Philosophical
American
Paper
Quarterly
2, April
17, Number
Volume
tell us both what
is true
and how
The claim: laws SCIENTIFIC
in nature,
explain
and explanations argue that these are entirely different functions and
to be kept apart should be kept distinct. Usually the two are conflated.
are
to
it. I shall
The second is commonly seen as a by-product
first. Scientific theories are thought to explain
of the descriptions
they give of reality. Once
is done, science can shut down.
of describing
tell
all there is to do. To describe nature?to
the
values
its
of
fundamental
of the
by dint
the job
That is
its laws,
its mass
constants,
distributions...?is
to explain it.
The opposite
This is a mistake, I shall argue ;a mistake which is
view is defended fostered by the covering law model of explanation.
by the D-N
The covering law model supposes that all we need to
a little logic,
model and by
know are the laws of nature?and
other theories of perhaps a little probability
then we
theory?and
explanation
know which factors can explain which others. For
ver?
example, in the simplest deductive-nomological
one
that
factor
model
the
law
says
sion,1
covering
explains another just in case the occurrence of the
second can be deduced from the occurrence of the
the
of nature.
laws
is just an example.
But the D-N model
which
to my
is relevant
explanation
science
are
offered
covering
own
claims
here,
In the sense
most
models
in the philosophy
recently
law models.
This
includes
of
of
not
statistical model,2 but
only Hempel's
also Patrick Suppes' probabilistic model of causation,3
Wesley
Salmon's
inductive
statistical
relevance
model,4
MUCH
it seems
and
even Bengt Hanson's contextualistic model.5 All these
accounts rely on the laws of nature, and just the laws
of nature, to pick out which factors we can use in
explanation.
A good deal of criticism has been aimed at Hempel's
original covering law models. Much of the criticism
objects that these models let in toomuch. On Hempel's
we
can
explain
to get
failure
Henry's
pregnant by his taking birth control pills, and we can
the storm by the falling barometer. My
explain
law models
objection is quite the opposite. Covering
let in too little. With a covering law model we can
explain hardly anything, even the things of which we
are most proud?like
the role of DNA
in the
inheritance of genetic characteristics, or the formation
of rainbows when
is refracted
sunlight
through
We
raindrops.
a covering
have
facto to lay down how we are
ipso
first given
1980.
EXPLAIN
account
Introduction
we
Division,
CARTWRIGHT
NANCY
theories must
of the
Meeting
Pacific
Association,
Philosophical
San Francisco,
Calif., March
27-29,
DOESN'T
THE TRUTH
VIII.
at the 54th Annual
presented
American
1980
cannot
with
phenomena
I shall argue, because we don't
law model,
laws
any
these
explain
Objection to D-N:
hardly any
covering laws
available
cover
which
them.
are
laws
Covering
scarce.
Many
phenomena
scientific
explanations
that
laws,
true
No
ceteris paribus
which
have
are
covered
not
are
is. They
at
perfectly
by
best
good
laws.
any
covered
by
which
generalizations?generalizations
hold only
conditions.
under special conditions,
ideal
usually
The literal translation is "other things
being equal"; but it would be more apt to read
"ceteris paribus" as "other things being right."
Sometimes we act as if this doesn't matter. We have
in the back of our minds an "understudy" picture of
ceteris paribus laws : ceteris paribus laws are real laws ;
they
aren't
can
stand
available
in when
and
not
functions,
only
For
ceteris paribus
the "ceteris
without
laws we
the
they
quite
would
can
perform
so well.
But
paribus"
the
same
this won't
do.
read
generalizations
to see
like
all
literally?
modifier?as
laws,
are
false. They are not only false, but held by us to be
law
false; and there is no ground in the covering
picture for false laws to explain anything. On the
other hand, with
the modifier
the ceteris paribus
be
but
true,
may
generalizations
they cover only
those few cases where the conditions are right. For
most cases, either we have a law which purports to
to
cover, but can't explain because it is acknowledged
be
false,
way,
or we
have
a law which
it's bad for the covering
doesn't
1
in C. G. Hempel,
C. G. "Scientific Explanation"
(New York: Free Press,
Aspects of Scientific Explanation.
Hempel,
2
C. G., ibid.
Hempel,
3
1970).
Suppes, Patrick. A Probabilistic Theory of Causality. (Amsterdam,
4
inWesley
Salmon
"Statistical Explanation"
Salmon, Wesley.
(ed.), Statistical Explanation and Statistical Relevance.
5
Stanford University,
What?"
Hanson,
1974).
(Mimeographed:
Bengt. "Explanations?Of
159
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cover.
Either
law picture.
1965).
(Pittsburgh,
1971).
Without the
modifier the "laws"
are false; with the
modifier they cover
too little
AMERICAN
l60
I. Ceteris
Laws
Paribus
QUARTERLY
Snell's law of page 21 in Klein's book is an
example of a ceterisparibus law, a law that holds only
The
I first started talking about the scarcity of
laws, I tried to summarize my view by
When
covering
Every law is
born to fail
PHILOSOPHICAL
in special
circumstances?in
case when
this
the media
are both isotropic. Klein's
statement on page 21 is
are no
"There
saying
exceptionless
generalizations."
not to be taken literally. Charitably, we are
clearly
Then Merrilee
Salmon asked, "How about 'All men
inclined to put the modifier "ceteris paribus" in front
are mortal' ?" She was right. I had been focussing too
to hedge it. But what does this ceterisparibus modifier
much on the equations of physics. A more plausible
do? With an eye to statistical versions of the covering
have
been
that there are no exceptionless
claim would
or Salmon's
law model
I-S picture,
(Hempel's
laws in physics. Indeed, not only are
quantitative
statistical relevance model, or Suppes' probabilistic
there no exceptionless
laws, but in fact our best model
we may
of causation)
suppose that the
candidates are known to fail. This is something like
unrefined Snell's law is not intended to be a universal
the Popperian
thesis that every theory is born refuted.
law, as literally stated, but rather some kind of
we
have proposed in physics, even at
Every theory
statistical law. The obvious candidate
is a crude
the time when
it was most firmly entrenched, was
statistical law \for themost part, at an interface between
known to be deficient in specific and detailed ways. I
... But
dielectric
media
is a refracted
there
this
ray
think this is also true for every precise quantitative
theory.
physics
But this is not the point I had wanted
some
are
laws
if they
were
at
treated,
least
for
the
whereas
exceptionless,
to make. For
time
others
being,
are not?
as
latter kind. In the optics text I use for reference (Miles
V. Klein, Optics) ,6 it first appears on page 21, and
:
without qualification
an
At
Law:
there
is (also)
in the plane
and
normal,
sin 6/sin
0t
between
dielectric
media,
ray in the second medium,
lying
an angle
of incidence,
the
9r with
making
law :
Snell's
obeying
a
=
interface
refracted
n2\nx
vx and v2 are the velocities
?
=
two media,
and nx
{c/v^, n2
refraction.
of
(6 is the angle
It
some
is only
Italics
incidence.
500
indices
of
when
the
law
is
from the "full electromagnetic
theory of
as
on page
we
law
Snell's
stated
learn
that
that
light"
21 is true only for media whose optical properties are
isotropic. (In anisotropic media, "there will generally
be two transmitted waves."7) So what is deemed true
is not really Snell's law as stated on page 21, but
derived
a refinement
rather
Snell's
Refined
isotropic,
refracted
at
incidence,
that:
sinO/sin
6
Klein,
Miles
of Snell's
Law:
an
ray
in the second
an
making
0f
=
law:
any two media which
dielectrics
between
For
interface
angle
n2\nx.
V., Optics.
are
optically
is a
there
lying in the plane of
the normal,
such
0r with
medium,
(New York,
think
For
laws they can generally
statistical
II. When
Laws Are
be identified with.
Scarce
Why do we keep Snell's law on the books when we
both know it to be false and have a more accurate
refinement available? There are obvious pedagogic
reasons.
there
are
But
and
are,
of explaining.
are
there
serious
reasons
these
I claim
scientific
ones?
I think
to do with
have
that specifying
to which
relevant
explanatorily
the
which
task
factors
is a job
others
done by science over and above
the job of laying out
the
laws
laws
be
nature.
of
known, we
can
added.)
later,
pages
in the
of propagation
(f/z>2) are the
where
do.
in an
and
ceteris
Snell's law is
even
"on the books".
Snell's
law
remain
though
they
admitted as being
of
and
the
the
incidence
angle of
(about
angle
literally false
refraction for a ray of light) is a good example of this
SneWs
are
most media
optically
anisotropic,
are
medium
two rays.
I
there
anisotropic
are no more
there
If
alternatives.
satisfactory
to be
true
are no
laws are
there
laws,
paribus
won't
a
law within
the
Once
to decide what
still have
nature
of
are
in explanation.
cited
are
explanations
We
permitted.
know
from
the
refined Snell's law that in any isotropic medium,
the
angle of refraction can be explained by the angle of
to the equation
sin 0/sin
incidence,
according
0r =n2?nx. To leave the unrefined Snell's law on the
books is to signal that the same kind of explanation
can
be
even
given
for
some
anisotropic
media.
The
pattern of explanation derived from the ideal situation
is employed even where the conditions are less than
ideal;
and
CP laws are used
in explanations to
show what factors
are eexplanatorily
relevant
kinds of factors
One thing that ceteris paribus laws do is to express
our explanatory
commitments. They tell what kinds
of
Statistical
reading of ceteris
paribus rejected
we
assume
that
we
can
understand
what
happens in nearly isotropic media by rehearsing how
light rays behave in pure isotropic cases.
This assumption is a delicate one, and it obviously
derives from certain metaphysical
views we hold
1970).
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Example:
Snell's law
the
truth
explain
doesn't
much
161
about the continuity of physical processes.
had more to say about it. But for the moment
I wish I must make metaphysical
models of reality, we had
as much
as
best make
the model
I intend
like our experience
on
an
to
out
an
I
that
So
model
the
of
the
it
is
would
Book
Nature
and
only
possible.
point
assumption,
best current Encyclopedia
of Science ; and current
assumption which (prior to the "full electromagnetic
a piecemeal hodgepodge
our
are
well
of
science
of
the
facts
goes
beyond
encyclopedias
theory")
knowledge
of different theories for different kinds of phenomena,
of nature. We know that in isotropic media, the angle
with only here and there the odd connecting
of refraction is due to the angle of incidence under
law for
the equation sin 0/sin 0t = n2/nx.We decide to explain
domains.
overlapping
The best policy is to remain agnostic, or at least not
in anisotropic
the angles
for the two refracted
rays
to let other important philosophical
same
manner.
in the
media
We
have
issues depend on
may
good
reasons for the decision?in
we are in a
the outcome.
We
don't
know
this case if the media are
whether
tidy
or
an
one.
two
the
universe
will
be
close
whichever
universe
But
rays
very
nearly isotropic,
untidy
are
we
the ordinary
of
in,
together, and close to the angle predicted by Snell's
activity
commonplace
sense.
turn
to make
law ;we believe in continuity of physical processes ; giving
It may
ought
explanations
out that in the Last Judgment God allows us to look
still this decision
is not forced by our
etc.?but
at the Book of Nature and we see that it is woefully
the
nature.
of
laws
of
knowledge
an
not
to have
we
not
We
of
this
decision
taken
could
be
if
Obviously
ought
incomplete.
analysis
were
tells us,
never
that
also had on the books a second refinement of Snell's
that we
then,
explanation
that in any anisotropic media,
all along, that the activity didn't make
the explaining
law, implying
sense
are
most
of
those
the time we did it.
different
from
Snell's
angles
given by
quite
as I shall argue,
law. But,
laws are scarce,
and often
The second difficulty for the ellipsis version of the
we have no law at all about what happens
in covering
law account is more pedestrian. But it is
conditions which are less than ideal.
based on the same fundamental
point: we should
D-N model: CP
no account
law theorists will tell a different story
of
which
dictates
that
Covering
adopt
explanation
laws offer at
most elliptical
explanations
use
about
the
From
their
of
ceteris
of view,
point
in explanation.
laws
paribus
ceteris paribus
explanations
are elliptical for genuine covering law explanations
from true laws which we don't yet know. When we
use a ceteris paribus "law" which we know to be false,
the
bet
law theorist
covering
the
about
what
form
us
supposes
true law
takes.
a
to be
making
For
example,
to retain Snell's unqualified law would be to bet that
the (at the time unknown)
law for anisotropic media
will entail values "close enough" to those derived
from the original Snell law.
I have two difficulties with this story. The first
But this assumes
extreme regularity arises
in nature
which
to think
that
an
from
extreme
I in fact believe
nature
that
is a
there
law
to cover
every
; in the extreme,
case.
I do not.
that natural objects are much
imagine
societies.
Their
is
behavior
like people
constrained
by
I
in
some
specific laws and by a handful of general principles,
but it is not determined
in detail, even statistically.
What happens on most occasions is dictated by no
law
at all.
This assumption
This is not a metaphysical
is unwarranted claim is that this
picture
alternative.
and
tired.
grown
contend
beauty
God may
picture that I urge. My
as the
is as plausible
have written just a few laws
or whomever,
Determinists,
covering law account of ceteris paribus laws has
this consequence.
For elliptical
explanations
just
aren't
the
admiration...
ing empirical
dictum
.But
there
is one
think
:
we're
are
they
explanations
to appear
in the
complete,
is not a law we have
in our
let
state,
in
D-N
theory,
a law
cases.
may
be
But
those
and
for
grounds
assurances
law which
correct
There
these
explanations;
be our
those
of a
saying
are
then
are
not
of
nature
:
our
they
that
grounds?
not
the
are
explanation
can
that we
we
at
know
any
law
covering
explanations
unknown
laws
nearly
I claim
laws
that
is supposed
"sin Qt&k(n2/nx) because sin 0 = k."
medium,
they
laws
test.
alone
explanations
are not our
cannot
at best
not.
we're
explaining,
are to be had. The
of
isotropic
only
nature.
time
what
The
are
not
can be
enough to tell us what kinds of explanations
at
a
that
time.
That
decision
and
it is
;
given
requires
law theorists make
just this decision that covering
when
they
wager
about
the
existence
of
unknown
laws. We may believe
do so on no ordinary
tested, nor are they
theory. Our grounds
in these unknown laws, but we
grounds: they have not been
derived from a higher
level
for believing
in them are only
as
for
good
as our
reasons
strategy,
explanatory
and
the
adopting
corresponding
no better.
may
that nature must be simple, tidy, an object of
and
we
time
explanations
What
law theorists tend
is well-regulated
of
The
possibility,
metaphysical
in. Covering
most
III. When
outstand?
in favor of untidiness
: if we
I have
been
maintaining
Laws Conflict
that
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there
aren't
enough
Another objection
against D-N: CP
laws do actually
explain
PHILOSOPHICAL
AMERICAN
l62
Science conains covering laws to go around. Why ?The view depends
many CP laws, on the
earlier.
picture of science that I mentioned
but far fewer
is broken
Science
into various distinct domains:
covering laws
.
.. We
have
laser
hydrodynamics,
genetics,
of domains.
laws like
IV. When
So far, I have
only argued
that
laws
argued
most
For example,
(ceteris paribus) adding salt to water
decreases the cooking time of potatoes;
taking the
water to higher altitudes increases it. Refining,
if we
spoke more carefully we might say instead, "Adding
the altitude constant
salt to water while keeping
the
whereas
time;
cooking
the
keeping
saline
increasing
the
content
fixed
it ;" or
increases
as
covering
But neither of these tells what happens when we both
add salt to the water and move to higher altitudes.
in the
Here we think that probably
somewhere
even
happen,
answer
it
though
is not
about
current
like diffusion,
heat
transfer,
processes
are described
well-known
various
by
Ohm's
law
for
current.
electric
But
these
laws: each is a ceterisparibus law which
only
happens
concentration
at work.
Most
in
happens
There
effects
The
example,
these
complex
is no general
of
the
same
or electric
separate
is true
although
laws which
cases
On
and
warm,
laws
a
have
from
a humdrum example. Last
in my garden. I know that
I planted them in composted
the
other
hand,
I also
know
that
I knew
care,
was
still
can't
take
the manure
roots
camelia
went
what
The
wrong.
are
not
true
a
not
quantum
available.
to combine
phenomenological
for other
disciplines
theory
is
what
describe
the
laws.
as well.
and
or may
notice,
But
not
even
camelias
some
It is
just
about
; still,
that
For
relativ?
it is not
covering
law. There
may
some
or
I didn't
to be
known
I made
since
confidence
But
factor
relevant.
to cases
peculiar
the uncertainty
that besets
matters
must
of fact. We
menaces
camelias.
other
deficiency
a factor which
have
is not
this uncertainty
other
Some
nitrogen
in the plants,
defect
genetic
one.
is the correct
responsible,
a reasonable
of
all
of
allow
to
effort
we may
to my
camelias,
this is the right explanation.
for the death of my
an
explanation
is no law that
true
any
camelias
from
that
says
just like mine, planted in soil which is both hot and
rich, die. To the contrary, they do not all die. Some
thrive ;and probably those that do, do so because of the
richness of the soil they are planted in.We may insist
that there must be some differentiating
factor which
case
a
the
under
law?in
soil which
brings
covering
is rich and hot, camelias of one kind die ; those of
another thrive. Iwill not deny that there may be such
a covering
law. I merely
repeat that our ability to
give
this
humdrum
explanation
laws
are
phenomena.
known,
these
Nevertheless,
our
precedes
edge of that law. In the Day
of Judgment,
suffice
may
in
loe. cit., p. 602.
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Claim: CP
laws, though
strictly speaking
no laws, provide
explanations
ceteris
high temperatures. So I did not know what to expect.
But when many of my camelias died, despite otherwise
phenom
ity are highly developed, detailed, and sophisticated,
there is no satisfactory theory of relativistic quantum
7
Klein
manure.
have
decribes what
are
theory for how
both
are
this is easy, for
explanations
So, we have an explanation
a
so
cause
as
(e.g.
long
single
or a
temperature
gradient)
gradient
some combination
involve
real life cases
and general
of causes;
ceteris
in nature,
role. But
are
paribus laws.
Let me illustrate with
year I planted camelias
camelias like rich soil so
eliminate
law for diffusion; Fourier's
law for shearing force; and
laws?Fick's
enological
for heat flow; Newton's
that
and
ceteris paribus
nevertheless,
explanations
explanation.
our
judgments
for oversight
common
our
of
part
would
what
folk wisdom. But this is not always the case. An
example which I have discussed before7 will illustrate.
Flow
the case. I have
half
scarce,
regularities
explanatory
of our
explanation
have
been
(x)(A(x) &-5(*)--/(*)).
is a precise
are
or
descriptions
that,
perfect
and
there
Anyway
died because they were planted in hot soil.
This is surely the right explanation
to give. Of
certain
that this
course, I cannot be absolutely
(x)(S(x)&-A(x)^I(x))
books
usually
paribus laws are no true laws. Ceteris paribus laws, read
to argue
ceterisparibus, (x) (A(x) -> ?/(*)).
while
Can Be Given
Explanations
fundamental
and
altitude
are
laws
intersect,
either false, if the ceterisparibus modifier is omitted, or
irrelevant tomuch real life, if it is included. It remains
ceterisparibus, (x) (S(x) -> I(x))
decreases
theories
Where
hard to come by.
literally
we have
Diagrammatically,
mechanics.
theory,
a lot of very detailed and sophisticated theories about
the various domains. But we
what happens within
in the
have
little theory about what
happens
intersection
QUARTERLY
to
the meantime
knowl?
when
explain
we
all
all
do
Example: a
CP law of
camelias in
hot soil
THE
give explanations;
what
CP laws are
required for
explanation even
where statistical
correlations are
available
kinds
In
explanations
to urge
I want
are
a
thesis.
If,
as
is
system,
possible, the world is not a tidy deterministic
this job of telling how we are to explain will be a job
which is still left when the descriptive task of science
is complete. Imagine for example (what I suppose to
actually be the case) that the facts about camelias are
irreducibly statistical. Then it is possible to know all
the general nomological
facts about camelias which
there are to know?for
that 62% of all
example,
camelias
in
just
the circumstances
of my
camelias
die,
and 38% survive.9 Still, one would not thereby know
in my garden. You
how to explain what happened
would still have to look to the Sunset Garden Book to
learn that the heat of the soil explains the perishing,
and the richness explains the plants which thrive.
IV.
Conclusion
I have said that in general scientific explanations
use ceteris paribus laws, laws which read literally as
Stanford University
accident.
MUCH
Statements
descriptive
but deemed
admissible.8
stronger
EXPLAIN
DOESN'T
and it is the job of science to tell us
of
fact,
TRUTH
163
of fact
are
false,
not
only
false even in the context of use. This
Explanatory
laws
their
by
very
nature
false,
is no
have
exceptions; only by unlikely circumstance will such
a law be literally true. Our picture of the explanatory
structure
of
are
there
nature
certain
this. We
requires
fundamental
laws
that
suppose
at work
in nature.
last year, Ernan McMullin
called
(At these meetings
these "structural laws".10) What objectively happens
is a consequence of the interplay of these fundamental
The
laws.
fundamental
describe
the
objectively
which
regularities
laws
occurring
occur
themselves
regularities;
are
in nature
do
not
rather,
the result
of the operation and interference of these fundamental
laws. It is part of the nature of an explanatory
law
that it hold only ceteris paribus?that
is, that it not
really hold at all. The laws which explain are not
laws in any literal sense.They do not tell what truly
happens in nature ;and conversely, a full knowledge
of what truly happens in nature, even what happens
and of necessity, does not tell how to
regularly
explain. The tasks of describing nature and of telling
how to explain it are distinct.
Received
September i, 1979
8
"How Do We Apply Science?"
in R. S. Cohen et al. (eds.), PSA 1974.
Nancy.
Cartwright,
(Dordrecht-Holland:
Reidel,
1976).
9
Various writers, especially Suppes (note 3) and Salmon
of more sophisticated
statistical facts will
(note 4), have urged that knowledge
to
suffice
determine what factors can be used in explanation.
I do not believe that this claim can be carried out.
Cf Cartwright,
Nancy,
"Causal Laws and Effective Strategies,"
in Nous (Nov., 1979). In that paper I argue that one
of causal
already needs a full complement
one
can
use
to
before
fix
statistical
laws
This
relevance.
causal
no
is
of
knowledge
however,
explanatory
knowledge;
singular
knowledge
so full knowledge
of the regularities
of nature is not enough to determine
facts, nor even of any regularities;
how we are to explain.
10
American Philosophical Quarterly, vol. 15, no. 2, (1979), pp. 139-147.
McMullin,
Ernan, "Structural Explanation,"
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