Found a draft paper/chapter/talk of David Albert’s somewhere on the internet, titled Physics and Chance (PDF). The main purpose of the paper is to argue that the probability distribution that “we have from Boltzmann and Gibbs, or something like it,” is true. And he wants to argue that it is true and not just a useful instrument for the purpose of predicting the values of particular parameters.
Albert uses David Lewis’ account of laws of nature to argue for the truth of the probability distribution. The Lewisian view is that the laws of nature are those true statements about the world that have the best combination of simplicity and informativeness. Albert argues that not only does Boltzmannian statistical mechanics satisfy this requirement, but also that the laws of the special sciences are not laws of nature. He thinks the only laws of nature are the fundamental laws of physics that give us the microdynamics of systems, plus Boltzmannian statistical mechanics, plus the Past Hypothesis. (I will lump Boltzmannian and Gibbsian statistical mechanics together for now, as Albert does.)
Albert first makes a case for the necessity of statistical mechanics when we want to predict which macrostates follow from which macrostates. This makes a prima facie case for statistical mechanics being an informative addition to the fundamental microdynamical laws. But this sort of informativeness, one based on macrostates, and specifically on macrostates that are amenable to human observation (we don’t know yet that stat mech would work for other types of macrostates, if they exist), seems thoroughly instrumental. (Perhaps informativeness itself is an inherently instrumental property — I’ll leave that as an open question.) So, if this type of informativeness, informativeness about macrostates, is the main support for statistical mechanics being part of the laws of nature, it’s not clear how Albert establishes the truth rather than the instrumental value of statistical mechanics.
My objection aside, Albert anticipates that objections to his view will arise from those who see laws in the special sciences as being explanatory independent of the laws of physics. He examines Philip Kitcher’s argument that Arbuthnot’s regularity, which was a constant preponderance of births of males over females in London, is explained not by microphysical principles but by R. A. Fisher’s argument from parental expenditure. Kitcher writes that the microphysical account “would not show that Arbuthnot’s regularity was anything more than a gigantic coincidence”. Albert pounces on the word “coincidence” and says that that’s where statistical mechanics has to come in. He says that it is only by reference to the statistical mechanical probability distribution that Kitcher’s talk of “coincidence” makes any sense.
On its face, this claim is utterly batty. After all, Arbuthnot did not consult the SM probability distribution before regarding it as a coincidence. He thought it was a coincidence from the point of view of a model that assumed sex determination worked like a “two-sided die”. Whether he was justified in using that model is beside the point. What’s important is that Arbuthnot, and the myriad other researchers in the special sciences who tried to explain away regularities, did not determine the coincidental character of those regularities by doing statistical mechanical calculations.
Albert admits this. He admits that we don’t explicitly consult statistical mechanics to decide if certain large-scale regularities we observe are coincidental. His only reply is that our lack of consultation isn’t any evidence against the existence of the SM probability distribution. Fine. But surely the burden of proof is on Albert here, to show how the distribution is relevant to the special sciences when the special sciences evidently carry on working, with reasonable success, without (usually) referring to statistical mechanics.
To be fair, Albert does have some sort of positive account of how it may be that the SM probability distribution grounds our identification of coincidences in the special sciences. He claims that if he were right that the laws of nature are just the microphysical laws and statistical mechanics, then some foggy, unconscious acquaintance with that probability distribution would have been hard-wired into organisms by natural selection.
This is highly implausible to me. Natural selection favours (among other things) characteristics instrumental to the survival of the organism. And as far as day-to-day survival is concerned, it seems far more useful, and far easier from a neural architecture point of view, to hard-wire the regularities of the special sciences directly into the brain, instead of hard-wiring some vague acquaintance with SM and expecting the brain to propagate those probabilities all the way up to make predictions about complex systems. It is also probably easier to simply hard-wire an ability to learn large-scale regularities.
In any case, the more problematic issue is that Albert’s attempt at a positive argument for the relevance of SM probabilities to special science explanations is made by asking us to assume first that he is right about the completeness of microphysics + stat mech. But that’s exactly what people like Kitcher are questioning when they bring up the independence of the laws of the special sciences.
The folk reductionism gets worse. Albert argues that his proposed package of the complete laws of nature explains macroscale happenings like the descent of man and Arbuthnot’s regularity, because if you started with his pet Past Hypothesis, with the uniform probability distribution over the microstates compatible with that, and propagated the probabilities forward in time according to classical statistical mechanics, you’d find that the descent of man and Arbuthnot’s regularity come out as highly probable events:
it is precisely because the account of the descent of man by random mutation and natural selection involves vastly fewer and more minor and less improbable such coincidences than any of the imaginable others that it strikes us as the best and most plausible explanation of that descent we have.
(I’ve left out Albert’s trademark emphases to avoid annoying readers.)
There are similar claims like this throughout the paper. At other points he claims that statistical mechanics also explains why large objects in our world do not spontaneously disintegrate into statuettes of the British royal family, because if we take the Past Hypothesis plus initial uniform probability distribution blah blah, we will find that the probability of large objects disintegrating thus is very low.
My problem with those claims is that there is no evidence whatsoever that if you indeed take the Past Hypothesis, put a uniform probability distribution on the initial states of the universe compatible with that, and evolve that thing forward in time, you’d really find that the descent of man, the longevity of macroscopic objects, etc. come out as highly probable events. Albert is asking us to accept these claims on faith, since we can’t make any serious attempt at those calculations. But if one is sceptical about the truth of traditional statistical mechanics in the first place, then one is hardly going to accept on faith the claim that it will indeed give the probabilities Albert wants for those macroscopic events.
So Albert’s attempt to subsume the special sciences to statistical mechanics is extremely weak. The implicit request for us to put our faith in SM is a more general problem that recurs throughout the paper. As mentioned earlier, Albert argues that we need stat mech to make the correct macroscopic predictions; to get correlations of the macroscopic properties of one event with those of a later event. In this way, stat mech is more informative than microdynamics alone, and thus should be considered a Lewisian law of nature. But part of his way of showing that we need stat mech to make the correct macroscopic predictions is to say that without stat mech, we would have no reason not to predict that any given stone won’t spontaneously distintegrate into statuettes of some royal family. Merely to get things right about the ordinary rigid objects of Newtonian physics, of the “projectiles and levers and pulleys and tops”, he says, we need SM, because otherwise how can we assume that these rigid objects can even remain intact while we apply Newtonian mechanics to them?
But the thing is, the medium-term integrity of pulleys and levers would hardly seem like something that has to be explained away except in the light of statistical mechanics. If someone hasn’t already accepted the whole spiel about how intact pulleys are “improbable” because the phase space of microstates of disintegrated pulleys is so much larger than that of non-disintegrated pulleys, why should he take the intactness of large-scale objects to be something that begs to be explained away? The explanatory need that SM is supposed to fulfill wouldn’t even exist unless you already accept [that version of] SM. Again, Albert doesn’t provide an argument that would engage someone who is skeptical of the predictive accuracy of a statistical mechanics that involves starting with the Past Hypothesis, putting a uniform over the microstates of the universe consistent with that, and so on.
Finally, I just don’t see how Fisher’s principle regarding sex ratios, and other principles of the special sciences, would not also qualify as laws of nature. Why would one regard the Past Hypothesis + microdynamics + statistical mechanics as more informative than microdynamics + principles of special sciences? Sure, there are many, many such principles, so one sacrifices simplicity, but one also gains a lot in informativeness. For there is no evidence whatsoever that Albert’s proposal for the laws of nature is more informative than the “dappled” proposal with its myriad special science “laws”. If anything, the latter has been shown to be informative, while we can never determine if the former is informative, due to computational difficulties freely admitted by Albert. And isn’t it also rather implausible that some probability distribution on the initial state of the universe in fact explains why, say, zebras have stripes?
Posted by Ponder Stibbons 
