In short, I am under the illusion that I changed my beliefs as a consequence of free will. However, I am also aware that this illusion exists and why it exists, and therefore would say that I have no choice but to have the beliefs I have if anyone wanted to press the point. Most people don't think about it this much though, so I rarely break it down this far.
I don't mean to be flippant with this question, I really don't, but how do you know that you have gone far enough? How do you know that this ultimate truth that you have discovered, namely, that "free will is an illusion" is not also an illusion itself? In view of the limitations inherent in insufficient model memory how do you justify this particular "stopping point"?
Cordially,
These are perfectly legitimate questions; I don't see anything flippant about them at all. There are a couple different ways to address these points, which I will do briefly.
First, there is the relatively simple matter of best hypothesis selection, such as the theorem attributed to Occam and proved much later by mathematicians. It becomes difficult to construct any "deeper" hypothesis that is not objectively worse than the one I constructed in my previous post. Therefore, I would be inclined to select my hypothesis because it is the most rational one, though I can't make a claim to its correctness in any absolute sense and can only claim that it is the best hypothesis available absent additional information. If a better hypothesis pops up, I'll gladly accept that. "Better hypothesis" is a fairly objective metric.
Second, the "free will is an illusion" bit is a consequence of the mathematics, and as such is provable within the set of axioms that we consider to be reality. Having inadequate model capacity has no bearing on the reality of that particular abstraction; even if there was "something more", that particular construction would still be correct. It is better to think of limitations in model capacity as "how much of the big picture is it mathematically possible for us to see", where the more model memory you have, the more distant relationships and "bigger pictures" you can discern in your universe. Anything in the universe that exceeds your capacity to meaningfully encode it will seem incomprehensible, even if there is nothing particularly special about the "incomprehensible" thing you are observing. We are already starting to see this with computers. A computer with the appropriate software is quite capable of slicing and dicing phenomena that humans find borderline inexplicable. We can comprehend the abstractions that the computer generates based on the patterns it discovers, but we are incapable of discovering such things ourselves. Very soon, we will have computer systems that could very well discover phenomena in the universe that is so complex that even the abstractions would be largely incomprehensible to humans. One can see how this might make for an interesting future. It should be noted that virtually no software exists that meets the criteria of a universal predictor for a bevy of reasons beyond the scope of this discussion, so most people have never experienced what a (large) computer with this class of software can do.
I don't make a claim to any kind of "ultimate truth", but I could convincingly argue that it is the most probable or best "truth" available with the axioms we generally agree on today. This could change as we discover new things, but such discoveries would more likely affect the variables rather than the equations as it were. I'm not really dead set on anything, but I do demand a rational and consistent framework, even if I'm not terribly pleased with the consequences.