"We also get into the philosophical issues that are absolutely inevitable in sensible discussions of this subject. No matter what anyone tells you, we cannot prove the Second Law of Thermodynamics using only Boltzmann’s definition of entropy and the underlying dynamics of atoms. We need additional hypotheses from outside the formalism. In particular, the Principle of Indifference, which states that we assign equal probability to every microstate within any given macrostate; and the Past Hypothesis, which states that the universe began in a state of very low entropy. There’s just no getting around the need for these extra ingredients. While the Principle of Indifference seems fairly natural, the Past Hypothesis cries out for some sort of explanation.

Not everyone agrees. Craig Callender, a philosopher who has thought a lot about these issues, reviewed my book for New Scientist and expresses skepticism that there is anything to be explained. (A minority view in the philosophy community, for what it’s worth.) He certainly understands the need to assume that the early universe had a low entropy — as he says in a longer article, “By positing the Past State the puzzle of the time asymmetry of thermodynamics is solved, for all intents and purposes,” with which I agree. Callender is simply drawing a distinction between positing the past state, which he’s for, and trying to explain the past state, which he thinks is a waste of time. We should just take it as a brute fact, rather than seeking some underlying explanation — “Sometimes it is best not to scratch explanatory itches,” as he puts it."

Brute Facts and Explanation

My objection to the idea of explaining boundary conditions originates in arguments by David Hume. Consider St. Thomas Aquinas’ classic cosmological argument for the existence of God. We assume that every effect in the universe must have a cause. Otherwise there would be no “sufficient reason” for the effect. But if every effect must have a cause, said Aquinas, we find ourselves in a dilemma: either there was an infinite chain of causes and effects or there was a first cause, the Uncaused Cause (God). Not believing an infinite chain of causation would be explanatory (for reasons that are not entirely compelling now), Aquinas concluded that there was an Uncaused Cause. Similar arguments from motion yielded an Unmoved Mover. There are several objections to these classic arguments. One reaction popular among students is to ask, as Hume did, what caused or moved God? This question raises many more. Should we posit an infinite regress of gods, in keeping with the original explanatory demand? Or should we ‘bend’ the explanatory demand so that in the case of God he doesn’t have to be caused by something distinct from himself? But then, one thinks, if it’s acceptable for something to cause itself or to selectively apply the explanatory demand, we have gone a step too far in positing God as the causer or mover of the universe. Just let the universe itself or the big bang be the “first’ mover or cause and be done with it.

Though the situation with the Past Hypothesis is more complicated, at root the above is my criticism of Price. What would explain a low entropy past state? The most natural thing to say is that an even lower entropy state just before the Past State would explain it. The natural ‘tendency’ of systems are to go to equilibrium, after all. The original low entropy past state would naturally and probably evolve from an earlier and lower entropy state. But now that lower entropy state is even more unlikely than the original. Either we just keep going, explaining low entropy states in terms of lower ones ad infinitum, or we stop. And when we stop, should we posit a first Unlow Low Entropy State (or in Price terminology, a Normal Abnormal State)? No. We should just posit the original low entropy state and be done with it.

.....

I see the same problem in Price’s claim that the Past State needs to be explained. What is it about the Past State that makes it needy of further explanation? Why can’t it simply be a brute fact or the Past Hypothesis be a fundamental law? One answer might be to accept that the Past State plus laws are empirically adequate yet find fault with them for lacking some theoretical virtue or other. Empiricists—those who see empirical adequacy as the only criterion that really matters—will not like this, but others will. Which theortical virtue is the Past State lacking? It is simple, potentially unifying with cosmology, and it has mountains of indirect evidence via our evidence for thermodynamics and whatever mechanics we’re considering. But still, it is highly improbable. Though we can reasonably worry about what exactly it means to say a state of the entire universe is improbable, we can postpone such worries here since that is not the source of Price’s problem. The standard probability distribution pulls its weight in science and seems to be a successful theoretical posit in science. Can the improbability of the state mean that it can’t be true or that it is needy of explanation? Well, the Past State can certainly be true; virtually everything that happens is unlikely. What about explanation? I don’t think explanation and probability have such a tidy relationship. Lots of low probability events occur and not all of them demand explanation. Arguably, low probability events can even function as the explananda, not merely the explanans. For example, an asteroid strike in the Yucatan region might explain the death of the dinosaurs, even though (arguably) the prior probability of the asteroid strike is lower than that of the dinosaurs’ extinction (see Lange 2001, p. 108). It is far from automatic that low probability events all deserve explanation. Furthermore, the sorts of explanations of the Past Hypothesis that Price envisions in his [1996] seem to me to be examples that are wildly speculative, potentially untestable, and not obviously more probable.

My own view is that there is not some feature of facts that make them potentially acceptably brute or self-explanatory, that make some facts okay as brute and others as not. We instead look at the theoretical system as a whole and see how it fares empirically, and if there are ties between systems then we look to various theoretical virtues to decide (if one is realist). What we don’t want to do is posit substantive truths about the world a priori to meet some unmotivated explanatory demand--as Hegel did when he notoriously said there must be six planets in the solar system. In the words of John Worrall [1996]

the worst of all possible worlds is one in which, by insisting that some feature of the universe cannot just be accepted as “brute fact”, we cover up our inability to achieve any deeper, testable description in some sort of pseudo-explanation—appealing without any independent warrant to alleged a priori considerations or to designers, creators and the rest. That way lies Hegel and therefore perdition. [13]

Price and the scientists he mentions are of course free to devise alternative theoretical systems without the Past Hypothesis. So far there is not much on the table. And what is on the table doesn’t look very explanatory, at least according to my (perhaps idiosyncratic) intuitions about explanation. (I try to back up this claim in section 6.)