Just because the states are the same doesn't mean the probability of being in that state are the same. It's only meaningful to discuss the probability of an outcome in terms of a probability distribution over possible outcomes.

In my example, I specified that the BB is in a reference class with all other brains, including the psychic cousin's. Given that they are both in the reference class, the fact that the BB and the cousin share the same cognitive history implies that the probabilities of their cognitive histories relative to this reference class are the same. The reference class is what fixes the probability distribution over possible outcomes if you're determining probabilities by relative frequencies, and if they are in the same reference class, they will have the same probability distribution.

I suspect Eliezer was thinking of a different probability distribution over brain states when he said the psychic's brain state is correlated with the deck of cards. The probabilities he is referring to are something like the relative frequencies of brain states (or brain state types) in a single observer's cognitive history (ETA: Or perhaps more accurately for a Bayesian, the probabilities you get when you conditionalize some reasonable prior on the sequence of instantiated brain states). Even using this distribution, the BB's brain state will be correlated with the top card.

More generally, for me to expect your beliefs to correlate with reality, I have to either think that reality is the cause of your beliefs, expect your beliefs to alter reality, or believe that some third factor is influencing both of them.

I can construct examples where for this to be true requires us to treat mathematical truths as causes. Of course, this causes problems for the Bayesian definition of "cause".

You seem to be exaggerating the generality of the causal Markov condition (CMC) when you say it is deeper and more general than the second law of thermodynamics. In a big world, failures of the CMC abound. Let's say the correlation between the psychic cousin's predictions and the top card of the deck is explained by the person performing the test being a stooge, who is giving some non-verbal indication to the purported psychic about the top card. So here we have a causal explanation of the correlation, as the CMC would lead us to expect. But since we are in a big world, there are a massive number of Boltzmann brains out there, outside our light cone, whose brain states correlate with the top card in the same way that the cousin's does. But there is no causal explanation for this correlation, it's just the kind of thing one would expect to happen, even non-causally, in a sufficiently large world. So the CMC isn't a universal truth.

Now, the CMC is a remarkably accurate rule if we restrict it to our local environment. But it's pretty plausible that this is just because our local environment is monotonically entropy-increasing towards the future and entropy-decreasing towards the past. Because of this feature of our environment, local interventions produce correlations that propagate out spatially towards the future, but not towards the past. When you drop a rock into a pond, waves originate at the point the rock hit the water and travel outwards towards the future, eventually producing spatially distant correlations (like fish at either end of the pond being disturbed from their slumber).

Imagine that there is a patch somewhere in the trackless immensity of spacetime that looks exactly like our local environment, but time-reversed. Here we would have a pond with a rock initially lying at its bottom. Spontaneously, the edges of the pond fluctuate so as to produce a coherent inward-directed wave, which closes in on the rock, transferring to it sufficient energy to make it shoot out of the pond. If you don't allow backward causation, then it seems that the initial correlated fluctuation that produced the coherent wave has no causal explanation, a violation of the CMC.

The second law is often read as a claim about the condition of the early universe (or some patch of the universe), specifically that there were no correlations between different degrees of freedom (such as the positions and velocities of particles) except for those imposed by the macroscopic state. There were no sneaky microscopic correlations that could later produce macroscopic consequences (see this paper). Entropy increase follows from that, the story goes, and, plausibly, the success of the CMC follows from that as well. There is a strong case to be made that the second law is prior to the CMC in the order of explanation.

I am confused by these posts. On one hand, Eliezer argues for an account of causality in terms of probability, which as we know are subjective degrees of belief. So we should be able to read off whether X thinks A causes B from looking at conditional probabilities in X's map.

But on the other hand, he suggests (not completely sure this is his view from the article) that the universe is actually made of cause and effect. I would think that the former argument instead suggests causality is "subjectively objective". Just as with probability, causality is fundamentally an epistemic relation between me and the universe, despite the fact that there can be widespread agreement on whether A causes B. Of course, I can't avoid cancer by deciding "smoking doesn't cause cancer", just as I can't win the lottery by deciding that my probability of winning it is .9.

For instance, how would an omniscient agent decide if A causes B according Eliezer's account of Pearl? I don't think they would be able to, except maybe in cases where they could count frequencies as a substitute for using probabilities.

On the other hand, while "post-utopian" is linked to "colonial alienation" and vice versa, these two elements don't connect to the rest of the causal fabric - so that must not be a universe.

If I really want to, there's an easy way for me to sidestep this. I just postulate something called "post-consciousness" which is caused both by colonial alienation and by particular arrangements of neurons in the brains of particular people (in a similar way to that in which epiphenomenalists would say consciousness is caused). Presto! A causal chain from my familiar causal fabric to colonial alienation.

In fact, we can add an extra node to any causal diagram without affecting the probabilities of observations only involving the other nodes, by making it an effect of all other nodes but not a cause of anything. By so doing we can connect the diagram up. Thus although we can't subvert the approach in Eliezer's post by postulating an ultimate cause (God), we can always subvert it by postulating an ultimate effect.

What I have said isn't normally a problem in real-life applications of the test `is it part of this connected causal fabric', since very often no such causal connection is postulated. My point is that this test can't in-principle rule out anything. It can only serve as an in-practice test by which we can temporarily rule out objects for which no such causal connection has been postulated.