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A Brief Argument for Descriptivism About Laws of Nature

Isaac Newton believed that F=ma was a law of nature. Leave aside for the moment the question of whether he was right - some philosophers might think that, although it turned out simply to be an approximation that worked well for matters of ordinary experience, it still counts as a legitimate law. That's not what I'm concerned with right now. What I'm concerned with is what it means to claim that F=ma is a law of nature. Because of this, I may sloppily speak of F=ma as having a referent when, according to some theories I will be considering, it might not have one at all. Since F=ma is merely a convenient example, this should not undermine the argument.

Those who accept the governing conception of laws of nature hold that the claim that F=ma is a law of nature is the claim that there is some thing or collection of things in the universe or some property or collection of properties of the universe and/or its contents that makes objects accelerate at a rate of F/m whenever a force is applied. They further claim that, strictly speaking, this thing or collection of things or property or collection of properties is the law.

In order to claim this, they must claim either (1) that the collection of symbols "F=ma" (in some context) refers to the law (or would refer to the law if such a law existed), or (2) the sentence "F=ma is a law of nature" contains some sort of idiom, so that we actually mean "F=ma describes the effects of a law of nature." I claim that both of these analyses are implausible.

(1) claims that "F=ma" refers to something very different than, for instance, "f(x)=y+5" or "y=mx+b", but why should this be so? Shouldn't all equations refer (if they refer at all) to the same sorts of things? Shouldn't an equation be a type of mathematical object, and shouldn't all of these refer to equations? One response would be to simply claim that the thing that makes objects accelerate at a rate of F/m is an equation, a mathematical object. This, however, does not seem to me to have much inherent plausibility. A better try would be to say that in the context of physics the reference passes beyond the equation to the law which makes the world obey the equation. This idea will be dealt with in our treatment of (2), to which we now turn.

(2) seems implausible, if for no other reason, simply because this doesn't strike me as the way we talk. If you were to ask a physicist who, sadly, had had little exposure to philosophy of science or metaphysics, whether F=ma was a law or merely described a law, I expect you would get a funny look. Nevertheless, let's consider for a moment the view that, whatever the syntax may indicate, it is true, at least in some contexts, that the referent of F=ma is an equation or some such mathematical object, and this object describes a law of nature. What sort of thing might this law be? Remember that we are claiming that the law, whatever it is, makes objects accelerate at a rate of F/m. The law is one of the things in the universe, but it is clearly not a physical object or a force or a quantity of energy. Although people who call themselves physicalists might believe in it, it is not really physical in the ordinary sense of the word. Rather, as I have argued before, it is at least something very like the Heraclitean logos, or perhaps even something more like a conventional deity. Philosophers who believe in a more Aristotelian theory according to which the law is a collection of potentialities, where potentialities are properties of physical things, will be in a somewhat better position to continue maintaining physicalism.

Suppose that there was such a thing. Do we really mean to make a metaphysical assertion about its existence when we say "F=ma is a law of nature?" I am highly doubtful of such a thing. Rather, "F=ma" is a description, and a law is simply an accurate description which has certain properties that I won't attempt to specify here.