Laws, necessities and properties: some old views, some new ones, and some arguments
Is it metaphysically necessary that like charges repel? One might think so: one might think that "charge" is partly defined by its theoretical role, so that this claim comes out analytic. Or one might think that science reveals to us the essence of properties, and that it is part of this essence of charge that like charges repel.
If that law about charges is metaphysically necessary, one might suspect that quite generally, nomological necessity coincides with metaphysical necessity (though see below for an argument against this suspicion):
N1) The actual laws are true at all possible worlds.
(N1) doesn't entail that the actual laws are true laws at all worlds. But there are reasons to believe this stronger claim, too: how could it be a merely accidental regularity (a truth, but not a law) in some world w that like charges attract? Wouldn't that entail that there is another world w' where this regularity fails to obtain? (Otherwise what makes the regularity accidental?) But the existence of w' contradicts (N1). So (N1) very naturally leads to
N2) The actual laws are laws at all possible worlds.
Nevertheless, one could resist that move. Take a world where there are no instances of charge. Must the laws of such a world contain (vacuous) claims about charge? Perhaps not. Certainly not if laws are anything like the simplest and best theories of what actually goes on in a world. If so, it will still be true at this world that like charges repel (albeit vacuously true), but it will not be a law.
On the other hand, even at the world without charge, wouldn't there be substantive counterfactuals about charge: if x and y had instantiated like charges, they would have repelled each other, rather than attracted each other or turned into elephants? What makes that counterfactual true if not the fact that there prevails, even at this world, a certain law governing charge?
At any rate, what is clear is that (N2) is perfectly compatible with worlds without instances of charge. That is, it does not entail:
N*) The actual laws are non-vacuous laws at all possible worlds (where being non-vacuous means having instances).
(N*) is incredible: why couldn't there be a world without instances of charge? The only argument I can think of for (N*) starts off from a combination of (N2) and a ban on vacuous laws. But why would anyone who rejects vacuous laws -- say, a strict regularity theorist -- accept (N2)?
A more reasonable strengthening of (N2) would be to rule out worlds where something is a law that is not a law in the actual world. (N2) allows for such worlds: it only demands that the laws of every world are a superset of the actual laws. But reasoning roughly similar to that leading from (N1) to (N2) leads from (N2) to
N3) at all worlds w, something is a law at w iff it is an actual law.
For how could it be an accidental regularity at the actual world that all Fs are Gs, but a law at another world? Wouldn't that entail that there is yet another world w' where some Fs are not Gs? But how could there be if laws are in general -- not only accidentally -- grounded in analytic or essential truths about properties, about F-ness and G-ness in this case?
(N*) also has an interesting converse:
N**) Any law at any world is a non-vacuous law at the actual world.
(N**) entails that there are no alien properties instantiated at other worlds and governed by laws there. One can get to (N**) by combining (N3) with a general ban on alien properties (i.e., properties not instantiated in the actual world). Again, this is rather incredible: it means that when we conceive of a world where, say, the magnitude of the electrostatic force between two point charges is inversely proportional to the cube of their distance (rather than the square), what we conceive of is absolutely impossible; it's not just a situation involving some other property, schmarge, which behaves a lot like charge but lacks some of its essential characteristics. If (N**) is true, there is no schmarge. And as with (N*), I can't think of any good argument for (N**). In particular, every reason for banning alien properties (like Armstrong's recombinatorialism) seems to be at odds with (N3).
Does anyone believe in (N**)? Sydney Shoemaker doesn't seem to like schmarge worlds very much, see fn.11 of "Causal and Metaphysical Necessity" (1998). But he gives no argument at all against them, and much of what he says appears to entail their existence.
Alexander Bird defends a position he calls "Strong Necessitarianism" in a paper called "Strong Necessitarianism" (2004). But his weak/strong distinction is orthogonal to my distinctions. He seems to believe that just as "necessarily, x=x" is only strictly true if x exists at all worlds, so "necessarily, all Fs are Gs" is only strictly true if the properties F and G exist at all worlds. I don't understand why he believes that, nor what he even means by a property "existing" at a world: he definitely doesn't mean "having instances". Anyway, his 'strong necessitarianism' then claims that the actual laws about a property F are strictly true at all worlds, whereas his 'weak necessitarianism' claims that they are true only at worlds where F exists. If existence of a property meant having instances, Bird's strong view would be roughly equivalent to (N*), ruling out worlds without charge, but not ruling out worlds with schmarge.
Let's return to the initial motivations for necessitarianism. I mentioned two: on one account, the laws are analytic, on the other, they are a posteriori necessities about fundamental properties. In a sense, the first account is about property terms, whereas the second is about the properties themselves. There are some interesting combinations of these issues.
First, properties. One might believe that so-called fundamental properties like charge or mass have at least some of their causal or nomic profile essentially: if something doesn't behave like charge in any way, it isn't charge.
P1) Properties like charge have some of their causal/nomic profile essentially.
There are different ways of incorporating this into a systematic metaphysics. One is a kind of counterpart theory about those properties: on this account, possible worlds are completely determined by their causal/nomic structure; the identity of the nodes in the structure -- the properties -- is irrelevant. (In other world, there are no quiddistic differences between worlds.) When we pick out a property, we first of all pick out a node in the structure of the actual world. Other nodes in other structures resemble this one in various (extrinsic) respects, and thereby qualify as its counterparts. Alternatively, one could say that properties do have an intrinsic such-ness, a quiddity, which by brute metaphysical necessity only occurs at certain nodes in possible structures and not at others. (This view would be compatible with quiddistic differences.)
Most necessitarians go for a stronger view:
P2) Properties like charge have all of their causal/nomic profile essentially.
The reasoning behind this step is a bit murky. Shoemaker says it would be hard to distinguish between accidental and essential parts of the profile. But the same is true for the properties of individuals, yet we don't believe that all our properties are essential to us. In fact, just as the silly claim about individuals, (P2) is incompatible with how we actually talk about counterfactual situations: after some indoctrination, most of us are inclined to say that (given certain facts about the actual world) if some stuff at some possible world isn't H2O, then it can't be water; but no-one is inclined to say that if some stuff at some world doesn't cover 60% of the earth, then it can't be water. Nor would we say that it can't be water if it doesn't boil at 100 degrees at an atmospheric pressure of 0.101325 MPa.
Of course, if (P2) is true, then presumably water couldn't fail to boil under these conditions. But unlike all the Kripkean cases of a posteriori necessities, this can't be established by conducting the relevant thought experiments. On the contrary, it presupposes that such thought experiments are highly unreliable. But on this basis, we need a completely different motivation for the necessity claims. The best strategy is perhaps to strengthen (P2) even further:
P3) Properties like charge are metaphysically individuated by their total causal/nomic profile.
That is, the profile is not only essential to those properties, but also constitutes an individual essence: something is charge iff it has the right profile. This is what most necessitarians seem to believe. The reasoning would then go as follows. Suppose it's a law that something being F causes it to be G. So being F confers G-causing powers. But properties are individuated by the powers they confer. So it is part of F's nature to confer G-causing powers.
I don't find any of the arguments for (P3) very convincing. The best ones draw upon problems with quidditism: quiddistic differences giving rise to ignorance about properties or being scientifically otiose. But one can reject quidditism without accepting (P3), e.g. by individuating properties by only some of their causal/nomic profiles. And all in all, it seems to me that the problems with (P3) -- being incompatible with our linguistic practice, denying the possibility of distinct properties playing symmetrical roles, making nonsense of the standard treatment of counterfactuals (which requires miracles), leaving no room for real intrinsic properties and duplication, relying on brute dispositional properties ungrounded in anything categorical, etc. -- are far worse than these problems with quidditism.
Moreover, even (P3) isn't strong enough to entail even the weakest form of necessitarianism, (N1). (P3) will only render metaphysically necessary nomological necessities which spell out the causal powers of properties. But there are probably other kinds of nomological necessities as well. To use Kit Fine's example (from "The Varieties of Necessity", 2002), it might be true that for all events e there is a state s of the world prior to e such that s is nomologically sufficient for e. And if this is true, it is quite likely itself a nomological necessity. But it doesn't mention any specific properties. So even if (P3) is true, there is no reason to believe this nomological necessity is a metaphysical necessity.
And certainly nothing in the vicinity of (P3) gives us any reason to believe (N*) or (N**).
OK. So much for properties. Now for property terms. One important distinction here is the one between broadly descriptivist accounts of terms like "charge" and broadly Kripkean accounts. On the descriptivist account, "charge" is at least partly defined by its theoretical role: it is analytic, not merely necessary, that if something doesn't even come close to satisfying [insert charge theory here], then it isn't charge. On the Kripkean account, nothing like this is analytic. For all we know a priori, as competent speakers of English, charge might turn out to be a property of surfaces that causes colour experiences in normal humans and has nothing at all to do with attraction or electromagnetic force.
The analyticity of the charge laws doesn't trivially entail their necessity. They might instead be a priori contingent, if they merely 'fix the referent' of "charge".
This leads to a more interesting distinction. Most necessitarians, and most anti-necessitarians, assume that terms like "charge" rigidly denote a certain property. Then it follows that if this property essentially plays role R, then "charge plays R" is a necessary truth; whereas if this property could equally well play the mass role, then "charge could play the mass role" is true.
But one might also suggest that "charge" is a non-rigid designator which, at any possible world, picks out what plays the charge role at that world, whether or not it is the same property that plays it here. "Charge" might, in other words, be synonymous with a non-rigidified description of the form "whatever plays this and that role". (Compare Lewis and Kim on "pain".)
This gives rise to some novel combinations, like:
quiddistic necessitarianism: our property names non-rigidly denote whatever quiddity plays the relevant role; so the laws (or at least some of them) are necessary, even though fundamental properties do not have any part of their causal/nomic profile essentially.
anti-quiddistic contingentism: fundamental properties are individuated by their causal/nomic profiles, yet our property names do not rigidly track these properties (instead, they might partly track a certain pattern of instantiation), so that all the laws are contingent.
I especially like the first option, quiddistic necessitarianism. It offers a way of accommodating the necessitarian intuition that something isn't charge if it doesn't behave like charge in a thoroughly anti-necessitarian metaphysics. And it is easily weakened to not lead into the implausible consequences of necessitarianism: for a quiddity to count as charge, it needn't completely satisfy our charge theory. It suffices if it roughly satisfies important bits of it; and whether it does can be vague and context-dependent. In effect, one gets the benefits of counterpart theory without really endorsing a counterpart theory for properties.