me:

Ah yes, thus my 'simplest model' qualifer in my last post! Yeah, in the simplest model where you have the finitely complex ASORs, and the infinite observer-histories that extract information from them, the counting is pretty clear cut — you can get a finite integer encoding for each of the original ASORs, and infinite integer encodings for the observers, and then apply Cantor's diagonal argument, just like with the integers and irrational numbers. But what about, for example, observers whose each 'time-instantaneous' thought was irreducibly infinitely complex? What about higher order 'power sets' acting on the 'aleph-1' observer histories (and so on and so on, eventually leading to structures higher than any cardinality...)?? Well you can make these statements, but do these fantastically complex ASORs actually exist? I think the correct answer is — Maybe! If they don't exist, and we are essentially just talking about turtle shells that are simultaneously both entirely green and entirely not green, then the 'simplest model' applies simply enough. If, however, you can 'reach the point at infinity', and proceed on in some time-like dimension to think different, infinitely complex thoughts, then stat. meta. may still be correct and reconcilable with your current existence as a puny finite creature. Namely, if you think of the infinite complexity thoughts as a natural continuation of the finite ones (say along the lines of Conway's surreal numbers, constructed with Dedekind cuts), then just as before where there is no finite top level of complexity where you would expect to find yourself — then there is also not even any one infinite level of complexity where you would expect to exist — instead again you expect to find yourself always climbing higher — including starting at a finite level of complexity, reaching the 'point at infinity' and keeping on going up to levels of unbounded cardinality.

Assuming stat. meta. is correct, I'm not sure which scenario I think encompasses reality — I lean both ways at times. In the current draft of the paper I retreat a little and say that I'm just going to focus on the simplest model — I say that it is an 'extraordinary enough' of an argument to be made. But you're quite right — if these infinitely complex ASORs actually do exist, and furthermore if we can not 'reach the point at infinity' in any universe, then since we are currently finitely complex, stat. meta. must be false.