Dear Marc,
wow, thanks for the in-depth discussion of my essay! This is, really, what I've hoped these contests to provide: some well thought-out feedback that challenges my ideas, opening opportunities to both clarify and revise them. Thanks for that!
I'm very happy to see we're in agreement on lots of topics---it always makes me feel a little less crazy to find that other people have thoughts in a similar directions. Still, though, I'm going to focus on the disagreements, because that's usually both more informative and more fun!
First of all, however, I don't think that, in many places, you're wrong to disagree---I recognize that there's many points in my essay on which one can be quite rationally of a different opinion. That's part of why I stressed the analogy of my two propositions to the Church-Turing thesis: I don't think there's a way to prove they are true; rather, I think of them as speculation that may be accepted on their explanatory and unifying power (or not, as the case may be).
So I can't really say much to try and persuade you if you disagree with my proposition 2: we simply make somewhat different background assumptions. I tend to think of the world as, at its roots, physical; you consider the physical to emerge from the abstract, mathematical realm, in the manner of Tegmark's mathematical universe.
My view of mathematics is simply a different one: I think of it as a science of structure---for instance, because the set of books on my shelf, ordered according to their thickness, has the same structure---an ordered set---as the set of my paternal ancestors, I can use the books to represent them, and, since Moby Dick is thicker than The Old Man and the Sea, and Moby Dick is mapped to Joe, while The Old Man is mapped to Jim, I can conclude that Joe is Jim's ancestor with just a look at my books. Mathematics then essentially concerns what's it about both sets of objects that enable me to do this, and that is that both share the same structure. One may study this structure, and other possible structures, in order to see what else one can use for modeling---and in the end, that's (mostly) what mathematics is about.
So proposition 2 seems very natural to me: every structure needs something to bear it, like every relation needs relata to subvene it (and indeed, one can analyze structure in terms of relations, and it's no coincidence that sets and relations are foundational to mathematics).
From the point of view that abstract structure may have an independent existence, however, I can appreciate that the proposition seems far less obvious. But I'm not really concerned with laying out the case for accepting it here: my essay really only concerns what would be the case, given that my two propositions are true.
The same goes, then, for the mind-dependence of computation: if it's true that computation must be physically instantiated, I think there's not much of a way around this. Consider finding a 'black box' somewhere in the vastness of space. You can see it's a complex system of dials, gears, lights and switches; you can also see that it changes its state in response to pushing some switches. But what I maintain you can't do is figure out what the system computes: there will always be other interpretations that are just as well-founded as yours that have it compute something entirely different.
The problem here is the same as figuring out what's written on a given page of text in a language you don't know. In principle, you can decode it as meaning anything that can be expressed in a text of that length, by treating it as a one-time pad. (To see how the two problems are equivalent, you could take the entire set of inputs and outputs of the black box, and consider it as the 'text'.)
But again: this hinges on the need to implement computations physically. Denying that probably gives you a way out---although it's not totally clear to me that you don't run into similar problems, only with abstract structures instead of physical systems at the 'bottom'.
The identification of qualia with the connections between mental models and the objects they model is also speculative, but flows from earlier speculation: given that all models are computational, and all computation is modeling (of some computable function, if nothing else), then the connection between mental models and their objects can't be computational---as that would lead to vicious regress.
But if that's the case, then these connections must seem quite mysterious to us: we can't model them, hence, we can't explain them; we can't communicate them, since we can't describe them. So those things, whatever they may be, must be ineffable in this way---I couldn't tell you what they are if you didn't already know.
Furthermore, they must, in some way, get our minds into contact with the properties of the things our mental models model: they must transport into our minds things like color, smell, feel and so on, as proxies for their physical qualities---reflectance, chemistry, solidity, etc. We know something reflects light of a certain wavelength because we see red; we know it is solid, because we feel it.
That's where my identification of these connections with qualia comes from: they're mysterious, ineffable things that bring us into contact with the external world---that make us experience that world.
But qualia can't directly be the models of the world themselves: take the situation where you suddenly become aware of a churchbell ringing, and nevertheless, you can count how many times it has rung already. Your mind didn't attend to the ringing beforehand, but still, it must have been present in your experience in some way. Or take a nagging headache you become aware of. Or make an experiment: when you listen to somebody talk, you ordinarily hear what is being said; but with a bit of effort, you can instead concentrate on how it's being said, hear the rhythm, the uhms, ahs, and ohs you ordinarily ignore, some peculiarity of the other person's dialect, and so on.
In both cases, you have the same phenomenal experience, but attend to it differently: if phenomenal experience (i.e. qualia) simply were our models of the world, then these two roles could not be separated.
But they can, and here's where the second mystery of the mind enters (apart from the 'hard problem' of phenomenal experience): intentionality. How do thoughts come to be about things?
This is, of course, just the subject of the last contest; and my last essay is a sort of companion piece to this one. Put both together, and you arrive at the following rough theory of the mind: there are ineffable, mysterious connections to the world outside that are present in the mind; these are organized by some self-referential process (my von Neumann mind) in order to form models of the outside world. Essentially, the von Neumann replication process organizes the structure of the subjective experience that ultimately connect the mind to the world into a model of the world.
It's me ordering the books according to thickness on my shelf, so that they may serve as a model of my paternal ancestors, only that the books are self-ordering; each book is mapped to one of my ancestors by means of the connection I have identified with qualia.
Taken together, I think this accounts for most of the problems with minds: they can look at themselves (via the von Neumann process) and organize themselves into different structural images of the world outside, whose qualities/properties are presented to them via qualia. Different structures, different ways of modeling the world, amount to differently focused attention: you use the same connections to the world to attend to the words that are spoken, and to how they are spoken.
It's from this point that I then go on to use the parallel to Gödelian incompleteness to argue for a necessary incompleteness of our models of the world---after all, they are categorically unable to model how they are connected up to it. That's why qualia seem so mysterious, and why every model of the world must leave out at least that bit. Hence, no model can encompass your 'maxiverse' (which I tend to call, as I already commented on Heinrich Päs' essay, the quagmire), and every model has a certain minimal, irreducible, and hence, apparently fundamental information associated to it.
Phew, that turned into half an essay of its own, there! I hope I didn't run you down with my train of thought, it can be hard to stop once it gets going.
I'm also happy you found something of value in my discussion with Philip, which I greatly enjoyed---I think you've confused me for him a couple of times, which I'll take as a compliment.
On the subject of FQXi membership, I think there may be some other qualification I don't match---I wasn't asked.
Again, thanks for this in-depth engagement with my essay, it was great to read your thoughts!
Cheers,
Jochen
