Righting a Wrong Question

This is one of my all-time favourite posts of yours, Eliezer. I can recognize elements of what you're describing here in my own thinking over the last year or so, but you've made the processes so much more clear.

As I'm writing this, just a few minutes after finishing the post, it's increasingly difficult not to think of this as "obvious all along" and it's getting harder to pin down exactly what in the post that caused me to smile in recognition more than once.

Much of it may have been obvious to me before reading this post as well, but now the verbal imagery needed to clearly explain these things to myself (and hopefully to others) is available. Thank you for these new tools.

I'm sure the meta-physicists will suggest something like the following. How do you know the causal chain you trace is meaningful? That is you are resting our ability to see thing on physics, and our ability to have a valid physics on being able to see things in the world. It is self-reinforcing but requires axioms taken on faith or blind chance to start things off. So is not really the same thing as meta-physics.

My reply would be to say, "Well, it works so far." And then get on with my life, and not worry about it.

``Why do I think I can avoid literary effects and reason directly instead?''

"Why do I think it is guaranteed that I think things for a reason, instead of for no reason at all?"

OK, time to play:

Q: Why am I confused by the question "Do you have free will?"? A: Because I don't know what "free will" really means. Q: Why don't I know what "free will" means? A: Because there is no clear explanation of it using words. It's an intuitive concept. It's a feeling. When I try to think of the details of it, it is like I'm trying to grab slime which slides through my fingers. Q: What is the feeling of "free will"? A: When people talk of "free will" they usually put it thusly. If one has "free will", he is in control of his own actions. If one doesn't have "free will" then it means outside forces like the laws of physics control his actions. Having "free will" feels good because being in control feels better then being controlled. On the other hand, those who have an appreciation for the absolute power of the laws of physics feel the need to bow down to them and acknowledge their status as the ones truly in control. The whole thing is very tribal really. Q: Who is in control, me or the laws of physics? A: Since currently saying [I] is equivalent to saying [a specific PK shaped collection of atoms operating on the laws of physics], then saying "I am in control" is equivalent to saying "a specific PK shaped collection of atoms operating on the laws of physics is in control". The laws of physics are not an outside force apart from me, they are inside me too. Q: Why do people have a tendency to believe their minds are somehow separate from the rest of the universe? A: Ugghhh... I don't know the details well enough to answer that.

Q: Why do I think there is something instead of nothing? A: Because I think I'm experiencing, well, something. Q: Why do I think I'm experiencing something?

A: uh... dang, the urge is overwelming for me to say "Because I actually am experiencing something. That's the plainest fact of all, even though evidence in favor of it seems to be at the moment the least communicable sort of evidence of them all."

argh!

So, I see at least two possibilities here:

Either I'm profoundly confused about something, causing me to seem to think that I can't possibly be experiencing the thought of thinking I'm conscious without, well... experiencing it. (I think I experience the thought that I'm consciouss? But it sure seems like I'm experiencing that thought... argh...) so either way there's some profound confusion going on in my head.

Or I'm confused partly because I'm trying to think of what sort of state of affairs could result in me seeming to think I'm conscious without actually being so (I'm not talking about philosophical zombies here, I mean from the inside), and am confused because it may really be as incoherent an idea as it seems to me.

The question of free will at least "feels" solvable. That it can be broken down into more basic things. These two (why is there something instead of nothing, and what's the nature of consiousness (as in "feels like from the inside"/qualia/etc) are the Langford philosophical basilisk questions. May not have anything to do with the nature of the question itself, but seems to fry my brain any way I bang my head at it. :)

Eliezer Yudkowsky: (can we drop the underscores now?): You did not break the "perception of wearing socks" into understandable steps, as you demanded for the perception of free will. You certainly explained non-confusingly some of the steps, but you left out a very critical step, which is the recognition of socks within the visual input that you receive. That is a very mysterious step indeed, since your cognitive architecture is capable of recognizing socks within an image, even against an arbitrary set of transformations: rotation, blurring, holes in the socks, coloration, etc.

And I know you didn't simply leave out an explanation that exists somewhere, because such understanding would probably mean a solution for the captcha problem. So I would have to say that made the same unacceptable leap that you attacked in the free will example.

What is the phrase 'free will' used to refer to? We cannot even start worrying about whether we need to answer or abolish the question until we understand what the question signifies.

We could ask ourselves "what happens when an immovable object meets an irresistible force?", and recognize that this question must be unasked. The reason why it's not a valid question is that the definitions of those two things turn out to be mutually contradictory once we analyze them down to their constituent parts.

And I know you didn't simply leave out an explanation that exists somewhere, because such understanding would probably mean a solution for the captcha problem.

I think there is a real something for which free will seems like a good word. No, it's not the one true free will, but it's a useful concept. It carves reality at its joints.

Basically, I started thinking about a criminal, say, a thief. He's on trial for stealing a dimond. The prosecutor thinks that he did it of his own free will, and thus should be punished. The defender thinks that he's a pathological cleptomaniac and can't help it. But as most know, people punish crimes mostly to keep them from happening again. So the real debate is whether imprisoning the thief will discourage him.

I realized that when people think of the free will of others, they don't ask whether this person could act differently if he wanted. That's a Wrong Question. The real question is, "Could he act differently if I wanted it? Can he be convinced to do something else, with reason, or threats, or incentives?"

From your own point of view that stands between you and being able to rationally respond to new knowledge makes you less free. This includes shackles, threats, bias, or stupidity. Wealth, health, knowledge make you more free. So for yourself, you can determine how much free will you have by looking at your will and seeing how free it is. Can you, as Eliezer put it, "win"?

I define free will by combining these two definitions. A cleptomaniac is a prisoner of his own body. A man who can be scared into not stealing is free to a degree. A man who can swiftly and perfetly adapt to any situation, whether it prohibits stealing, requires it, or allows it, is almost free. A man becomes truly free when he retains the former abilities, and is allowed to steal, AND has the power to change the situation any way he wants.

Quantum magic isn't free will, it's magic.

"The nice thing about the second question is that it is guaranteed to have a real answer, whether or not there is any such thing as free will."

Who guaranteed this?

The claim that every fact, such as someone's belief, has a definite cause, is a very metaphysical claim that Eliezer has not yet established.

The problem with this blog is that you occasionally say amazingly insightful things but the majority of your posts, like this one, say something blindingly obvious in a painfully verbose way. But then it could be that some of the things that are amazingly insightful to me are blindingly obvious to someone else, and vice versa. Oh well.

I'll give (a few of them) a shot.

"Why do I think I have free will?" There seem to be two categories of things out there in the world: things whose behavior is easily modeled and thus predictable; and things whose internal structure is opaque (to pre-scientific people) and are best predicted by taking an "intensional stance" (beliefs, desires, goals, etc.). So I build a bridge, and put a weight on it, and wonder whether the bridge will fall down. It's pretty clearly the case that there's some limit of weight, and if I'm below that weight -- whether I use feathers or rocks -- the bridge will stay up; otherwise it will collapse. Very simple model, reasonably accurate.

In contrast, if I ask my officemate to borrow his pen, he may or may not give it to me. Trying to predict whether he will is impossible to do precisely, but responds best (for laypeople) to a model with beliefs, goals, memories, etc. Maybe he's usually helpful, and so will give me the pen. Maybe I made fun of his shirt color yesterday, and he remembers, and is angry with me, and so won't.

This "intensional stance" model requires some homunculus in there to "make a decision". It can decide to take whatever action it wants. I can't make it do anything (in constrast to a bridge, which doesn't "want" anything, and responds to my desires).

This is the theory element that gets labeled as "free will". It's that intensional actors appears to be able to do any action that they "want" or "decide" to do. That's part of the theory of predicting their future actions.

So, why do humans have free will but computers don't? Because most computers have behavior that is far easier to understand than human behavior, and no predictive value is gained by adopting the intensional stance towards them.

"Why do I think time moves forward instead of backward?"

Basically, because of entropy.

There are actually two questions here: first, why does time (appear to) flow at all? And second, why does it flow only forwards?

If the whole universe were composed only of a single particle, say a photon, you couldn't even notice time passing. Every moment would be identical to every other moment. Time wouldn't even flow.

So first you need multiple entities, in order to have change. So now let's say you had the same single photon, bouncing forever between two parallel mirrors. Now time would flow (you could watch a movie of the photon, and notice changes from frame to frame). But it wouldn't particularly flow forwards or backwards. If someone gave you a movie of the bouncing photon, but it wasn't labeled which side was the start and which the end, you'd have no way to tell. There isn't really a "forward" or "backward" in time in that situation.

So what it takes is a complex universe, with order and chaos. And then it's just a matter of probabilities. Eggs are vastly more likely to scramble than to descramble; shattered cups rarely bounce off the floor and spontaneously reassemble; etc. The laws of physics don't prevent these things. They're just exceedingly unlikely. So if you had an unlabeled film, you could tell which side was the "past" and which the "future", since in one direction all the action was extremely probable, while in the other direction every action is exceedingly unlikely.

So, in our normal, macroscopic world, we imagine an arrow of time, a past we can never change, and a future that can be altered by our free will.

Even though relativity tells us that the REAL universe doesn't have absolutely reference frames, that time passes differently in different frames, that it doesn't even make sense to ask whether two events apart in space are even simultaneous or not, that time doesn't really mean anything "before" the big bang or inside a black hole, that really the whole evolution of the universe is a single fixed state vector of space-time, and time never flows at all.

But a (false) concept of linear time with a fixed past and a changable future, helps us quickly make useful decisions in our typical lives.

"Why do I think I was born as myself rather than someone else?"

So we adopt the intensional stance towards other humans. We imagine they have some "deciding" homunculus inside them, that makes choices. We don't know how it works or any of its internal structures, but it is influenced by beliefs, desires, memories, etc.

We know that much can change about the "mere body", while the homunculus seems the same. We age over decades. We lose a limb or eyesight in an accident. We get a heart transplant from a cadaver. We learn to drive a car, and "become one" with the vehicle. It appears that much can change with these external things, but we see both in ourselves (and our memories of our younger selves), and in the self-reported feelings of others, that despite drastic changes the core "us" is relatively unchanged. We see lifelong criminals attempt to "turn over a new leaf", and yet at some point their core surfaces again, apparently never having changed at all; only the surface facade was different.

So it's not at all unreasonable (or so it seems) to suppose that the mysterious and apparently-constant "I" (perhaps a soul of some kind) could have arrived much the same, but in drastically different circumstances. Perhaps 1000 years ago. Or black instead of white. Or a king instead of a peasant.

Hence it MUST have been just a random lottery that caused me to be "born as myself, rather than someone else."

(The truth, of course, is that we're "nothing more" than the product of our genetics plus our environmental history. If our circumstances had been different, we wouldn't have been the same person. For that matter, you aren't the same person today that you were a decade ago, despite your illusion that there is some core "I" that is conserved.)

"Why do I think reality exists?"

We could well be in a matrix world, with all an illusion. Or, perhaps we arrived just a moment ago, but intact with false implanted memories. (Sort of like the creationist explanation of evidence for evolution.)

The assumption that "reality exists" is mere convenience. It's helpful in order to predict my future observations (or so my current memory suggests to me). Even if this is a matrix world, there is still the EXACT SAME theory of "reality", which would then be used to predict the future illusions that I'll notice.

The beauty of this method is that it works whether or not the question is confused.

I have to admit, to me the "Why do I think I was born as myself rather than someone else" example seems so confused that I'm having difficulty even parsing the question well enough to apply the method.

"Why do I think I was born as myself rather than someone else?"

Because a=a?

Tiiba, you might be interested in For the law, neuroscience changes nothing and everything.

A=A is not a tautology.

Usually the first A is taken broadly and the second A narrowly.

The second, as they say, carries a pregnancy.

This seems to me a special case of asking "What actually is the phenomenon to be explained?" In the case of free will, or should I say in the case of the free will question, the phenomenon is the perception or the impression of having it. (Other phenomena may be relevant too, like observations of other people making choices between alternatives).

In the case of the socks, the phenomenon to be explained can be safely taken to be the sock-wearing state itself. Though as Eliezer correctly points out, you can start farther back, that is, you can start with the phenomenon that you think you're wearing socks and ask about it and work your way towards the other.

It looks like the basic recipe for complacency being offered here is:

Something mysterious = Thoughts about something mysterious = Thoughts = Computation = Matter doing stuff = Something we know how to understand.

But if you really follow this procedure, you will eventually end up having to relate a subjective fact like "being a self" or "seeing blue" to a physical fact like "having a brain" or "signalling my visual cortex".

It seems that most materialists about the mind have a personal system of associations, between mental states and physical states, which they are happy to treat as identities (e.g. mental process X is physical process X', "from the inside"), and which are employed when they need to be able to interpret their own experience and their own thinking in material terms.

If you keep asking why, you will need to justify these alleged identities. In fact, if you really keep asking why, in my experience the identities appear untenable and based on a crude and radically incomplete description of the subjective facts, and you end up being interested in metaphysics, from both sides, material and mental.

Mitchell, what reason is there to think that materialism is false, other than our not-understanding exactly how mental events arise from physical ones? A lot of science has been done about the brain; we know that at least there is a very, very intimate connection between mental events and physical brain events. To me, it seems much more parsimonious to suppose that there really is a (not yet fully understood) identity between mental process X and physical process X, than to say that mental process X is actually occurring in some extraphysical realm even though it always syncs up in realtime with physical process X.

"Why do I believe I am conscious?" = "Why am I conscious?"

Z. M., let me answer you indirectly. The working hypothesis I arrived at, after a long period of time, was a sort of monadology. Most monads have simple states, but there is (one hypothesizes) a physics of monadic interaction which can bring a monad into a highly complex state. From the perspective of our current physics, an individual monad is something like an irreducible tensor factor in an entangled quantum state. The conscious self is a single monad; conscious experience is showing us something of its actual nature; any purely mathematical description, such as physics presently provides, is just formal and falls short of the truth.

Now all that may or may not be true. As far as I am concerned, thinking in terms of monads has one enormous advantage, and that is that there is no need to falsify one's own phenomenology in order to fit it to a neurophysical apriori the way that, say, Dennett does. Dennett dismisses phenomenal color and the subjective unity of experience as "figment" and "the Cartesian theater", respectively, and I'm sure he does so because there is indeed no color in a billiard-ball materialism, and no Cartesian theater in a connectionist network. But for the neo-monadologist, because consciousness is being mapped onto the state of a single monad, the ontological mismatch does not arise. We will have a formal physics of monads, described mathematically, and then the fully enriched ontology of the individual monad, to be inferred from conscious phenomenology, and there is no need to convince yourself that you are actually a collection of atoms or a collection of neurons.

The downside is that there had better be a very high-dimensional coherent quantum subsystem of the brain which is physically and functionally situated so as to play the role of Cartesian theater, or else it's back to the theoretical drawing board.

But having dreamed up all of that, what do I see when I look at current attempts to understand the mind? The subjective facts are only crudely understood; and then they are further falsified and dumbed-down to fit the neurophysical apriori; but people believe this because they think the only alternative is superstition and dualism. It's certainly a lot easier to see it so starkly, when you have an alternative, but nonetheless it is possible to sense that something is going wrong even when you don't have the alternative. And that is why I object to this happy process of dissolving one's metaphysical questions in cognitive materialism. It is simply an invitation to deceive oneself in all those areas where physics-as-we-know-it is inherently incapable of giving an answer. Better to maintain the tension of not knowing, and maybe think of something new as a result.

James Blair: I've read JH's "On Intelligence" and find him overrated. He happens to be well known, but I have yet to see his results beating other people's results. Pretty theories are fine with me, but ultimately results must count.

Mitchell, I think it's far too early to give up on the materialist program, which has so far been a smashing success. Consciousness is (as it is said) a hard problem, but even if no one ever finds a solution, one might at least first give solemn consideration to the possibility (I forget exactly where I read it proposed--Hofstadter?) that humans are just too stupid figure out the answer, before vindicating Leibniz.

Frank, what does that have to do with the quality of the paper I linked?

Z. M., "my" monads aren't much like Leibniz's. For one thing, they interact. It could even be called a psychophysical identity theory, it's just that the mind is identified with a single elementary entity (one monad with many degrees of freedom) rather than with a spatial aggregate of elementary entities (a monadic self will still have "parts" in some sense, but they won't be spatial parts). I suppose my insistence that physical ontology should be derived from phenomenological ontology, rather than vice versa, might also seem anti-materialist. (What I mean by this: In fundamental physics, the states of things are known by sets of numerical labels whose meaning is totally relative. All we know from the equation is that cause X turns state A into state B. It tells us nothing about state A in itself. But phenomenology offers us a direct glimpse of something, as Psy-Kosh struggles to express, a few comments back. At some level, it is what we have to work with and it is all we have to work with.) But the main thing is to get away from the assumptions of the neurophysical apriori, because they are inhibiting and distorting what passes for phenomenology today. The description of consciousness is probably best pursued in the almost-solipsistic frame of mind described by Husserl, in which one suspends the question of whether things actually exist, and focuses on the states of consciousness which somehow constitute their appearance. Being able to entertain the possibility of idealism is very conducive to this.

If (let us say) the brain really does have a functionally consequential coherent quantum subsystem, a sharply defined physical entity which really-and-truly is the self, and whose states are literally our states of consciousness, I would expect materialistically pursued neuroscience to eventually figure it out, because neuroscience does include the search for correlations between subjective experience and the physical reality. (Though if it were true, it might save a few years to have the hypothesis already out there in the literature, rather than having to wait for it to become screamingly obvious.) The same may go for whatever other unorthodox possibilities I haven't thought of. It is true that I am ready to give up right now on all existing materialist theories of consciousness; they are manifestly unable to explain even what color is.

So scientifically, I make a noise in favor of metaphysics because I think that will get us to the truth faster. Unfortunately, I doubt I can do the argument justice in off-the-cuff blog comments. I will just have to make an effort and write something longer. The other thing that worries me is the conjunction of information technology with antimetaphysical theories of the mind. There's even less of a reality check there than in neuroscience, when it comes to the attribution of mental properties. But that's a whole other topic.

"So, why do you believe you've stopped beating your wife?"

I...er...I...crap.

If Eliezer has his way, consciousness is not a "hard problem" at all, since asking why people are conscious is the same as asking "why do people think they are conscious," while "thinking one is conscious" is identified with a physical state of one's brain.

The reason Eliezer cannot have his way is that the identity or non-identity of physical and mental reality is irrelevant to explanation. For example, presumably light of different colors is identical to light of different wavelengths. But if I ask, "why does that light look red," it is NOT a sufficient explanation to say that the light has a certain wavelength, NOR to say that my brain reacts to this wavelength in such and such a physical way. It is easy to see that the explanation is insufficient because given the explanation (info about wavelengths and brain states), one would not be able to draw the conclusion that the light would look red, unless one is given the info that a certain brain state is equivalent to seeing red. But this is the point: why is this brain state equivalent to seeing red? The question, "Why do I think that this brain statement is equivalent to seeing red," is now not helpful at all, because presumably the reason I think they are identical is because they are identical. But why are they identical? This is just what has not been explained, and cannot be explained. So there is an actually unanswerable question (at least as far as anyone knows, by any concepts anyone has yet conceived of), and it is not a meaningless question.

Mitchell, Unknown, I worry you may have misunderstood the point.

The question "Why am I conscious?" is not meant to be isomorphic to the question "Why do I think I'm conscious?" It's just that the latter question is guaranteed to be answerable, whether or not the first question contains an inherent confusion; and that the second question, if fully answered, is guaranteed to contain whatever information you were hoping to get out of the first question.

"Explain" is a recursive option - whenever you find an answer, you can hit "Explain" again, unless you hit "Worship" or "Ignore" instead. If the answer to "Why do I think I'm conscious?" is "Because I'm conscious"; and you can show that this is true evidence (that is, you would not think you were conscious if you were not conscious); and you carry out this demonstration without reference to any mysterious concepts (i.e., "Because I directly experience qualia!" contains four mysterious concepts, not counting "Because"); then you could hit the "Explain" button again regarding "Because I'm conscious."

The point is that by starting with a belief, you start with an unconfused thing - the belief may be about something confused, but the belief itself is just a cognitive object sitting there in your mind. Even if its meaning is self-contradictory, the representation is just a representation. "This sentence is false" is paradoxical when you try to interpret it, but there is nothing paradoxical about writing four English words between quote marks, it happens all the time.

If you're asking "Why is the sentence 'This sentence is false' both true and false?" you'll end up confused, because you dereferenced it in the question, and the referent is self-contradictory. Ask "Why do I think the sentence 'This sentence is false' is both true and false?" and you'll be able to see how your mind, as an interpreter, goes into an infinite loop - suggesting that not every syntactical English sentence refers to a proposition.

By starting with a belief, un-derefenced, inside quote marks, you start with an unconfused thing - a cognitive representation. Then you keep tracing back the chain of causality until you arrive at something confusing. Then you unconfuse it. Then you keep tracing.

It really does help to start with something unconfused.

Unknown said: So there is an actually unanswerable question (at least as far as anyone knows, by any concepts anyone has yet conceived of), and it is not a meaningless question.

1) No one knows what science doesn't know.

2) Perhaps you should ask "Why do I think this question is unanswerable?" rather than "Why is this question unanswerable?"

"Why do I think I have free will?" "Because I do," is a perfectly good answer (assuming free will). Trying to trace that back to anything is question begging. "Why do I think I need to deny my free will?" Wouldn't I need to ask that question to be sure that my original answer isn't based on bias?

Since our introspection ability is so limited, this method sounds like it could easily end up resulting in, not the correct explanation of the belief and explanation-away of the phenomenon, but a just-so story that claims to explain away something that might actually exist. This is not a Fully General Counterargument; a well-supported explanation of the belief is probably right, but more support is needed than the conjecture. Look how many candidate explanations have been offered for belief in free will.

Eliezer, in the last few posts you have proposed a method for determining whether a question is confused (namely, ask why you're asking it), and then a method for getting over any sense of confusion which may linger even after a question is exposed as confused ("understand in detail how your brain generates the feeling of the question"). The first step is reasonable, though I'd think that part of its utility is merely that it encourages you to analyse your concepts for consistency. As for the second step, I do not recall experiencing this particular form of residual confusion; if I'm analysing a question and I still feel confused, I would think it was because I was not finished with the analysis.

So what's my problem? The issue is whether this procedure helps in any way with the answering of philosophical or metaphysical questions. I can see the first step leading to (1) a double-check that your concepts make sense (2) attention to epistemic issues. (1) is OK. But (2) is certainly a place where presuppositions can insert themselves. Suppose I'm asking myself "Why are there no positive integers a, b, c, n, with n > 2, such that a^n + b^n = c^n?" If I go reflexive and instead ask "Why do I think there is no such set of integers?", I might notice that this is merely an inductive generalization on my part, from the observed fact that no-one has ever found such a set of integers. And then, if I have a particular epistemology, I might say "But inductive generalizations can never be proved, and so my original question is pointless, because I will never know if there are indeed no such sets, short of being lucky enough to find a counterexample!" And maybe I'll throw in a personal confusionectomy just to finish the job; and the result would be that I never get to discover Wiles's proof of the theorem.

It is a somewhat silly example, but I would think that it illustrates a real hazard, namely the use of this procedure to rationalize rather than to explain.

I think the confusion may have arisen from the incongruous title to this post. Inserting 'Why do I believe...' before your query is an excellent heuristic, but you can't right a wrong question. You can only get better at recognising them.

Frank, what does that have to do with the quality of the paper I linked?

James, everything. The paper looks very much like the book in a nutshell plus an actual experiment. What does the paper have to do with "And I know you didn't simply leave out an explanation that exists somewhere, because such understanding would probably mean a solution for the captcha problem."? I find these 13 and 12 year old papers more exciting. And here is some practical image recognition (although no general captcha) stuff.

I retract the statement that the question about the relationship between the subjective and objective is unanswerable. I started to see how it is possible to answer it.

Nice post, and great method.

On free will, I'd like to pose a question to anyone interested: What do you think it would feel like not to have free will?

(Or, what do you think it would feel like to not think you have free will?)

"Why do I think I have free will?"

One answer might go like this: "But I don't think that. If I use W to denote the proposition that I have free will, I can think of no experiments whose results might provide evidence for or against W. I don't assign a high subjective probability to (W|). For any other proposition Y, I don't see any difference between the probability of (Y|W) compared to (Y|~W)".

"Nevertheless I choose to assume W because I often find it easier to estimate P(Y|W) than to directly estimate P(Y), especially when I can influence P(Y) by an act of 'will'."

A belief doesn't have to be useful to be valid; an assumption doesn't have to be true to be useful.

(Note: this comment is a reply to this comment. Sorry for any confusion.)

Sereboi, I think once again we're miscommunicating. You seem to think I'm looking for a compromise between free will and determinism, no matter how much I deny this. Let me try an analogy (stolen from Good and Real).

When you look in a mirror, it appears to swap left and right, but not up and down; yet the equations that govern reflection are entirely symmetric: there shouldn't be a distinction.

Now, you can simply make that second point, but then a person looking at a mirror remains confused, because it obviously is swapping left and right rather than up and down. You can say that's just an illusion, but that doesn't bring any further enlightenment.

But if you actually ask the question "Why does a mirror appear to switch left and right, by human perception?" then you can make some progress. Eventually you come to the idea that it actually reverses front and back, and that the brain still looks to interpret a reflected image as a physical object, and that the way it finds to do this is imagining stepping into the mirror and then turning around, at which point left and right are reversed. But it's just as valid to step into the mirror and do a handstand, at which point top and bottom are reversed; it's just that human beings are more bilaterally symmetric than up-down, so this version doesn't occur to us.

Anyway, the point is that you learn more deeply by confronting this question than by just stopping at "oh, it's an illusion", but that the mathematical principle is in no way undermined by the solution.

The argument I'm making is that the same thing carries through in the free will and determinism confusion. By looking at why it feels like we have choices between several actions, any of which it feels like we could do, we learn about what it means for a deterministic algorithm to make choices.

I don't know whether this question interests you at all, but I hope you'll accept that I'm not trying to weaken determinism!

If we ask "why does reality exist instead of not exist?", it's like asking "why does existence exist instead of not exist?". Well that's because it's existence. That which is or is a part of reality, is what exists. Something being a part of reality or reality itself is a sufficient condition for that thing existing. So of course reality exists, it's the base case.

A more complicated question is "why is existence like this as apposed to some other way?". That's the business of physicists, and i don't have an answer.

This reminds me of "Why do I have qualia?" I've also asked "Why do I think I have qualia?" I then realized that that's still not quite enough. The right question (or at least one I have to answer first) is "What do I think 'qualia' are?" I'm still thoroughly confused by this question. You could try that with free will too.

"Why does reality exist?"

I think the problem with this question is the use of the word "why." It is generally either a quest for intentionality (eg. "Why did you do that?) or for earlier steps in a causal chain (eg. Why is the sky blue?). So the only type of answer that could properly answer this question is one that introduced a first cause (which is, of course, a concept rife with problems) or one that supposed intentionality in the universe (like, the universe decided to exist as it is or something equally nonsensical). This is probably (part of) why answering this question with the non-explaination "God did it" feels so satisfactory to some--it supposes intentionality and creates a first cause. It makes you feel sated without ever having explained anything, but the question was a wrong one in the first place, because any answer would necessarily lead to another question, since the crux of the question is that of a causal chain.

I think a better question would be "How does reality exist?" as that seems a lot more likely to be answerable.

I believe I'm wearing socks, because I can see socks on my feet.

As for me, I mainly believe I'm wearing socks because I can feel socks on my feet. :-)

Either way, the question is guaranteed to have an answer. You even have a nice, concrete place to begin tracing—your belief, sitting there solidly in your mind.

In retrospect this seems like an obvious implication of belief in belief. I would have probably never figured it out on my own, but now that I've seen both, I can't unsee the connection.

"Tracing back the chain of causality, step by step, I discover that my belief that I'm wearing socks is fully explained by the fact that I'm wearing socks. This is right and proper, as you cannot gain information about something without interacting with it."

Maybe I'm being pedantic on this point, but doesn't the interaction with the socks constitute the act of putting them on which actually fully explains that you're wearing them? Of course, you can go back further along the causal chain to the reason you put them on - perhaps the room was cold, or you had to put on boots to go outside. Regardless, the more we regress backwards on this chain, the farther from the change in state from Socks_off to Socks_on would we find ourselves in the causal sequence of events leading up to your wearing them.

That being said, wouldn't the circular explanation - I'm wearing socks because I'm wearing socks - actually be the explanation arrived at as we approach the causal chain's resulting state of affairs where we're wearing socks instead of not wearing socks? The 'new information' is actually gained by the interaction with the socks preceding our wearing them or our resulting need to explain this phenomenon.

"Why was I born as myself rather than someone else?" versus "Why do I think I was born as myself rather than someone else?"

This never got solved in the comments.

I was sitting in microeconomics class in twelfth grade when I asked myself, "Why am I me? Why am I not Kelsey or David or who-have-you?" Then I remembered that there are no souls, that 'I' was a product of my brain, and thus that the existence of my mind necessitates the existence of my body (or something that serves a similar function). Seeing the contradiction, I concluded that I had reasoned, incoherently, as if 'I' were an ontologically fundamental mental entity with some probability of finding itself living some particular lives. That's unsurprising, because as a great deal of cognitive science and Eliezer's free will solution has demonstrated, humans often intuitively evaluate 'possibility' and plausibility by evaluating how easy it is to conceive of something, as a proxy. "I can conceive of 'being someone else,' thus there must be some probability that I 'could have been someone else', so what is the distribution, what is its origin, and what probability does it assign to me being me?"