Isaac Newton's argument for intelligent design:

Were all the planets as swift as Mercury or as slow as Saturn or his satellites; or were the several velocities otherwise much greater or less than they are (as they might have been had they arose from any other cause than their gravities); or had the distances from the centers about which they move been greater or less than they are (as they might have been had they arose from any other cause than their gravities); or had the quantity of matter in the sun or in Saturn, Jupiter, and the earth (and by consequence their gravitating power) been greater or less than it is; the primary planets could not have revolved about the sun nor the secondary ones about Saturn, Jupiter, and the earth, in concentric circles as they do, but would have moved in hyperbolas or parabolas or in ellipses very eccentric. To make this system, therefore, with all its motions, required a cause which understood and compared together the quantities of matter in the several bodies of the sun and planets and the gravitating powers resulting from thence.... And to compare and adjust all these things together in so great a variety of bodies, argues that cause to be, not blind and fortuitous, but very well skilled in mechanics and geometry.

-- Letter to Richard Bentley

He gave Harry instructions for what to do in the event that they encountered an auror, so clearly he'd at least anticipated the possibility that a duel would happen at some point during the prison break. We're also told that Harry's maneuver with the mirror is something he'd "practiced...in the Chaos Legion," so Quirrell should also have anticipated that Harry would be watching the duel if/when it happened. At the very least, he knows that Harry will be able to hear it.

So. The duel was not outside Quirrell's plan. Therefore his actions during the duel must also have been deliberate and have been part of the plan. If those actions seem to foil the plan, then...it was never the real plan. And the real plan must somehow be furthered by Quirrell's actions. So the only way I can make sense of Quirrell's behavior is to think that he was deliberately trying to provoke the reaction he got from Harry.

Why? What does it gain him? Well, it leaves Harry exposed to Dementors. And coincidentally enough, this is the second time that Quirrell's actions have left Harry exposed to Dementors. At which point I decide that it's not coincidence at all. So my theory is really just trying to answer the question, "Why does Quirrell want Harry exposed to Dementors?"

Rule I

We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.

To this purpose the philosophers say that Nature does nothing in vain, and more is in vain when less will serve; for Nature is pleased with simplicity, and affects not the pomp of superfluous causes.

Rule II

Therefore to the same natural effects we must, as far as possible, assign the same causes.

As to respiration in a man and in a beast; the descent of stones in Europe and in America; the light of our culinary fire and of the sun; the reflection of light in the earth, and in the planets.

Rule III

The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever.

For since the qualities of bodies are only known to us by experiments, we are to hold for universal all such as universally agree with experiments; and such as are not liable to diminution can never be quite taken away. We are certainly not to relinquish the evidence for the sake of dreams and vain fictions of our own devising; nor are we to recede from the analogy of Nature, which is wont to be simple, and always consonant to itself. . .

Rule IV

In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions.

This rule we must follow, that the argument of induction may not be evaded by hypotheses.

Isaac Newton, Philosophiae naturalis: Rules of Reasoning in Philosophy

Set Theory and the Continuum Hypothesis by Paul Cohen is good, and starts from a pretty low level if I recall, but you'll want experience in formal reasoning before reading through it. Do you have any experience with formal math?

We can't even specify most of our top-node values with any kind of precision or accuracy -- why should we care if (a) they change or (b) a world that we personally do not live in becomes optimized for other values?

Where you don't have any preference, you have indifference, and you are not indifferent all around. There is plenty of content to your values. Uncertainty and indifference are no foes to accuracy, they can be captured as precisely as any other concept.

Whether "you don't personally live" in the future is one property of the future to consider: would you like that property to hold? An uncaring future won't have you living in it, but a future that holds your values will try to arrange something at least as good, or rather much better.

Also see Belief in the Implied Invisible. What you can't observe is still there, and still has moral weight.

One of the systematic changes in MoR is that things which are sufficiently powerful are artifacts, and things which are artifacts are sufficiently powerful: The Marauder's Map was originally devised by Slytherin as part of the creation of Hogwarts and only slightly twisted by the Marauders (Ch. 25), and the Cloak of Invisibility is now in a class of its own compared to standard invisibility cloaks or Disillusionment (Ch. 54).

Rowling, of course, wrote that thing with Moody's eye before she decided the Cloak of Invisibility was a major artifact. So if Moody's eye can still see through it in MoR, it's going to be because either Moody's eye is also a major artifact, or, more likely, a specialized artifact devoted to seeing through invisibility (a specialized, specific artifact can defeat a generally more powerful artifact if the specialization is narrow enough).

Chapter 51 (emphasis added):

As Professor Quirrell stood up from where he'd bent over by the pouch, and put away his wand, his wand happened to point in Harry's direction, and there was a brief crawling sensation on Harry's chest near where the Time-Turner lay, like something creepy had passed very close by without touching him.

Chapter 54:

"Sorry," whispered the eleven-year-old boy, "here," and he held out the wand toward Bahry.

Bahry barely stopped himself from snarling at the traumatized boy who'd just saved his life. Instead he overrode the impulse with a sigh, and just stretched out a hand to take the wand. "Look, son, you're really not supposed to point a wand at -"

The wand's end twisted lightly beneath Bahry's hand just as the boy whispered, "Somnium."

Seems to indicate that Quirrell casted some kind of spell on Harry at that point in Chapter 51.

Anyone have any ideas as to what this is about?

Slowly, slowly, as Professor Quirrell had instructed, the pouch began to float toward Harry, who waited alert for any sign the pouch was opening, in which case Harry was to use the Hover Charm to propel it away from him as fast as possible.

Why does he need to float the pouch about at all? Why not just pick it up?

Re: 54:

Harry can still salvage the situation somewhat, if I understand the ending. They're going to know Bella escaped, but Harry can still put Quirrel in his pouch (since he's in snake form) and hide with Bella under the invisibility cloak, right? Or can Aurors see through the cloak in HP:MOR? I think in canon nobody can penetrate the Cloak's invisibility.

I noticed something odd in chapter 17, which seems relevant:

Harry was rather confused. "But this could be important, yesterday I got this sudden sense of doom when -"

"Mr. Potter! I have a sense of doom as well! And my sense of doom is suggesting that you must not finish that sentence!" ... "This isn't like you!" Harry burst out. "I'm sorry but that just seems unbelievably irresponsible! From what I've heard there's some kind of jinx on the Defense position, and if you already know something's going to go wrong, I'd think you'd all be on your toes -" ... "I see," Harry said slowly, taking it all in. "So in other words, whatever's wrong with Professor Quirrell, you desperately don't want to know about it until the end of the school year. And since it's currently September, he could assassinate the Prime Minister on live television and get away with it so far as you're concerned."

Professor McGonagall gazed at him unblinkingly. "I am certain that I could never be heard endorsing such a statement, Mr. Potter. At Hogwarts we strive to be proactive with respect to anything that threatens the educational attainment of our students." ... "Oh, I doubt that, Mr. Potter. I doubt that very much." Professor McGonagall leaned forward, her face tightening again. "Since you and I have already discussed matters far more sensitive than these, I shall speak frankly. You, and you alone, have reported this mysterious sense of doom. You, and you alone, are a chaos magnet the likes of which I have never seen. After our little shopping trip to Diagon Alley, and then the Sorting Hat, and then today's little episode, I can well foresee that I am fated to sit in the Headmaster's office and hear some hilarious tale about Professor Quirrell in which you and you alone play a starring role, after which there will be no choice but to fire him. I am already resigned to it, Mr. Potter. And if this sad event takes place any earlier than the Ides of May, I will string you up by the gates of Hogwarts with your own intestines and pour fire beetles into your nose. Now do you understand me completely?"

As Harry observes, this exchange is extremely out of character for McGonagall. Telling Harry not to voice his concerns about Quirrel, I could believe; but cutting him off mid-sentence, and them making such a graphic, violent threat if he does, I can not. It is so out of character, in fact, that I think it must be a symptom of being Imperiused.

We know that Voldemort used to use Imperius quite a bit, and the only real reasons he might stop would be if someone figured out how to detect it (which hasn't happened), or if his new form didn't have the power. One Imperiused person rules out the second possibility, so if if Quirrelmort put an imperius on McGonagall, he has almost certainly used it elsewhere too.

Which brings us to Harry's attempted breakout of Bellatrix. Breaking in to Azkaban to rescue Bellatrix Black, I could just barely believe. Pretending to be Voldemort while doing so, however, pushes credibility too far. From Chapter 52 to Chapter 54, Harry is Imperiused. There are just too many things stupid and suspicious about the plan to believe that Harry overlooked all of them.

And that brings us to the question of what Imperius actually does. And this, I think, explains the chapter title, "The Stanford Prison Experiment", which otherwise seems not to fit at all. The conclusion of that famous experiment was that if you give someone a role - even a fake role, like a prison guard over subjects in a psychology experiment who are technically free to leave - then they adopt it as part of their identity, including the evil parts, and become blind to the wrong things they do as part of that identity. So perhaps that's what Imperius does: it assigns its target a particular role, which their mind will bend to accommodate. That would also explain why the title was redacted for part 1, which takes place before the Imperius curse was cast.

Here are some abnormalities in Harry's mind:

This was it, this was the day and the moment when Harry started acting the part.

And in another part of him, like he was just letting another part of his mind carry out a habit without paying much attention to it...

Professor Quirrell had instructed Harry, calmly and precisely, how he was to act in Bellatrix's presence; how to form the pretense he would maintain in his mind.

The only problem with this theory, is that Harry believes that Quirrel can never use magic on him. His Patronus and Quirrel's Aveda Kevadera certainly didn't interact well, and there seems to be an issue if they touch. But the theory that they can never use magic on each other, seems to have appeared from nowhere; there is no evidence for it whatsoever, except the sense of doom. Perhaps that idea was planted, to make the idea that Harry was Imperiused seem less plausible?

When Harry powered up his Patronus, Quirrell was not able to get him to stop verbally. This suggests that Harry is not Imperiused.