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.

Platonism and Ockham's razor

One of the main objections against Platonism is that it offends against Ockham's razor by positing a large number of fundamental entities. But the Platonist can give the following response: By positing these fundamental entities, I can reduce the number of fundamental predicates to one, namely instantiation. I don't need fundamental predicates like "... is charged" or "... loves ...". All I need is a single multigrade fundamental predicate "... instantiate(s) ...", and I can just reduce the claim that Jones is charged to the claim that Jones instantiates charge, and the Juliet loves Romeo to the claim that Julie and Romeo instantiates loving. In other words, the Platonist's offenses against Ockham's razor in respect of ontology are largely compensated for by a corresponding reduction of ideology.

Largely, but so far not entirely. For the Platonist does need to introduce the "... instantiate(s) ..." predicate which the nominalist has no need for. On pain of a Bradley-type regress, the Platonist cannot handle that predicate using her general schema.

(But maybe Platonist can go one step further. She can eliminate single quantifiers from her ideology, too, using the Fregean move of replacing, say, ∃xF(x) with Instantiates(Fness, instantiatedness). Extending this to nested quantifiers is hard, but perhaps not impossible. If that task can be completed, then it seems that our Platonist has gained a decisive advantage over the nominalist: she has only one fundamental predicate and no quantifiers other than names (if names count as quantifiers). Not so, though! For this move needs to be able to handle complex predicates F, and the property Fness corresponding to such a complex predicate will probably have to stand in various structural relations to other properties, and we have complication.)

Two problems for conspecificity as primitive

Here is something growing out of last night's neo-Aristotelian metaphysics class with Rob Koons. Suppose we take the relation of conspecificity as a primitive, in order to be a nominalist about species. (The context here is Aristotelian, so "species" may include "Northern leopard frog", but it may also include "electron".) Then we will have a hard time making sense of claims like:

1. Possibly, none of the actual members of x's species exist (in the timeless sense), but there is some member of x's species.

Suppose for instance x is an electron. Then, surely, there is a possible world where there are electrons, but none of the actual world's electrons exist. But to make sense of (1) on an account that takes conspecificity to be primitive would require a conspecificity relation between an electron in the actual world and an electron in the possible world. But how can there be a relation one of whose relata does not exist? (Intentional relations are like that, but I don't think we want conspecificity to be like that.) The realist about species doesn't have this particular problem. She just explains (1) by saying that if s is the species of x, then possibly none of the actual members of s exist but s nonetheless has a member. Also, if one takes conspecificity as primitive but allows the existence of non-actual individuals, the problem disappears, since then we can unproblematically relate a non-actual individual with an actual one.

The problem here is that of interworld conspecificity. What makes an individual a₁ in a world w₁ conspecific to an individual a₂ in w₂? If there is an individual a₂ in w₁ conspecific to a₁ who also exists in w₂ and is conspecific to a₂, by transitivity of (Aristotelian) conspecificity this is not a problem. We can generalize this solution by saying that a₁ in w₁ is conspecific to a₂ in w₂ provided that there are chains of worlds W₁,...,W_n and entities A₁,...,A_n such that

• W₁=w₁, W_n=w₂, A₁=a₁, and A_n=a₂
• b_i is in both W_i and in W_i+1 for i=1,...,n−1
• b_i and b_i+1 are conspecifics in W_i+1 for i=1,...,n−1.

For this approach to give a good account of interworld conspecificity it has to be the case that conspecificity is transitive and that species membership is essential. (But the approach can also work if species membership is not essential, as long as we have individual forms, and the membership of an individual form in a species is essential. For then we can give the story not in terms of chains of particulars, but chains of individual forms.)

The above account does, however, entail the following metaphysical principle:

2. Whenever worlds w₁ and w₂ contain individuals a₁ and a₂ who are members of species s (understood nominalistically), then there is a finite chain of possible worlds, starting at w₁ and ending at w₂, such that every pair of successive members of the chain has a common member of s.

Is (2) true? Well, it seems hard to come up with counterexamples to it, at least. If we could imagine a species whose possible members could be divided into two classes, A and B, such that no member of A could exist in a world that contains a member of B, then we would have a violation of (2). But I am not sure we have much reason to think such species exist.

But now consider a different problem for the account. Two photons can collide and produce an electron-positron pair. Suppose we are in a world where there are lots of photons, but only one collision has occurred, producing electron e (and a positron that I don't care about). We now want to be able to say this:

3. A pair of photons p₁ and p₂ jointly have the power of producing an electron.

Presumably this should reduce to some claim about how they have the power of producing a conspecific to e. But that is an extrinsic characterization of the power of the photons. Yet it is an intrinsic feature of the joint power of p₁ and p₂ that it is a power to produce an electron (and a positron). Moreover, supposing that no collisions occurred, and hence there was no e in sight, we would still want to be able to say this:

4. A pair of photons p₁ and p₂ jointly have the power of producing a conspecific to something that photons p₃ and p₄ jointly have the power of producing.

Tricky, tricky. Here is a suggestion. We slice powers, considered as particulars ("x's power to do A") finely enough that we can talk of a particular power that p₁ and p₂ jointly have (or maybe one has the power to operate on the other in some Aristotelian way), the power of producing an electron (this power can only be exercised together with a power to produce a positron). Now, we can talk of the primitive conspecificity not just of particles, but of productive powers, and we can characterize the conspecificity of two entities disjunctively:

5. e₁ and e₂ are conspecific (non-primitively) if and only if either e₁ and e₂ are primitively conspecific or e₁ results from the exercise of a power primitively conspecific to a power the exercise of which results in e₂ or e₁ results from the exercise of a power which results from the exercise of a power primitively conspecific to a power the exercise of which results in a power the exercise of which results in e₂ or ....

Assuming that powers are characterized by what they produce, any disjunct further down in the disjunction entails all the disjuncts further up in the disjunction. Now we can make sense of (3) and (4) in an intrinsic way, in terms of the conspecificity of the powers of producing electrons. Moreover, we can make the chain-of-worlds move as needed for non-primitive conspecificity. This will yield a very complicated analogue of (2), but that analogue will, if anything, be even more plausible than (2).

This is all too messy, but maybe mess is unavoidable.