Can someone give a hint as to why the claim made in the abstract [...] should not be considered ludicrous?
Well maybe just a hint? Maybe. I puzzled for quite a while over the article, and really don't grok it, but I *think* the author's "mu-strategy" *might* be paraphrased as follows: Suppose we have some target v(t) from F = {f:R->S} that we want to define a strategy that constructs a "causal predictor" w(t) for v. They claim that such a strategy is plausible because "diagonalizing against" it would require R to be well-ordered. I believe their construction of w(t) is: First define an arbitrary well-ordering on the set of all functions F (thus I guess requiring AC). Let's call this "complexity". Then, for each t, set w(t) = f[t](t), where f[t] is the "simplest" f such that f[t](tau) = v(tau) for all tau strictly < t. That is, w(t) has the value at t of the "simplest" f which correctly predicts the past values of v(t) strictly prior to t. Note that the f[t] picked can still guess the wrong value of v(t). But at different t values the f[t] it picks can change, and whenever it picks one that guesses wrong at t it must pick different ones for all greater t. So as t increases the "causal correctness" of each f[t] must never decrease and moreover the "complexity" also never decreases. They remark that the natural interpretation of "complexity" gives Occam's Razor, but could just as well be the opposite (Occam's Hair?) Apparently they then show (assuming I got all this right) that this strategy produces a w(t) that "usually" guesses right at most t. Moreover it usually will keep each new f around "epsilon into the future" (not sure if that's a fixed epsilon or varies with t). I must admit I don't really "get" all this, and may have got it quite wrong. They refer to "well-known hat puzzles", where a line of prisoners is supposed to guess their own hat colors, hearing only the previous guesses, then generalizing that to indexing the prisoners with higher ordinals (the Beagle Boys in omega-land?). To my taste the exposition suffers from the common fault of not stating clearly up front a road map of how it's going to get where it intends to go, and from gratuitous distracting generalization and analogy--"a black hole does not give a practical time machine." But then, I'm probably both confused AND cranky. Hopefully someone on this list will provide a better exposition!