I think David Hume said something more or less like this when discussing the likelihood of miracles; that if you witnessed a miracle, you ought to conclude you were insane.
I am not sure I buy into this. For one thing, I see a problem with falsifiability. If there is nothing that I could see to convince me that magic might work, I am not objecting to the reality of magic on rational grounds, but as a sort of knee-jerk. It's like the doubleplus loony creationist types who think the devil planted archaeopteryx.
There are reasons I think magic in the Harry Potter sense is not true, reasons that could be argued against (e.g., show me a plausible medium for magic to be carried in). I don't think it would be very rational to make it sort of... axiomatic that magic is false. That seems to in fact be the attitude Eliezer is criticizing in the character of Harry's father.
So yeah, some probability mass goes to the "hallucination/insane" hypothesis, but not very much. Most goes to the "I don't know what's going on here at all, but she did just apparently turn into a cat" hypothesis.
Miracles are one-time events, whereas magic spells are repeatable (in every fictional universe I've seen, anyway).
Update: Please post new comments in the latest HPMOR discussion thread, now in the discussion section, since this thread and its first few successors have grown unwieldy (direct links: two, three, four, five, six, seven).
As many of you already know, Eliezer Yudkowsky is writing a Harry Potter fanfic, Harry Potter and the Methods of Rationality, starring a rationalist Harry Potter with ambitions to transform the world by bringing the rationalist/scientific method to magic. But of course a more powerful Potter requires a more challenging wizarding world, and ... well, you can see for yourself how that plays out.
This thread is for discussion of anything related to the story, including insights, confusions, questions, speculation, jokes, discussion of rationality issues raised in the story, attempts at fanfic spinoffs, comments about related fanfictions, and meta-discussion about the fact that Eliezer Yudkowsky is writing Harry Potter fan-fiction (presumably as a means of raising the sanity waterline).
I'm making this a top-level post to create a centralized location for that discussion, since I'm guessing people have things to say (I know I do) and there isn't a great place to put them. fanfiction.net has a different set of users (plus no threading or karma), the main discussion here has been in an old open thread which has petered out and is already near the unwieldy size that would call for a top-level post, and we've had discussions come up in a few other places. So let's have that discussion here.
Comments here will obviously be full of spoilers, and I don't think it makes sense to rot13 the whole thread, so consider this a spoiler warning: this thread contains unrot13'd spoilers for Harry Potter and the Methods of Rationality up to the current chapter and for the original Harry Potter series. Please continue to use rot13 for spoilers to other works of fiction, or if you have insider knowledge of future chapters of Harry Potter and the Methods of Rationality.
A suggestion: mention at the top of your comment which chapter you're commenting on, or what chapter you're up to, so that people can understand the context of your comment even after more chapters have been posted. This can also help people avoid reading spoilers for a new chapter before they realize that there is a new chapter.