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# LAWS, SCIENTIFIC

On the standard picture there are three kinds of facts. Some facts cannot have been otherwise. These facts include the conceptual truths (e.g., the fact that Rebecca is taller than Abe if Abe is shorter than Rebecca) and the mathematical truths (e.g., that 2 + 1 = 3). The remaining facts (i.e., the "contingent" ones) are divided between the other two classes: (1) the laws of nature (and their contingent logical consequences), such as the fact that all copper objects are electrically conductive, and (2) the "accidents," such as the fact that Jones has ten fingers and the fact (one can suppose it is a fact, though humanity may never discover it) that there never exists a solid gold cube larger than a cubic mile.

It is widely believed that one of science's chief goals is to discover the laws of nature. Philosophers have studied the role that the concept of natural law plays in scientific reasoning.

## Laws versus Accidents: Necessity and Counterfactuals

An accident just happens to obtain. A gold cube larger than a cubic mile could have formed, but the proper conditions for it to have done so happened never to arise. In contrast, it is no accident that an electrically insulating copper object never formed, since the natural laws prohibit such a thing. In short, events must conform to the laws of naturethe laws have a kind of necessitywhereas accidents are mere coincidences. The kind of necessity characteristic of laws (and their logical consequences) is usually called nomic or physical necessity to distinguish it from various stronger varieties of necessity (such as logical, conceptual, and metaphysical necessity) possessed by various facts that cannot have been otherwise.

Had Bill Gates wanted to build a large gold cube, then there would have been a gold cube exceeding one cubic mile. But even if Gates had wanted to build an electrically insulating copper object, all copper objects would still have been electrically conductive, since events are obliged to conform to the natural laws. In other words the laws govern not only what actually happens but also what would have happened under various circumstances that did not actually happen. The laws support counterfactuals (i.e., facts expressed by statements of the form "Had p been the case, then q would have been the case"). Consequently, scientists use the laws to ascertain, for example, the conditions that would have prevailed on Earth had Earth been ten times nearer to the Sun. The laws are preserved under this counterfactual supposition. In contrast, an accident would not still have held, had p been the case, for some p that is nomically possible (i.e., consistent with all the laws' logical consequences).

Counterfactuals are notoriously context sensitive. For example, when one is emphasizing how baseball pitching talent has declined over the years, one might correctly remark that were Babe Ruth playing in the major leagues today, he would hit an astounding 120 home runs in a single season. But in a different context, one might correctly remark that were the Babe playing today, he would hit only ten homers per season, since by now he would be an old man. Which facts are to be held fixed under some counterfactual supposition, and which are allowed to vary, depends somewhat on one's interests in entertaining that supposition. But it appears that in any context, the laws would still have held under every nomic possibility. This idea is sometimes called nomic preservation.

## Laws versus Accidents: Explanation and Induction

Laws have an explanatory power that accidents lack. For example, a certain powder burns with yellow flames, not another color, because the powder is a sodium salt and it is a law that all sodium salts, when ignited, burn with yellow flames. The powder had to burn with yellow flames considering that it was a sodium salt. This "had-to-ness" reflects the law's necessity. In contrast, that a couple has two children is not explained by the fact that all the families on the couple's block have two children, since this fact is accidental. Were a childless couple to move onto the block, this couple would not encounter an irresistible opposing force.

One believes that it would be mere coincidence if all U.S. presidents elected in years ending in 0 died in office. Hence, one's discovery that Warren Harding (elected in 1920) died in office fails to justify raising one's confidence that whoever was elected in 1840 died in office. A candidate law is confirmed differently: That one sample of a given chemical substance melts at 383 degrees (in standard conditions) is evidence, for every unexamined sample of that substance, that its melting point is 383 degrees (under standard conditions). This difference in inductive role between laws and accidents seems related to the fact that laws, unlike accidents, express similarities among things that reflect their belonging to the same natural kind. The electron, the emerald, and the electromagnetic force are all natural kinds, whereas the families on a block and the gold cubes do not form natural kinds (though gold objects, cubical and otherwise, constitute a natural kind).

## Difficulties Distinguishing Laws from Accidents

The previous discussion is the standard view of the scientifically relevant differences between laws and accidents. Insofar as the same claims play all these special roles, scientific reasoning apparently recognizes an important distinction here, which philosophers label as the difference between accidents and laws. (Obviously, this distinction involves what laws do rather than which facts happen to be called "laws"; Archimedes' principle of buoyancy, the axioms of quantum mechanics, and Maxwell's equations are all laws of physics.) However, it is notoriously difficult to capture the laws' special roles precisely.

For example, suppose one tries to distinguish laws from accidents on the grounds that laws support counterfactuals differently from accidents. That a car's maximum speed on a dry, flat road is a certain function of its gas pedal's distance from the floor is not a law (since it reflects accidental features of the car's engine). Nevertheless, this function supports counterfactuals regarding the car's maximum speed had the pedal been depressed to one-half inch from the floor, though not had certain changes been made to the engine. Indeed, all gold cubes would still have been smaller than a cubic mile even if Jones had been wearing a different shirt today. Of course, there are some nomic possibilities under which the gold-cubes generalization would not still have held. But circularity threatens if one uses the concept of nomic possibility to delimit the range of counterfactual suppositions under which a fact must be preserved for that fact to qualify as a logical consequence of the laws.

Likewise, a car's pedal-speed function, despite being accidental, can apparently be confirmed inductively. Moreover, when coupled with the road's condition and the pedal's position, it can explain the car's maximum speed. So although a fact's lawhood apparently makes a difference to science, it is difficult to identify exactly what difference it makes. This problem's stubbornness has led some philosophers to suggest that it is a mistake to distinguish laws sharply from accidents. There are merely various facts, each having a range of counterfactual suppositions under which it is preserved.

## Are there Laws Outside of Fundamental Physics?

Some so-called laws are plainly accidentsif they are true at all. Kepler's first law of planetary motion (that planets trace elliptical orbits) presupposes that the planets' masses happen to be negligible compared to the Sun's (since otherwise, the planets would be disturbed by their mutual gravitational influences) and that no body collides with a planet, knocking it out of its orbit. Some philosophers believe that the fundamental laws of microphysics (whatever they turn out to be) are the only genuine natural laws. This opinion is sometimes prompted by the fact that all events are ultimately nothing but the outcome of microphysical processes governed by the fundamental laws.

However, along with the laws of fundamental physics there might seem to be additional laws holding independent of the universe's microphysical details. The second law of thermodynamics, according to which the entropy of a closed system is likely to increase, seems not to reflect any peculiarities of the fundamental forces governing the universe's ultimate constituents; even if gravity had been twice as strong as it actually is, for example, the perfume molecules from a recently opened bottle would be more likely to spread quickly throughout the room than to remain in the bottle. Likewise, the principle of natural selection, according to which fitter traits are more likely to increase their prevalence in a closed population, seems like it would still hold whatever the laws of fundamental physics might have been.

Additionally, the second law of thermodynamics appears to require that certain initial microconditions be rarefor example, that the perfume molecules within recently opened bottles not usually be arranged so that whenever one molecule threatens to escape from the bottle, another happens to come along and knock it back inside. That the perfume molecules in recently opened bottles are indeed not so coordinated would seem to be an accident rather than a nomic necessity. Accordingly, perhaps the second law is not a law at all.

The principle of natural selection is perhaps also not a law, but a conceptual truth. That a trait is "fitter" in a given environment may simply mean that it is more likely to become increasingly common in subsequent generations. Nevertheless, both the second law of thermodynamics and the principle of natural selection appear to undergo inductive confirmation, to support counterfactuals, and to explain events in the manner of natural laws.

## Laws of Inexact Sciences: the Problem of Ceteris Paribus

A "special" or "inexact" science (such as anatomy, ballistics, ecology, economics, marketing, or psychology) might appear to seek (or perhaps even to have already found) facts that in these sciences play the various roles characteristic of laws. However, there are three main obstacles to regarding Boyle's law (that the product of a gas's pressure P and its volume V is constant) as a law of gases, to regarding Gresham's law (that agents hoard sound money and spend currency of more dubious value) as a law of economics, or to regarding the area law (that larger islands have greater biodiversity) as a law of island biogeography. Each of these obstacles has persuaded some philosophers to deny that inexact sciences have laws.

First, any such "law" comes with a ceteris paribus qualification. Though ceteris paribus means roughly "all other things being equal," a given qualification may be better captured as the idea that the specified correlation holds "normally," "in the ideal case," "in the absence of disturbing factors," or as long as certain other factors have certain values. The law is "hedged" in some way. For example, the gas in a container departs significantly from Boyle's law when its temperature is changed, some of the gas escapes, or the pressure is high. These circumstances are ruled out by the ceteris paribus proviso to Boyle's law. But what exactly does "PV is constant, ceteris paribus " mean?

If it means that PV is constant unless it is not, then the "law" is a trivial, noncontingent truth rather than an interesting discovery. If instead ceteris paribus is shorthand for a list of every factor allowed by fundamental microphysics and able to cause a gas's PV to vary, then Robert Boyle could not have discovered his law, since he did not know some of these factors (e.g., gas molecules adhering to the container's walls or attracting one another). Alternatively, some philosophers contend that Boyle's law describes only fictitious "ideal gases" that lack any interfering factors. But then it is unclear how observations of actual gases could confirm Boyle's law or how knowledge of Boyle's law could justify scientists in using it to predict the behavior of actual gases. Boyle had neither the concept of an ideal gas nor an account of what makes a gas ideal (e.g., that it consists of molecules without mutual attraction and occupying no finite volume). Such an account is not part of Boyle's law. Rather, the extent to which an actual gas has constant PV is explained by the extent to which it resembles an ideal gas.

Apparently then, ceteris paribus in Boyle's law refers only to the disturbing factors of which Boyle was aware (high pressure, changes to the gas's temperature, and so forth). There may be no complete list of these factors. Obviously (to shift examples), Gresham's law does not apply if the society is wiped out, if its members believe that hoarding the sounder currency causes illness, and so forth. Part of understanding Gresham's law is knowing how to recognize whether some factor qualifies as disturbing. One can catch on to which factors these are without having to read a complete list of them. (Nonexperts may even [in an attenuated sense] understand the ceteris paribus proviso without being able to tell themselves whether some factor qualifies as disturbing, just as they understand other technical terms: by virtue of knowing who the relevant experts are to whom they should defer.)

## Laws of Inexact Sciences: the Problem of Truth

However, societal events are ultimately nothing but the outcomes of microphysical processes. Certain sequences of microevents permitted by the fundamental laws of physics involve a society's members hoarding the weaker currency and spending the sounder. In one such sequence each member of the society happens whenever he or she spends money to forget momentarily which currency is sounder, because as chance would have it, some neuron in each agent's brain behaves at that moment in a manner that the fundamental microlaws deem extremely unlikely, but nevertheless possible. The ceteris paribus proviso to Gresham's law does not rule out this freakish sequence of events, since economists surely do not need to grasp the subtleties of fundamental microphysics to understand the proviso to Gresham's law.

In other words, not all exceptions to a macrolevel "law" can be specified in the vocabulary of the macroscience. For example, it might require physics (or at least neurology) to specify certain circumstance in which an agent would depart from a psychological "law." The ceteris paribus proviso fails to cover those exceptions.

This is the second obstacle to regarding inexact sciences as having genuine laws: The alleged laws are false or, if true, merely accidentally so. Perhaps, however, one should relax the requirement that genuine laws be exceptionless in favor of holding that a law be sufficiently accurate for the relevant purposes. The proviso to Boyle's law neglects to mention a host of petty influences that make the PV of actual gases vary somewhat. Still, Boyle's law with its proviso (which rules out the major interfering factorsthe ones that scientists cannot afford to neglect) is often enough close enough to the truth for various purposes in chemistry, theoretical and practical. Fully understanding Boyle's law requires knowing the range of purposes for which it can safely be applied. Likewise, the freakish sequence of neural events mentioned earlier is too rare to make Gresham's law unreliable for the purposes of economics.

The limited range of a special science's interests influence which facts qualify as laws of that science. Consider another example: The human aorta carries all the body's oxygenated blood from the heart to the systemic circulation. This reference to "the human aorta" (a generic), rather than to all or to most human aortas, apparently indicates that one is dealing here with a policy of drawing influences that, although fallible, is sufficiently reliable for certain purposesin this case for forming expectations about medical patients in the absence of more specific information regarding them. In human medicine this fact about the human aorta apparently functions as a law in connection with counterfactuals, explanations, and inductions. However, this aorta fact is merely an accident of natural history; it might not have held had evolutionary history taken a different path. Still, medicine does not treat evolutionary history as a variable. A physician might say that the shooting victim would not have survived even if he or she had been brought to the hospital sooner, since the bullet punctured his or her aorta and the human aorta carries all the body's oxygenated blood from the heart to the systemic circulation. (This aorta fact would still have held had the victim been brought to the hospital sooner.) But it would not be medically relevant to point out that the victim might have survived had evolutionary history taken a different course. Accordingly, that the human aorta carries all the body's oxygenated blood to the systemic circulation may be a law of human physiology even if it is an accident of physics.

## Laws of Inexact Sciences: the Problem of Necessity

But (to shift examples) even if the law that larger islands have greater biodiversity (all other thingssuch as their distance from the mainlandbeing equal) is sufficiently reliable for the purposes of island biogeography, what makes this fact an island-biogeographical law? What makes it necessary? This is the third obstacle to inexact sciences having genuine laws of their ownthat is, to their being autonomous.

Recall nomic preservation : that the laws would still have held under any counterfactual supposition that is logically consistent with every law. There appears to be no set of truths that is closed under logical consequence and that contains accidents (except the set of all truths) where every member of the set would still have been true under every counterfactual supposition that is logically consistent with every member of the set. Accordingly, it has been suggested that a truth n is a nomic necessity exactly when n belongs to a stable set, where a set is stable exactly when it includes every logical consequence of its members, it does not contain every truth, and its members are not only true but also all preserved under as broad a range of counterfactual suppositions as they could all logically possibly benamely, under every supposition that is logically consistent with every member. On this view necessity involves possessing maximal invariance under counterfactual perturbations. No necessity is possessed by an accident, even one (such as a car's pedal-speed function) that would still have held under many counterfactual suppositions. (The set consisting of a car's pedal-speed function, with its logical consequences, is unstable since its members would not all still have held under engine alterations with which the pedal-speed function is logically consistent.) Stability allows one to draw a sharp distinction between laws and accidents. It also gives one a way to escape the circle involved in specifying the nomic necessities as the truths that would still have held under every nomic possibility.

This conception of nomic necessity can easily be relativized to particular sciences. Perhaps the area law belongs to a set of claims that are all sufficiently reliable for the purposes of island biogeography, where the set does not contain all such claims and where its members would all still have been sufficiently reliable under any counterfactual supposition that is not only consistent with all of them being reliable but also relevant to island biogeography. In that case the set's members are collectively as resilient under counterfactual suppositions relevant to island biogeography as they collectively could be. Therefore, they possess nomic necessity for island biogeography.

On this view a special science's laws need not include every detail of the fundamental microphysical laws. For example, biological species would still have been distributed according to the laws of island biogeography (if there are any such laws) even if creatures were made of a continuous rigid substance rather than molecules, contrary to microphysical laws. Whether a given special science is autonomous remains for scientific research to discover. Whether the fundamental microphysical laws are privileged among the natural laws (e.g., in having greater generality or being strictly true) remains philosophically controversial.

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Marc Lange (2005)