An Argument Against the

Unification Account of Explanation

Michael Strevens

Draft of May 1999

Abstract

This paper argues that an increase in the known unifying power of

a theory is often not accompanied in an increase the perceived quality

of its explanations. The theory may explain many new things, but

it does not explain the old things any better just because it now ex-

plains the new things. This strongly suggests that unification accounts

of explanation are mistaken. I conclude with a discussion of the ex-

planatory role of unification in science. A surprising consequence of

the discussion is that unification has explanatory role only in a non-

Humean world, a world with real causal powers and laws of nature.

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1 The Unification Account of Explanation

According to unification accounts of explanation1 (Friedman 1974; Kitcher

1981, 1989), to explain a phenomenon2 is to show that it can be derived from

the same theory as many other phenomena, that is, to show that it belongs

to a set of phenomena which can be unified in the sense that they can all be

derived from a single theory.

A generic form of the unification account, then, might require that an

explanation of a phenomenon E do three things:

1. Present a theory T ,

2. Present a sufficiently large and perhaps diverse set of phenomena P to

which E belongs, and

3. Show that P can be derived in the right sort of way from T .

To flesh out the view, two things must be provided: an account of what counts

as deriving P from T in the “right sort of way”, and an account of what

counts as a “sufficiently large” (or sufficiently diverse) set of phenomena.

The central element in the latter account is usually a measure of something

called the “degree of unification” achieved by the derivation of P from T . The

1. The unification account is foreshadowed in Kneale (1949, 91–2) and Hempel (1965a,488).

2. “Phenomenon” in this paper will refer to any kind of thing that science claims toexplain, for example, events, sequences of events, laws, and ongoing “effects” such as theaurora borealis.

2

strength of the explanation given by T is—importantly for what follows—

then usually taken to be proportional to the degree of unification achieved.

In the remainder of this section, I will briefly summarize the unification

accounts of Friedman and Kitcher. Friedman holds that the derivation may

be any deductive argument. He defines the degree of unification achieved

by a derivation as a measure of how much smaller T is than P , where the

size of these sets is deemed proportional to the number of independently

acceptable lawlike sentences required to characterize the content of each.

(Friedman does not offer a precise characterization of “independent accept-

ability”. A necessary condition for independent acceptability, however, is

logical independence. Also left open is the question of what counts as a

“lawlike sentence”; possibly a certain class of universal generalizations, as in

Hempel and Oppenheim (1948, §6) is intended.) The account of explanation

is then roughly as follows: T explains E (together with everything in P) just

in case the degree of unification achieved by deriving P from T is greater

than zero (I omit some details here).

Kitcher agrees with Friedman that all derivation is by deductive argu-

ment (Kitcher 1989, §5). But not all deductive arguments are legitimate

derivations. To find out which kinds of derivation (or argument patterns,

as Kitcher calls them) are legitimate, one must look to the unifying theory,

which will include not only statements about the world (laws, facts and so

on), but also claims about what kinds of arguments may be used to derive

phenomena from these statements (Kitcher 1989, §4.6). That is, the theories

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themselves state which kinds of derivation are legitimate.

This raises the question of whether there is any limit on the kinds of

argument patterns that might be endorsed by a theory. Can a theory rec-

ommend an apparently non-explanatory argument such as A.B, therefore

B? Kitcher builds into his definition of unifying power a desideratum that

the argument patterns recommended by the unifying theories be stringent, a

condition which he argues counts heavily against intuitively non-explanatory

derivations such as that of A from A.B. An argument pattern is stringent to

the degree that it is “difficult to satisfy” (Kitcher 1989, 433). In particular,

a stringent argument pattern restricts the non-logical vocabulary that can

appear in its instantiations (the tighter the restriction, the more stringent

the argument pattern).3 Kitcher does not say so, but as I understand it, the

point of stringency is to restrict argument patterns to those that owe their

success to the existence of real patterns in nature. Since unification is an

attempt to identify such patterns, the stringency requirement is a natural

one for a unification theory to propose. This is a important topic, but as it is

tangential to the argument I present in this paper, I will say no more about

it.

Kitcher’s definition of the degree of unification is as follows (Kitcher 1989,

435). A theory T ’s unifying power:

3. This is just one component of stringency. The other is tightness of the restrictionthat an argument pattern puts on the logical form of its instantiations; again, the tighterthe restriction, the more stringent the argument pattern.

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1. Increases with the size of P ,

2. Decreases with the size of T , and

3. Increases with the stringency of the arguments recommended by T .

Kitcher’s conception of unifying power is very close to Friedman’s, but with

the notion of stringency doing roughly the work of the notions of independent

acceptability and lawlikeness.

What Kitcher does with the notion of unifying power, however, is rather

different. For Friedman, any unifying theory counts as explanatory. For

Kitcher only the most unifying theories count as explanatory. Kitcher calls

the set of theories that best unify all the phenomena4 the explanatory store.

A derivation of E from T explains E just in case T belongs to the explanatory

store (and the derivation is endorsed by T ).

2 The Objection

The feature of unification accounts to which I will object is the identifica-

tion of explanatory power with unifying power, in particular, the claim that

4. To be faithful to Kitcher, this should read “all the known phenomena”, since Kitcheris giving an account of what counts as an acceptable explanation relative to what is known,not an account of the correct explanation (Kitcher 1989, 431). But the account of correctexplanation is roughly the account I assume in the main text (Kitcher 1989, §8). I willnot spell out the differences here, as it is the account of acceptable explanation to whichmy objection in section 2 is mainly directed.

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as the unifying power of a theory increases, so does the power of its expla-

nations. I will lay out my objection and then consider various replies, in

particular, the strategy of denying that on a unification account, there must

be a proportional relation between explanatory and unifying power.

I will begin with my least strong counter-example, to indicate the kind of

pressure I hope to put on the unification account. Consider Boyle’s law, the

law that in a gas held at a constant temperature, pressure is inversely propor-

tional to volume. (Perhaps the law is even more familiar in its mathematical

form, PV = k, where k is a constant.) From Boyle’s law a phenomenon can

be deduced for every known gas: for oxygen, that when a quantity of oxygen

is kept at constant temperature, its pressure varies inversely with volume;

for radon, that when a quantity of radon is kept at constant temperature,

its pressure varies inversely with volume, and so on. The unifying power of

Boyle’s law is proportional to the number of such generalizations. Thus if

explanatory power is proportional to unifying power, the explanatory power

of Boyle’s law is proportional to the number of gases. This has the conse-

quence that, when a new gas—say, vapor of element number 118—is created,

any explanation that makes use of Boyle’s law becomes more powerful.

I will deal with one line of response to this counter-example right away.

The counter-example assumes that, when a new phenomenon comes into

existence, the unifying power of a theory may change, increasing if the new

phenomena can be derived from the theory. But the unificationist might

reasonably reply that the unifying power of a theory is to be judged not

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relative to currently existing phenomena, but relative to all the phenomena

that have ever and will ever exist. In a world where element 118 is fated to

be created, the unifying power of Boyle’s law ought to take into account the

law’s ability to cover the behavior of the element even before it exists. Thus

the unifying power of a theory can never change.

In response, I recast the counter-example so that it centers on the per-

ceived unifying power and explanatory force of Boyle’s law. When element

118 is discovered, we see that Boyle’s law unifies one more phenomenon than

it did before, and so—if we are unificationists—we ought to think that our

explanation of the relation between pressure and volume in all gases has

turned out to be better than we previously realized. But we do not think

this—for example, we do not think that the explanation of the behavior of

oxygen is any better after the creation of 118—so we are not unificationists.

The unification account does not capture our explanatory practices.

The epistemically relativized version of the counter-example assumes that

if explanatory power is proportional to unifying power, then perceived ex-

planatory power will be proportional to perceived unifying power. This is

not, I think, a controversial assumption. Kitcher, in particular, presents his

unification account in an explicitly epistemically relativized form that has the

proportionality of perceived explanatory and unifying power is an immediate

consequence. The only reason for a unificationist to resist the assumption

would be a worry that our explanatory practices are quite mistaken, and so

are not very close to the correct explanatory practices. The philosophical

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literature on explanation has ignored this possibility and, for the remainder

of this section, so will I. But it is taken up again in the first part of section 3

and in the last part of section 4.

The other counter-examples in this section will be presented in the epis-

temically relativized form. However, it is rather unwieldy to be always saying

“perceived explanatory power” instead of “explanatory power”, and so, like

Kitcher himself, I sometimes leave out the “perceived”. There should be no

misunderstanding, because relativization is always intended.

Now I return to the Boyle’s law counter-example. To recap, if we were

unificationists, the discovery of element 118 would give us reason to think

that the explanation of oxygen’s behavior was better than we had supposed.

But this train of thought seems perverse. The reason, I think, is that we

intuitively think of the power of an explanation as being determined solely

by the explaining theory T and its relation to the explanandum E. On

the unification account, however, the power of the explanation depends to a

great degree on the relation of T to a set of phenomena that are not being

explained. The unification theory makes explanation into an implicitly three

place relation. It is the inclusion of the third term—the phenomena that

can be explained, but are not being explained—into the explanatory relation

that is, I suggest, the great weakness of the unification account.

The counter-example I have presented is not particularly strong, even in

its epistemically relativized version. First, we are accustomed to thinking of

the kinetic theory of gases, not Boyle’s law, as being the theory that explains

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the Boylean behavior of oxygen. (On Kitcher’s account, Boyle’s law might

even be ruled out as an explainer of the behavior, since the more unifying

kinetic theory takes its place in the explanatory store.)

Second, it might be denied that the behavior of a particular gas is the

kind of explanandum for which the unification account is designed to provide

explanations in the first place. Perhaps only very broad generalizations, such

as Boyle’s law itself, are worthy explananda.

Third, and most important, the proponent of the unification account

might object that I have failed to take into account the importance of the

variety of phenomena unified. In the case I have presented, the phenomena

that are unified are just instantiations of exactly the same type of phenom-

enon over and over again. After the Boylean behavior of ten thousand gases

has been unified, it just does not seem very significant that the behavior of

one more gas has been added to the pile. As it happens, neither Friedman

nor Kitcher take the variety of phenomena unified into account when calcu-

lating unifying power—and there may be considerable technical difficulties

in doing so—but perhaps it is something that needs to be done all the same.

(One could borrow techniques, perhaps, from work on the related problem in

confirmation theory.) Taking this strategy to the extreme, one might count

every kind of phenomenon only once in calculating unifying power. Unifying

power would be proportional the the number of types of phenomena unified.

Now let me present a case that has none of the above flaws. Consider a

unifying theory used as an example by Friedman, the kinetic theory of gases.

9

The kinetic theory is generally agreed to entail the truth of, and hence to

explain, a number of laws obeyed by gases, including Boyle’s law, Charles’s

law, Avogadro’s law (these three make up the ideal gas law), Graham’s law of

effusion (concerning the escape of a gas from a small hole),5 and many other

laws concerning diffusion (which can be derived to order from the kinetic

theory).

The unification account of explanation is committed to the proposition

that the explanatory power of the kinetic theory is proportional to the num-

ber of gas laws explained. Thus, for example, the degree to which it explains

Boyle’s law is enhanced by the fact that it also explains Graham’s law. Again,

this seems perverse. The quality of the kinetic theory’s explanation of Boyle’s

law depends on what the kinetic theory says about the pressure and volume

of gases, but not on what it says about the rate with which a gas escapes

from a small hole. Seeing that effusion behavior can be understood does not

enhance our understanding of Boyle’s law.

The point can be emphasized by considering the historical development

of the kinetic theory. It is generally agreed that the first correct explanation

of Boyle’s law was that of Daniel Bernoulli in his Hydrodynamics of 1738.

Bernoulli assumed that gases are made up of fast, independently moving

particles, and that pressure is proportional to the number of these particles

impacting a container wall in a given time. He then showed that it followed

5. Not to be confused with Graham’s law of diffusion, an earlier result but an altogethertrickier proposition.

10

from pretty much purely geometric considerations that, when the volume of

gas is decreased, the number of impacts, and hence the pressure, increases by

the same factor. Bernoulli made a couple of false steps, but his explanation

(in the cleaned-up form in which I have presented it) is still presented as the

explanation of Boyle’s law in modern textbooks.6

Amedeo Avogadro presented the hypothesis that is now known as Avo-

gadro’s law in 1811. Thomas Graham discovered his effusion law in 1846.

In the following decades various scientists including John Herapath, Rudolf

Clausius and James Clerk Maxwell either improved or for the first tine pre-

sented explanations of the different gas laws. (For the historical story I am

relying mainly on Brush 1983.) If scientists were unificationists, then each

time one of these laws was explained by kinetic theory, the kinetic explana-

tion of Boyle’s law would be seen to become more powerful. By the twentieth

century, the kinetic theory was known to have several times as much unify-

ing power as it was known to have in 1738. (Obviously any specific figure

is controversial, but just look at the number of behaviors of gases that were

not known to Bernoulli in 1738.) The unificationist is committed, then, to

holding that Bernoulli’s explanation has for us moderns several times more

explanatory power than it had for Bernoulli’s contemporaries—that is, that

in 250 years it has become several times as good an explanation as it used to

be. This is obviously wrong. The explanation has improved to some degree,

6. It is worth noting that modern explanations of Boyle’s law leave out assumptions ofthe kinetic theory crucial to the derivation of other phenomena that the theory explains.

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but not because of the success of kinetic theory in other areas. Rather, it is

because the kinetic theory and the derivation of Boyle’s law from the theory

have been improved.

It is important to bear in mind that I am not saying that the kinetic

theory has not become regarded as a much better theory. It has, probably

by a large factor, but this is mainly due to the fact that we have much better

reason than we used to for believing it to be true (in part because it explains

so many different phenomena). Its increased unifying power is an intrinsic

virtue, as well (see section 4). But this is not the same as saying that the

theory gives a better explanation of Boyle’s law. Boyle’s law has become

better unified with other phenomena, but not better explained.

One final pass: when Bernoulli published his explanation, Boyle’s law

and a few other, less well formulated facts were the only behaviors of gases

that the kinetic theory could reasonably be hoped to explain.7 These facts,

if written down, would be at least as compact as the kinetic theory of gases,

and would contain about as many assertions (or so I claim—obviously there

is room for disagreement here).8 Thus the unifying power of the kinetic

7. Chief among the other behaviors was the positive relationship between temperatureand volume in a gas at constant pressure (V = kT ), eventually known as Charles’s law. Atthe time Bernoulli wrote, no precise formulation of the law was known, due to the absenceof a well-defined temperature scale. In particular, it was not known that volume variedlinearly with temperature. But Bernoulli nevertheless derived this relationship. Thus heexplained a fact not yet known to be true.

8. The reader should not confuse the kinetic theory of gases with the atomic theory ofmatter. The atomic theory was held to have much unifying promise (though not much

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theory after Bernoulli’s explanation was—zero. But then it follows that, on

the evidence available in 1738, the kinetic theory did not, after all, explain

Boyle’s law. That, I think, is a reductio of the unification account.9 Suppose

that the kinetic theory first achieved positive unifying power in 1847 when

Herapath derived Graham’s law of effusion from the kinetic theory (the exact

time and the identity of the derived law hardly matter). Then according to

the unification account, Bernoulli did not explain (in the sense of enhancing

current understanding of) Boyle’s law when he derived it from the kinetic

theory in 1738. (As Kitcher would say, the explanation was not acceptable

to Bernoulli or his contemporaries.) Rather, Boyle’s law was first explained

in 1847, when Herapath used the kinetic theory to derive . . . Graham’s law!

I will try one more example, which I think combines the power of the two

Boyle’s law examples: the case of the Darwinian explanation of biological

adaptation. It has the flavor of the first of the two Boyle’s law examples,

where it is the law that is doing the explaining, but it does not suffer from that

example’s three flaws. First, Darwinian explanation is very much used today.

Second, it is certainly a variety of explanation that unification theorists hope

to account for (Kitcher explicitly, but any account of theoretical explanation

that could not make sense of explanation in all of evolutionary biology would

of this was realized) in the seventeenth century. The kinetic theory is the view that heatis a kind of molecular motion, rather than a substance (caloric). There were (incorrect)atomic explanations of Boyle’s law before Bernoulli’s (due to Boyle and Newton) that didnot make use of the kinetic theory.

9. But see Friedman’s claim reported in section 3 below.

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have to be counted rather feeble). Third, the different explananda are as

varied as life itself.

According to Kitcher (1989, §4.6.2), there is a Darwinian pattern of ar-

gument called Simple Selection that has its explanatory force because it

unifies many different biological phenomena, more precisely, because the pres-

ence of many different adaptations can be derived using this single pattern.

On the unification account, then, the perceived explanatory power of Dar-

win’s theory is proportional to the perceived unifying power of Simple Se-

lection, which is to say, to the number of biological adaptations known to

be out there in the world. But the number of biological adaptations known

to be out there is constantly increasing.

Now imagine God looking down on his creation, the planet earth, four

billion years ago. (Two important facts about God: first, he is not a product

of natural selection; second, he cannot see into the future.) So far there is

no life, and so God does not know of any adaptations. He is omniscient with

respect to present and past, however, so as soon as they begin to appear, he

knows about them and about the process that produced them. A billion years

later, life appears and natural selection begins to have its effect. For the first

time, an adaptation is produced by natural selection.10 Does God understand

the adaptation? Not according to the unification account. Darwinian theory

is considerably more complex than a description of the first ever adaptation,

10. I cheerfully acknowledge that it is hard to say exactly what would count as the firstadaptation. But I think that the point of the story does not turn on this narrative device.

14

hence has negative unifying power, hence does not explain (by God’s lights),

the appearance of the adaptation. (Of course, much later, we count it as an

acceptable explanation.)

Then the adaptations start to accrue. For a while, the Darwinian theory

still lacks unifying power, and God is unable to understand their appearance

in terms of the natural selection that is so manifestly producing them all

around him. At last, the complexity of the description of the adaptations

exceeds the complexity of Darwinian theory, by just a little bit. It dawns on

God that natural selection might count as an acceptable explanation—though

just barely acceptable—for the adaptations. For the first time, a Darwinian

explanation becomes acceptable for all adaptations that have occurred so

far, including that very first adaptation that God was until now unable to

explain. (If the world had ended before now, the adaptations would have

been for all time inexplicable!) Meanwhile, every time a new species evolves,

Darwinian explanations become just a little bit better. Just as God begins

to really understand the emergence of life, the Cambrian explosion occurs.

There are now thousands of times as many adaptations as there were before.

Darwin’s theory blossoms with the tree of life; Darwinian explanations are

suddenly very acceptable. God is finally able to appreciate the glory of his

creation.

There is something very wrong with this story; I hope that it is clear that

it stems from the equation of explanatory and unifying power.

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3 Unificationist Replies

There are two kinds of reply to the objection I have raised. First, one may

enthusiastically accept all the absurd consequences of the unification account.

This line does not seem promising, but it is suggested by a surprising com-

ment of Friedman’s:

Consider . . . the kinetic theory of gases. The theory explains phe-

nomena involving the behavior of gases, such as the fact that

gases approximately obey the Boyle-Charles law [PV = kT , the

law explained by Bernoulli], by reference to the behavior of the

molecules of which gases are composed. For example, we can de-

duce that any collection of molecules of the sort that gases are,

which obeys the laws of mechanics will also approximately obey

the Boyle-Charles law. How does this make us understand the

behavior of gases? I submit that if this were all the kinetic the-

ory did we would have added nothing to our understanding. We

would have simply replaced one brute fact with another. But

that is not all the kinetic theory does—it also permits us to de-

rive other phenomena involving the behavior of gases, such as the

fact that they obey Graham’s law . . . (Friedman 1974, 194)

In short, Bernoulli did not explain Boyle’s law. That he did is a lie perpet-

uated by historians of science and the writers of textbooks. Furthermore,

teachers of physics and chemistry who purport to convey an understanding

of Boyle’s law to their students by deriving it from the kinetic theory are

frauds—except, of course, for those who derive Graham’s law as well. By

deriving Graham’s law, they really do convey an understanding of Boyle’s

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law.

As I stated earlier, such conclusions strike me as unacceptable. I do not

understand why Friedman does not think otherwise. Perhaps he regards as

non-negotiable the posit that explanation is the reduction of the number of

facts accepted as brute, and thus holds that the posit is not vulnerable to

a reductio. I refer readers sympathetic to this line of thought to section 4,

where I argue that the posit leads inexorably to a causal view of explanation,

not a unification view. (I should add that on a causal view, the kinetic theory

clearly explains Boyle’s law.)

The other reply that the unificationist can make is inspired by the obser-

vation that Friedman and Kitcher do not, in the formal exposition of their

accounts, provide a measure of explanatory power. They say what it is to

be a good explanation, but not what it is for one good explanation to be

better than another. Of course, by identifying explanatory power with uni-

fying power they commit themselves to filling in this gap in the way I have

assumed above (if explanatory power and unifying power are identical, they

cannot but be proportional). But it is worth asking what would be left if

the gap remained unfilled, that is, if a unification-based account were offered

that explicitly did not make distinctions of explanatory power, save for the

distinction between good and bad explanations.

I will perform this experiment on Kitcher’s account. As before, an expla-

nation is a good explanation if it goes by way of an argument pattern that

belongs to the explanatory store, that is, if it goes by way of one of the set of

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the argument patterns that best unifies all the phenomena. But now I add:

goodness of explanation does not come in degrees. No matter how well or

how badly the explanatory store unifies the phenomena, explanations taken

from the store are equally good. A disunified world can be understood to

the same degree as a unified world.

Will such an account capture our explanatory practices? I think not.

Consider a world where all of life is the result not of evolution by natural

selection but of random (and extremely lucky) collisions of atoms, as sug-

gested by some of the early atomists. Biological “adaptations” in such a

world would have to be unified by an argument pattern in which each “adap-

tation” is derived from the proposition that certain very improbable initial

conditions held, together with a statement of the laws of atomic mechanics.

(I am assuming that the world is deterministic so as to avoid the question of

how to treat probabilistic explanation.) Such a unification is not very good.

In particular, the argument pattern suffers from a lack of stringency (since

just about any physically possible event can be derived if one is allowed to

posit ridiculously unlikely initial conditions). But it is a unification all the

same, and it is the best possible under the circumstances.

Now, according to the version of the unification account under considera-

tion, in both our world and the world where life appears by chance, adapta-

tions are equally well explained. To put it another way, we are in a position

to understand equally well why adaptations emerge in either world. But this

is simply not true. (If there was ever an explanation that deserved to be re-

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garded as “simply replacing one brute fact with another” it is the atomists’

explanation of biological adaptation.) There are degrees of understanding,

and thus of explanation. Any account of explanation must make sense of this

fact.

Although a unification account that denies the proportionality of explana-

tory power to unifying power is undesirable for the reason just given, I will

finish by arguing that, on either of the two usual motivations for a unification

account, proportionality is compulsory. That is, if the motivations justify a

unification account at all, they justify one in which explanatory power is

proportional to unifying power. Anyone moved to hold a unification account

in one of the two usual ways, then, is committed to holding an account that

is vulnerable to the objection made in section 2.

The first motivation stems from a very traditional empiricist view of the

nature of science. On this view, the only facts to which we have access (epis-

temic and perhaps semantic) are, as David Lewis puts it, “local matters of

particular fact, just one little thing and then another” (Lewis 1986, Introduc-

tion, ix ). Old-fashioned empiricists such as Hume hold that the particulars

are facts about sense impressions; modern empiricists such as Lewis that

they are physical facts about local arrangements of physical qualities. All

empiricists agree that further facts—about causes and laws, in particular—

must, if they exist at all, be higher order properties of the basic, local facts,

or to put it another way, they must be facts about patterns of basic facts (in

a broad sense of “pattern”). This is the doctrine that Lewis calls “Humean

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supervenience”. Insofar as science discovers something other than the basic

facts, it must be discovering patterns in the basic facts.

All higher order scientific activity, on the view I am describing, is con-

cerned with the discovery and deployment of patterns. There is a strand in

this tradition according to which all pattern discovery is directed towards

the end of finding the most unifying set of patterns, in the same sense of

“unifying” employed by Friedman and Kitcher. Lewis holds, for example,

that the laws of nature are the deductive closure of the set of axioms that

best unifies all the basic facts (Lewis 1994).11 In its purest incarnation, this

strand of empiricism holds that only two activities are proper to science: dis-

covering the basic facts and discovering the most unified description of these

facts. This attitude is well exemplified by the philosophy of Ernst Mach,

who held that the goal of science is “intellectual economy”. These unifica-

tion empiricists, as I will call them, originally held that explanation, being

a metaphysical pursuit, was not a proper goal of science (Duhem is another

important figure here, although he was not quite an empiricist). If, as later

empiricists decided, explanation is a legitimate scientific activity, then for a

unification empiricist it can only be a kind of unification. Hence the moti-

vation for a unification account of explanation. Explanation is essentially a

11. Lewis’s view, more precisely, is that the laws are the closure of the axioms that bestcombine simplicity and strength, where simplicity is a measure of how few and how simplethe axioms are and strength is a measure of the number of basic facts entailed (or highlyprobabilified) by the axioms. Obviously, the sum of simplicity and strength is a measureof the unifying power of the axioms in the sense of Friedman and Kitcher.

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matter of showing how nicely the explanandum fits into a unifying system of

laws. Understanding comes in appreciating the niceness of fit.

For a unification empiricist, the scientific component of explanation is not

distinct from the process of unification (though the pragmatic component

might be). Explanation is just a kind of unification, a kind where the basic

fact to be incorporated into the unified corpus is called the explanandum, and

the unifying theory is called the explanans. Thus the power of an explanation

just is the unifying power of the explanans, as my objection to the unification

account assumes.

A second and rather different motivation for the unification theory (just

how different will emerge in section 4) is that explicitly endorsed by Friedman

and Kitcher: understanding comes from reducing the number of fundamen-

tal, hence incomprehensible, facts that the scientist must accept about the

universe. The goal of explanation is to achieve such a reduction, not so much

to increase understanding but to reduce incomprehension. This picture is (if

it says all there is to say about understanding) rather pessimistic: we begin

science with a massive deficit of understanding, and our goal is to raise our

understanding to as near zero as possible. Always, however, our understand-

ing is negative. Or to put it another way, on this picture we never actually

understand a single thing about the world; the best we can do is to reduce

the number of things that there are not to understand.

On this view, the understanding induced by an explanation is directly

proportional to the number of brute facts removed by the unification, that is,

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to its unifying power. Thus explanatory power is, again, directly proportional

to unifying power. A unification account of explanation motivated in the

Friedman-Kitcher style must accept this proportionality.

4 Unification and Explanation

I must take care of one source of lingering doubt. I have shown, I think,

that explanatory power is not unifying power, but it remains very plausi-

ble that unification has something to do with explanation. This is, I think,

a real insight of the unification account. Unifying power is not just a sci-

entific virtue of a theory, it is an explanatory virtue. In this section I say

what kind of virtue I think it is, and I show that accepting unifying power

as an explanatory virtue does not commit me to a unification account of

explanation.

In what follows I propose that unifying power is an explanatory virtue of

a theory as a whole, but it contributes nothing to the power of the theory’s

explanations of individual phenomena. As I will say, unifying power is a

global explanatory virtue of a theory. But how is it virtuous? The unifying

power of a theory, by unanimous agreement, depends on two things: the size

and variety of the set of phenomena unified (the theory’s strength, in Lewis’s

terminology; see note 11), and the simplicity of the unifying theory. I will

argue that strength and simplicity are distinct global explanatory virtues;

a unifying theory is good because it possesses both virtues, but there is no

22

synergy between the two. I will therefore discuss the explanatory advantages

of strength and simplicity separately, starting with strength.12

Strength If a theory is strong, it explains many phenomena. (This is not

itself a definition, but it follows from all unificationist definitions of strength

that I know of.) Thus, in the simplest possible sense, a stronger theory is

a more explanatory theory—it explains more things. It is of the greatest

importance to see that the explanatory power that a theory has in virtue

of its strength is an extensive power, not an intensive power. A theory

that is twice as strong as another is twice as explanatory because it explains

twice as many phenomena, not because it explains each phenomenon twice

as well.13 To confuse the two, I think, is the fundamental mistake made by

the unification account. It is also precisely the mistake that lays open that

account to the objection made in this paper.

In the Darwinian example, for example, as new adaptations appear the

explanatory power of Darwinian theory is seen to increase in the extensive

12. It should be noted that strength and simplicity are generally agreed to be virtues ofa scientific theory for non-explanatory, as well as explanatory, reasons. Strength—roughly,the number and variety of true predictions made by a theory—is valued because a strongtheory is better confirmed. Simplicity is valued for various reasons: a simple theory iseconomical, is more likely to accurately reflect the way things are, is more aestheticallypleasing. Although in what follows I focus exclusively on the explanatory value of strengthand simplicity, I do not mean to imply that strength and simplicity are not valuable inthese other ways as well.

13. For simplicity’s sake, I am ignoring the contribution that diversity makes tostrength, on some versions of unificationism, but similar observations apply.

23

sense, but not in the intensive sense. As life evolves, Darwinian theory ex-

plains more phenomena, but its individual explanations do not become any

better.

Can the unification account be saved by reinterpreting unification as an

extensive explanatory virtue? No. Such an account would say nothing about

what relation must obtain between theory and explanandum in a good expla-

nation, only that there should be a lot of relations of this sort—which is to

say that the theory would say nothing about what kind of thing explanation

is.

Simplicity How is the simplicity of a theory explanatorily valuable? I be-

lieve that Friedman and Kitcher have given the right answer to this question:

it is better to explain the same set of phenomena with a simple theory than

with a complex theory because a simple theory makes fewer unexplained

posits. Unlike Friedman and Kitcher, however, I believe that this “reduction

in incomprehensibility” is an explanatory benefit that is independent of and

additional to the virtue that a theory accrues by being able to explain that

phenomena. Suppose that two theories explain the same set of phenomena

equally well (according to some account of explanation other than the uni-

fication view). Then one ought to prefer the explanations supplied by the

simpler theory because it takes less for granted. But this preference does

not mean that one thinks that the simpler theory explains each individual

phenomenon better than the more complex theory. The power of individual

24

explanations is unaffected by simplicity; simplicity is an additional benefit of

the complete package—like strength, a global virtue.

The reader might think that I have conceded too much. If, as I have said,

reducing the number of fundamental facts that must be accepted without

explanation is an explanatory virtue, does that not open the way for a return

of the unification account? I will lay out this worry in more detail. I have

suggested that Friedman and Kitcher are correct in holding that reducing

the number of “brute” facts does the world an explanatory service (although

I deny that this is the only explanatory service we can perform). Call the

Friedman-Kitcher view with which I agree brutal reductionism. Now consider

the act of showing that some particular fact, previously thought to be brute,

can be derived from a theory of known unifying power. Does not this act

qualify, according to brutal reductionism, as an explanatorily salutary act?

Therefore, does brutal reductionism not entail that such acts of unification

are acts of explanation?

The anti-unificationist can easily circumscribe brutal reductionism by fiat

so that this argument does not go through, by insisting as I have that the

fruit of brutal reduction—simplicity—confers explanatory goodness only on

theories, not on their individual explanations. But the worry is that the fiat

is unjust. If brutal reduction is a good thing, why should it be circumscribed?

In this final section of the paper I hope to answer this objection by ar-

guing that brutal reductionism only makes sense on a causal account of ex-

planation, and hence cannot be used to justify the unification account. The

25

argument has two parts. First, I show that if the standard empiricist view

of metaphysics is correct, brutal reductionism has no appeal. Second, I show

that brutal reductionism only makes sense in the kind of world envisaged by

the realist about causation and laws of nature.

The empiricist metaphysics I have in mind is essentially David Lewis’s

view, described in section 3. This view has two pertinent features: (a) the

only accessible (for Lewis, the only) fundamental facts are local matters of

particular fact, and (b) the theories we construct, laws and all, make claims

only about patterns of these local facts. Now, on such a view, in what

sense does unification reduce the number of fundamental facts that must be

taken for granted? Rather obviously, in no sense at all. On the empiricist

view, a unifying theory simply summarizes the fundamental local facts. The

existence of a a good summary, does not show that local matters of fact

summarized are not fundamental, nor does it show that the elements of the

summary—the laws in the unifying theory—are fundamental. This could

never be the case for an empiricist, whose most basic belief is that laws are

not fundamental and local facts are. Given empiricism, there was never any

question which facts were fundamental; all local facts are fundamental, and

so they must all simply be taken for granted. This is one of the things that

realists find so disconcerting about the Humean view.

Empiricism, then, provides no basis for brutal reductionism (though an

empiricist might adopt the unification view of explanation for some other

reason). What view of the nature of the world can justify brutal reduction-

26

ism? It would have to be a view on which to show that a local fact can

be derived from a theory is to give some reason to think that the local fact

is not fundamental, and that the theory is. This can only be the case, I

think, in a world where the existence of local facts somehow metaphysically

depends on the existence of the entities mentioned in theories, in particular,

on laws of nature. The only such world known to modern metaphysics is the

world proposed by realists about laws of nature such as David ?. In such

a world, local facts obtain because laws of nature bring them about, where

the “because” is a metaphysical—a causal—“because”. To show that a fact

can be derived from a theory (in the right sort of way) is to show that it was

caused in accordance with some law of nature in the theory, and so that the

fact is not fundamental. (I will simply say that the law causes the fact.)14

When many facts are shown to be brought about by a single law, the facts

are seen not to be fundamental; only the law remains as a brute posit. Thus

the number of posits that must be accepted as brute is reduced.

This justification of brutal reductionism tacitly makes a very interesting

assumption: that, when a fact is shown not to be fundamental because it was

caused by a law, the fact is no longer incomprehensible (otherwise unifica-

tion does nothing to reduce the number of fundamental incomprehensibles).

That is, showing that a fact was caused by a law of nature makes the fact

14. Not all theories contain entities that are clearly laws of nature, and in those thatdo there is usually more than one law. Talking about “the law” that brings about a factaccording to a theory should be understood as an expository convenience.

27

comprehensible. But to say that showing that a fact is caused is what makes

it comprehensible is to endorse a causal account of explanation. That brutal

reduction is a good thing is a position that should lead one not to a uni-

fication account, but to a causal account of the explanation of individual

phenomena. Friedman and Kitcher began with the right intuition, but they

have taken it in entirely the wrong direction.

28

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