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.
1
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
3
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.
4
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
6
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
7
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
8
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.
11
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
12
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.
13
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
16
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
17
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-
18
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
19
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.
20
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,
21
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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