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John, thanks for reading.
I am pretty sure that probability is not real, and I think that people like Laplace, Bayes, de Finetti, and Jaynes, have made that case more convincingly than I can.
I didn't make any comment on the nature of time in my essay at all, although I do intuitively with your position that it is a measure of relative change.
As to infamous cats, I do not think there are any times when I can make a definite statement about the cat. I do an experiment when I put the unfortunate fellow in the box, namely looking at him to see if his tail moves. I do a second experiment identical to this when I open the box. Based on what I know about the conditions in the box (cyanide capsules, nuclear decay, and whatnot), I can make an estimate, a bet, as to what the result of the second experiment will be. At no time can I legitimately claim I know the state of a cat, initially, in between, or at the end. I can only ever know the result of an experiment, and I only do two of them.
I definitely do not argue that "all circumstances leading to a particular event exist". I argue exactly the opposite: there is only one set of circumstance leading to an event. I argue for a very strict determinism, but one in which we do not know initial or intermediate conditions precisely so that we cannot know the future outcomes. Note that just because I do not know the causal sequence does not mean there is no causal sequence. This is precisely Jaynes' Mind Projection Fallacy. I agree there is no God's eye view, but this is only because there is not possible to have perfect information, even for this God person. Thus, just because God does not know the causal sequence does not imply that there is no causal sequence.
I didn't exactly follow your point about superluminous transport of information. I argue that quantum theory is a theory of experiments, not a physical theory, and thus it makes no sense to speak of QM as either local or non-local - it is entirely epistemic. Therefore the locality or non-locality of QM is irrelevant to any question of the speed of information transfer. Nothing at all about the physical world can be concluded from any apparent locality or non-locality of QM.
Too bad about the cake thing though, I quite like cake and I like to share it too.
Thanks very much for reading and commenting. Mark