25th Aug 2011

1 min read

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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Eliezer Yudkowsky which is not supposed to be publicly available (which includes public statements by Eliezer that have been retracted).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.

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Harry Potter and the Methods of Rationality discussion thread, part 8 — LessWrong

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[anonymous]15y40

All the axioms of ZF seem reasonable.

The axiom of foundation seems pretty ad hoc to me. It's there to patch Russell's paradox. I see no reason not to expect further paradoxes.

We arrived at the axiom of infinity from a finite amount of experience, which seems troubling to me.

This is an extremely finite, weird statement.

It's a very cool construction, but it's a finite one that we can verify by hand or with computer assistance. Of the things that ZF claims exist, some of them have this "verifiability" property and some don't. At the very least don't you agree that's a crucial distinction, and that we ought to be strictly less skeptical of constructible, computable, verifiable things than of things like uncountable ordinals?

JoshuaZ15y30

Also, there's another respect in which foundation doesn't impact Russell issues at all. Whether one accepts foundation, anti-foundation or no mention of foundation, one can still get very Russellish issues if one is allowed to form the set A of all well-founded sets. Simply ask if A is well-founded or not. This should demonstrate that morally speaking, foundation concerns are only marginally connected to Russell concerns.

1JoshuaZ15y

Also one other remark: Foundation isn't there to repair any Russel issues. You can get as a theorem that Russell's set doesn't exist using the other axioms because you obtain a contradiction. Foundation is more that some people have an intuition that sets shouldn't be able to contain themselves and that together with not wanting sets that smell like Russell's set caused it to be thrown in.

3JoshuaZ15y

Sure foundation is by far the most ad-hoc axiom. But it is also one of the one's that is easiest to see doesn't generally matter. For pretty much any natural theorem if a proof uses foundation then there's a version of the theorem without it. Since not-well founded sets don't fit most of out intuition for sets as things like boxes that's not an issue. None of the serious apparent paradoxical properties go away if you remove foundation. [...] Yes, certainly but by how much? If our intuition can go this drastically wrong on small finite objects why should I trust my intuition on objects that are even further removed from my everyday experience? I mean it isn't like I need 30 or 40 sided dice to pull this off. In fact you can actually make much smaller than 6 sided dice that are non-transitive. Working out the minimum number of sides (assuming that each die in the set doesn't need to have the same number of sides) is a nice exercise that helps one understand what is going on.

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