>>43
he appears to have come around to a more strict computational viewpoint himself
Yes, in the latest version of his paper, CUH(Computational Universe Hypothesis) is the one he thinks is most likely, which is no wonder given the strange mess that happens when you look at all those uncountable ordinals in most infinitary set theories (and then you have independence results of various axioms, which makes things even more complicated). One particular problem is that even if we find ourselves a potential hypercomputational oracle (such as doing funky things around black holes), there is no way to know for sure wether we truly have oursleves a hypercomputational oracle (for we are only capable of arithmetic/computation). It's also possible that traces of complex-enough computations would give us the illusion of a hypercomputational oracle, without actually having one.
Some thoughts on wether physics based on uncountable entities makes sense or not (beyond computation):
http://arxiv.org/abs/math/0411418 http://arxiv.org/abs/math/0404335
Some thoughts on how QM (MWI-like) appears too naturally when considering a computational multiverse and why there may be no need to assume more than that:
http://iridia.ulb.ac.be/~marchal/publications/CC&Q.pdf
http://arxiv.org/abs/physics/0001020
Some interesting thought experiments on how CUH could (appear to) fail:
http://lesswrong.com/lw/55e/a_potential_problem_with_using_solomonoff/
http://lesswrong.com/lw/4iy/does_solomonoff_always_win/