In my last post about the felt need for “explanations” when we hear or read about an episode of interesting coincidences, I mentioned something that needs perhaps a bit of an explication.
The phenomenology of this felt need for explanations here points us ultimately to a form of lawlike necessity which is independent of the succession of events. This is not to say that such a necessity actually obtains in the world; it just means that this is what is ultimately expected in this need: it is, so to speak, the implied form of admissible explanations. But the considerations of counterfactuals point to a form of necessity, and our various findings that saw the phenomenon (or the need for explanation) disappear — go out of phase, so to speak — suggested that we’re looking for a type of necessity that has nothing to do with one event bringing another about. I have already gestured briefly at the (somewhat rarer) type of explanation we’d have to look for, given these directions we extracted from the phenomenology.
Explanations based on nomic constraints have the characteristics we’ve uncovered. Let’s go through a typical example, to understand how such explanations work. I’ll use one from the physics of special relativity. So here’s a phenomenon that “needs explanation”: you have two exactly synchronized high-precision clocks, one of which you put on a fast airplane, while you keep the other with you at your ground location; very soon, the clocks diverge, with the one on the plane running slower. What’s going on here?
An explanation for this phenomenon would be expressed in a singular explanatory statement, roughly like so: “The plane’s clock runs more slowly than clocks on Earth because it is moving at high speed relative to the Earth’s surface.” To get at the underlying laws, let’s look first at a more general formulation: “Clocks moving at high speed relative to the Earth’s surface run slower (than clocks on the surface).” This is not yet the most generalized formulation possible, of course, but we can already use this form to probe whether we have a lawlike connection. We do that using counterfactuals:
“Had we put a different, identical clock on the same plane, would it also have run slowly?” — Yes, because the effect follows from the high-speed motion, not from the particular clock.
“If I had kept this clock on Earth, would it have run slowly?” — No, because then there would have been no relative motion.
“If I had placed it on a geostationary satellite, would it have run slowly?” — No, because there would be no high-speed motion relative to Earth’s surface. (Actually, it would run faster, because the weaker gravitational field also influences how fast time runs; this, however, is no longer special but general relativity, and I’ll leave it aside here.)
The counterfactual probing points to a structural necessity: whenever the condition (of high-speed relative motion) holds, the phenomenon occurs, regardless of the particulars of the object involved. Further probing would reveal more of the specifics involved in this condition: it doesn’t have to be a fast plane, for example (the phenomenon can be observed even with cars, if measured with sufficiently precise instruments). The most general condition which still holds would be in terms of any time measurement at all (no specific clocks) and any relative movement (not just on Earth, and not just in vehicles, etc.). It would still be necessary (support counterfactual scenarios) in the same way. But note that it isn’t based on anything happening that would bring about the clock’s slower movement. (There is no “cause” here, in the sense that we’d have to introduce preceding events.) It’s based on the structural features of space, time, and relative motion: namely, the lawlike constraint that no motion can be faster than the velocity of light, and its consequences on the calculation of speed, lapsed time, covered space, and so on.
There are nomic constraints like that in other areas (think of the second law of thermodynamics, or the Heisenberg uncertainty principle). The term “constraint” refers to the logical form which an explanation based on it will take: structural features (such as the topology of spacetime, or the total amount of entropy) are restricted or limited in certain (often quantifiable or at least formalized) ways, and thus can be used to explain phenomena. (Compare this to the logical form a causal explanation would take: there, a preceding and a succeeding event are identified, and a necessary connection, i.e. a causal law, holding between the types of these events or their qualities is what explains why the latter occurred following the former.) The term “nomic” (“lawlike”) refers to the necessity with which the constraint holds: it is invariant over all possible scenarios — which is why we can probe such necessity using counterfactual statements.
The examples I have given so far, which all come from physics, are very general and quite universal. This, however, has primarily to do with the kind of explanation that is often sought in physical theories: namely, explanations that refer to the most general, universal laws that govern physical phenomena (in the most unified way, it is typically added, i.e. with the smallest number of laws, in their most simple and elegant formulations, which together predict and explain all observable physical phenomena). But the lawlike character does not depend on this generality or universality: it only expresses a specific form of necessity. There can be less general, or we might say, more local laws (nowadays often called “ceteris paribus laws”); and consequently, less general, more local nomic constraints (which are just one kind of laws that can underlie explanations). These would still have the nomic character (and thus be stable under counterfactual scenarios), but apply only within a more limited domain. The constraint is then defined by the structural features of a particular system, rather than something very general (such as spacetime or entropy).
Local nomic constraints like that are used in physics, too (with the restriction to a particular system clearly specified). As an example, I’ll use the conservation of momentum in an isolated Newtonian system: if two ice skaters push off against each other on a frictionless surface, the sum of their momenta will be the same after the push as before it. The conservation law is explicitly restricted to these two bodies that make up the system; it will no longer hold if an external force acts on them (e.g. a gust of wind catches one skater’s jacket and speeds her up). But within the structural conditions that define the isolated system, it holds with the same necessity as any of the more general physical laws we have discussed. The explanation for why the skaters move apart, each with their particular speed, is governed by the momentum constraint: any configuration of bodies in that system must satisfy it. No internal causal sequence (say, one skater deciding halfway through the push to stop moving) could produce an outcome that violates it, because the constraint fixes the total momentum of the system regardless of such events. We can probe the lawlike character again with counterfactuals: had one skater deflected sharply at the last moment to avoid the other, they would have passed each other and continued in new directions, but with the total momentum exactly the same as before. We can come up with other scenarios (different pushes, different masses, arbitrary changes of direction) but none of them, so long as the system remains isolated, would result in a different total momentum. There is no counterfactual scenario in which the sum changes; that’s what makes it a lawlike (though local) constraint.
If I’m correct in my analysis of the felt need for explanation with our phenomenon, then, it is explanations based on such nomic constraints (most likely of the more local sort) that we’re ultimately looking for. So the next question would be, of course: what would a nomic constraint look like which explains our phenomenon (and does such a constraint, in fact, exist)?
