Tuesday, September 12, 2023

On two problems for non-Humean accounts of laws

There are three main views of laws:

  • Humeanism: Laws are a summing up of the most important patterns in the arrangement of things in spacetime.

  • Nomism: Laws are necessary relations between universals.

  • Powerism: Laws are grounded in the essential powers of things.

The deficiencies of Humeanism are well known. There are also deficiencies in nomism and powerism, and I want to focus on two.

The first is that they counterintuitively imply that laws are metaphysically necessary. This is well-known.

The second is perhaps less well-known. Nomism and powerism work great for fundamental laws, and for those non-fundamental laws that are logical deductions from the fundamental laws. But there is a category of non-fundamental laws, which I will call impure laws, which are not derivable solely from the fundamental laws, but from the fundamental laws conjoined with certain facts about the arrangement of things in spacetime.

The most notorious of the impure laws is the second law of thermodynamics, that entropy tends to increase. To derive this from the fundamental laws, we need to add some fact about the initial conditions, such as that they have a low entropy. The nomic relations between universals and the essential powers of things do not yield the second law of thermodynamics unless they are combined with facts about which universals are instantiated or which things with which essential powers exist.

A less obvious example of an impure law seems to be conservation of energy. The necessary relations between universals will tell us that in interactions between things with precisely such-and-such universals energy is conserved. And it might well be that the physical things in our world only have these kinds of energy-conserving universals. But things whose universals don’t conserve energy are surely metaphysically possible, and the fact that such things don’t exist is a contingent fact, not grounded in the necessary relations between universals. Similarly, substances with causal powers that do not conserve energy are metaphysically possible, and the non-existence of such things is at best a contingent fact. Thus, to derive the law of conservation of energy, we need not only the fundamental laws grounded in relations between universals or essential powers, but we also need the contingent fact that conservation-violators don’t exist.

Finally, the special sciences (geology, biology, etc.) are surely full of impure laws. Some of them perhaps even merely local ones.

One might bite the bullet and say that the impure laws are not laws at all. But that makes the nomist and powerist accounts inadequate to how “law” gets used in science.

The Humean stands in a different position. If they can account for fundamental laws, impure laws are easy, since the additional grounding is precisely a function of patterns of arrangement. The Humean’s difficulty is with the fundamental laws.

There is a solution, and this is for the nomist and powerist to say that “law of nature” is spoken in many ways, analogically. The primary sense is the fundamental laws that the theories nicely account for. But there are also non-fundamental laws. The pure ones are logical consequences of the fundamental laws, and the impure ones are particularly important consequences of the fundamental laws conjoined with important patterns of things in nature. In other words, impure laws are to be accounted for by a hybrid of the non-Humean theory and the Humean theory.

Now let’s come back to the other difficulty: the necessity worry. I submit that our intuitions about the contingency of laws of nature are much stronger in the case of impure laws than fundamental laws or pure non-fundamental laws. It is not much of a bullet to bite to say that matching charges metaphysically cannot attract—it is quite plausible that this is explained by thevery nature of charge. It is the impure laws where contingency is most obvious: it is metaphysically possible for entropy to decrease (funnily enough, many Humeans deny this, because they define the direction of time in terms of the increase of entropy), and it is metaphysically possible for energy conservation to be violated. But on our hybrid account, the contingency of impure laws is accounted for by the Humean element in them.

Of course, we have to check whether the objections to Humeanism apply to the hybrid theory. Perhaps the most powerful objection to a Humean account of laws is that it only sums up and does not explain. But the hybrid theory can explain, because it doesn’t just sum up—it also cites some fundamental laws. Moreover, it may be the case that the patterns that need to be added to get the impure laws could be initial conditions, such as that the initial entropy is law or that no conservation-violators come into existence. But fundamental law plus initial conditions is a perfectly respectable form of explanation.


Fr M. Kirby said...

I am confused by this statement regarding powerism and nomism:

"The first is that they counterintuitively imply that laws are metaphysically necessary. This is well-known."

Is nomism really the claim that the laws of physics obtain because the underlying mathemtical relationships are necessary truths in some sense? (That is how I am trying to make sense of the definition given for nomism.) This seems a claim only made by those such as Tegmark who say that all equations are necessarily instantiated physically (i.e., physical reality is strictly identifiable with mathematical reality), hence there is a multiverse. For everybody else, I would have thought, while mathematical or logical necessity applies once certain axioms are accepted and their implications developed, this type of necessity (one that "obtains" for reationships between abstract objects) is never an absolute necessity for concreta but a conditional one, following an if-then structure. In particular, "if material objects exist that 'obey' these equations, then certain things will happen to them in accordance with those equations". However, the contingency referred to in your previous post means that which of the particular equation/s that are in fact actualised physical laws (out of the infinity of possible equations) is not necessitated, either mathematically or in any other way. Is nomism really inconsistent with any of that? If so, it would apply equally to the pure and impure laws.

As for powerism, if laws are grounded in things' essences, then any necessity of operation is still contingent upon the existence of the things in question. I just don't see the metaphysical necessity. But perhaps I am overinterpreting the phrase and misunderstanding completely.

I can't help but wonder whether nomism and powerism (construed as contingentist explanations by my reckoning) can be harmonised with each other by positing that substantial essences include necessarily rationally comprehensible Forms, and thus would be expected to conform to some sort of logically consistent mathematical pattern in their quantitative aspects and interactions with other substances. Perhaps the nomic view is simply equivalent to considering the powers of essences as they interact, holistically.

On another point, the law of conservation of mass-energy MAY in fact be broken at the cosmic scale due to accelerated expansion and dark energy, and is said to be broken temporarily by virtual particles at QM micro-scales according to some (but not all) physicists. In any case, these qualifications of energy conservation are dependent on the laws already known.

Fr M. Kirby said...

Sigh. I should have previewed first. The last sentence of my longest paragraph above should have read something like this: "If nomism is consistent with accepting the fundamental metaphysical contingency I have outlined, then that acceptance would apply equally to the pure and impure laws."

Also, my second last paragraph should have "quantitatively" after "considering" in its last sentence.