Journal
of the American Scientific Affiliation 32.1 (March 1980) 5-13.
[American Scientific Affiliation,
Copyright © 1980; cited with permission]
Philosophical and Scientific Pointers
to Creatio ex Nihilo
William
Lane Craig
Deerfield,
IL 60015
To answer Leibniz's question of why
something exists rather than
nothing, we
must posit three alternatives: the
universe either had a
beginning or
had no beginning; if it had a beginning, this was either
caused or
uncaused; if caused, the cause was either personal or not
personal. Four lines of evidence, two philosophical and
two
scientific,
point to a beginning of the universe. If
the universe had a
beginning,
it is inconceivable that it could have sprung uncaused out
of absolute
nothingness. Finally, the cause of the
universe must be
personal in
order to have a temporal effect produced by an eternal
cause. This confirms the biblical doctrine of creatio
ex nihilo.
". . . The first question which
should rightly be asked,"
Wrote
Gottfried Wilhelm Leibniz, is "Why is there some-
thing rather
than nothing?"1 I want
you to think about
that for a
moment. Why does anything exist at all,
rather
than
nothing? Why does the universe, or
matter, or any-
thing at all
exist, instead of just nothing, instead of just
empty space?
Many great minds have been puzzled by this
problem.
For example,
in his biography of the renowned philoso-
pher Ludwig
Wittgenstein, Norman Malcolm reports,
. . . he said that he sometimes had a
certain experience which could
best be
described by saying that 'when I have it, I wonder at the
existence of
the world. I am then inclined to use such phrases as
"How
extraordinary that anything "should exist!" or "How ex-
traordinary
that the world should exist!"'2
5a
CREATIO EX NIHILO 5b
Similarly,
the English philosopher J. J. C. Smart has said,
". . .
my mind often seems to reel under the immense
significance
this question has for me. That anything
exists
at all does
seem to me a matter for the deepest awe."3
Why does something exist instead of
nothing? Unless
We are
prepared to believe that the universe simply
popped into
existence uncaused out of nothing, then the
answer must
be: something exists because there is an
eternal,
uncaused being for which no further explanation
is
possible. But who or what is this
eternal, uncaused
being? Leibniz identified it with God. But many modern
philosophers
have identified it with the universe itself.
Now this is
exactly the position of the atheist: the
universe
itself is
uncaused and eternal; as Russell remarks, ". . . the
universe is
just there, and that's all."4
But this means, of
course, that
all we are left with is futility and despair,
for man's
life would then be without ultimate significance,
value, or
purpose. Indeed, Russell himself
acknowledges
that it is
only upon the "firm foundation of unyielding
despair"
that life can be faced.5 But
are there reasons to
think that
the universe is not eternal and uncaused, that
there is
something more? I think that there
are. For we
can consider
the universe by means of a series of logical
alternatives:
Universe
beginning no
beginning
caused not
caused
personal not
personal
WILLIAM LANE CRAIG 6a
By
proceeding through these alternatives, I think we can
demonstrate
that it is reasonable to believe that the uni-
verse is not
eternal, but that it had a beginning and was
caused by a
personal being, and that therefore a personal
Creator of
the universe exists.
Did the
Universe Begin?
The first and most crucial step to be
considered in this
argument is
the first: that the universe began to
exist.
There are
four reasons why I think it is more reasonable
to believe
that the universe had a beginning.
First, I shall
expound two
philosophical arguments and, second, two
scientific
confirmations.
The first
philosophical argument:
1. An actual
infinite cannot exist.
2. A
beginningless series of events in time is an actual infinite.
3.
Therefore, a beginningless series of events in time cannot exist.
A collection of things is said to be
actually infinite only
if a part of
it is equal to the whole of it. For
example, which
is
greater? 1, 2, 3, . . . or 0, 1, 2, 3, .
. . According to prevailing
mathematical
thought, the answer is that they are equiva-
lent because
they are both actually infinite. This
seems
strange
because there is an extra number in one series
that cannot
be found in the other. But this only
goes to
show that in
an actually infinite collection, a part of the
collection
is equal to the whole of the collection.
For the
same reason,
mathematicians state that the series of even
numbers is
the same size as the series of all natural num-
bers, even
though the series of all natural numbers con-
tains all
the even numbers plus an infinite number of odd
numbers as
well. So a collection is actually
infinite if a part
of it is
equal to the whole of it.
Now the concept of an actual
infinite needs to be
sharply distinguished
from the concept of a potential
infinite. A potential infinite is a collection that is
increasing
WILLIAM LANE CRAIG 6b
without
limit but is at all times finite. The
concept of
potential
infinity usually comes into play when we add
to or
subtract from something without stopping.
Thus,
a finite
distance may be said to contain a potentially in-
finite
number of smaller finite distances. This
does not
mean that
there actually are an infinite number of parts
in a finite
distance, but rather it means that one can keep
on dividing
endlessly. But one will never reach an
"infi-
nitieth"
division. Infinity merely serves as the
limit to
which the
process approaches. Thus, a potential
infinite
is not truly
infinite--it is simply indefinite. It is
at all points
finite but
always increasing.
To sharpen the distinction between an
actual and a
potential
infinite, we can draw some comparisons be-
tween
them. The concept of actual infinity is
used in set
theory to
designate a set which has an actually infinite
number of
members in it. But the concept of
potential
infinity
finds no place in set theory. This is
because the
members of a
set must be definite, whereas a potential
infinite is
indefinite--it acquires new members as it grows.
Thus, set
theory has only either finite or actually infinite
sets. The proper place for the concept of the
potential
infinite is
found in mathematical analysis, as in infini-
tesimal
calculus. There a process may be said to
increase
or diminish
to infinity, in the sense that the process can be
continued
endlessly with infinity as its terminus.6 The
concept of
actual infinity does not pertain in these opera-
tions
because an infinite number of operations is never
actually
made. According to the great German mathe-
matician
David Hilbert, the chief difference between
an actual
and a potential infinite is that a potential infinite
is always
something growing toward a limit of infinity,
while an
actual infinite is a completed totality with an
actually
infinite number of things.7 A
good example con-
trasting
these two types of infinity is the series of past,
present, and
future events. For if the universe is
eternal,
as the
atheist claims, then there have occurred in the past
WILLIAM LANE CRAIG 6c
an actually infinite
number of events. But from any point
in the
series of events, the number of future events is
potentially
infinite. Thus, if we pick 1845, the
birthyear
of Georg
Cantor, who discovered infinite sets, as our point
of
departure, we can see that past events constitute an
actual
infinity while future events constitute a potential
infinity. This is because the past is realized and
complete,
whereas the
future is never fully actualized, but is always
finite and
always increasing. In the following discussion,
it is
exceedingly important to keep the concepts of actual
infinity and
potential infinity distinct and not to confuse
them.
A second clarification that I must make
concerns the
word
"exist." When I say that an
actual infinite cannot
exist, I
mean "exist in the real world" or "exist outside
the
mind." I am not in any way
questioning the legitimacy
of using the
concept of actual infinity in the realm of
mathematics,
for this is a realm of thought only.
What I
am arguing
is that an actual infinite cannot exist in the
real world
of stars and planets and rocks and men.
What
I will argue
in no way threatens the use of the actual in-
finite as a
concept in mathematics. But I do think
it is
absurd that
an actual infinite could exist in the real world.
I think that probably the best way to show
this is to use
examples to
illustrate the absurdities that would result
if an actual
infinite could exist in reality. For
suppose we
have a
library that has an actually infinite number of books,
on its shelves.
Imagine furthermore that there are only
two colors,
black and red, and these are placed on the
shelves
alternately: black, red, black, red, and so forth.
Now if
somebody told us that the number of black books
and the
number of red books is the same, we would prob-
ably not be
too surprised. But would we believe
someone
who told us
that the number of black books is the same
as the
number of black books plus red books?
For in this
latter
collection there are all the black books plus an in-
finite number
of red books as well. Or imagine there
are
WILLIAM LANE CRAIG 6d
three colors
of books or four or five or a hundred.
Would
you believe
someone if he told you that there are as many
books in a
single color as there are in the whole collection?
Or imagine
that there are an infinite number of colors
of
books. I'll bet you would think that
there would be
one book per
color in the infinite collection. You
would
be
wrong. If the collection is actually
infinite then ac-
cording to
mathematicians, there could be for each of
the infinite
colors an infinite number of books. So
you
would have
an infinity of infinities. And yet it would still
be true that
if you took all the books of all the colors and
CREATIO EX NIHILO 7a
added them
together, you wouldn't have any more books
than if you
had taken just the books of a single color.
Suppose each book had a number printed on
its spine.
Because the
collection is actually infinite, that means
that every
possible number is printed on some book.
Now this
means that we could not add another book to
the
library. For what number would we give
to it? All
the numbers
have been used up! Thus, the new book
could not
have a number. But this is absurd, since
objects
in reality
can be numbered. So if an infinite
library could
exist, it
would be impossible to add another book to it.
But this
conclusion is obviously false, for all we have to
do is tear
out a page from each of the first hundred books,
add a title
page, stick them together, and put this new
book on the
shelf. It would be easy to add to the
library.
So the only
answer must be that an actually infinite library
could not
exist.
But suppose we could add to the
library. Suppose I
put a book
on the shelf. According to the
mathematicians,
the number
of books in the whole collection is the same
as
before. But how can this be? If I put the book on the
shelf, there
is one more book in the collection. If I
take
it off the
shelf, there is one less book. I can see
myself
add and
remove the book. Am I really to believe
that
when I add
the book there are no more books in the col-
lection and
when I remove it there are no less books?
Suppose I
add an infinity of books to the collection.
Am I
seriously to
believe there are no more books in the col-
lection than
before? Suppose I add an infinity of
infinities
of books to
the collection. Is there not now one
single book
more in the
collection than before? I find this hard
to
believe.
But now let's reverse the process. Suppose we decide
to loan out
some of the books. Suppose we loan out
book
number
1. Isn't there now one less book in the
collection?
Suppose we
loan out all the odd-numbered books. We
have loaned
out an infinite number of books, and yet
CREATIO EX NIHILO 7b
mathematicians
would say there are no less books in the
collection. Now when we loaned out all these books, that
left an
awful lot of gaps on the shelves.
Suppose we push
all the
books together again and close the gaps.
All these
gaps added
together would add up to an infinite distance.
But,
according to mathematicians, after you pushed the
books
together, the shelves will still be full, the same as
before you
loaned any out! Now suppose once more we
loaned out
every other book. There would still be
no less
books in the
collection than before. And if we pushed all
the books
together again, the shelves would still be full.
In fact, we
could do this an infinite number of times,
and there
would never be one less book in the collection
and the
shelves would always remain full. But
suppose we
loaned out
book numbers 4, 5, 6, . . . out to infinity.
At
a single
stroke, the collection would be virtually wiped
out, the
shelves emptied, and the infinite library reduced
to
finitude. And yet, we have removed
exactly the same
number of
books this time as when we first loaned out all
the odd
numbered books! Can anybody believe such
a library
could exist in reality?
These examples serve to illustrate that an
actual infi-
nate cannot
exist in the real
world. Again I want to under-
line the
fact that what I have argued in no way attempts
to undermine
the theoretical system bequeathed by Can-
tor to modern
mathematics. Indeed, some of the most
eager
enthusiasts of trans-finite mathematics, such as
David
Hilbert, are only too ready to agree that the concept
of actual
infinite is an idea only and has no relation to the
real
world. So we can conclude the first
step: an actual
infinite
cannot exist.
The second step is: a beginningless
series of events in
time is an
actual infinite. By "event" I mean something
that
happens. Thus, this step is concerned
with change,
and it holds
that if the series of past events or changes just
goes back
and back and never had a beginning, then, con-
sidered all
together, these events constitute an actually
CREATIO EX NIHILO 7c
infinite
collection. Let me provide an
example. Suppose
we ask
someone where a certain star came from.
He re-
plies that
it came from an explosion in a star that existed
before
it. Suppose we ask again, where did that
star come
from? Well, it came from another star before
it. And
where did
that star come from?--from another star before
it; and so
on and so on. This series of stars would
be an ex-
ample of a
beginningless series of events in time.
Now if
the universe
has existed forever, then the series of all past
events taken
together constitutes an actual infinite.
This is
because for
every event in the past, there was an event
before
it. Thus, the series of past events
would be infinite.
Nor could it
be potentially infinite only, for we have seen
that the
past is completed and actual; only the future can
be described
as a potential infinite. Therefore, it
seems
pretty
obvious that a beginningless series of events in time
is an actual
infinite.
But that leads us to our conclusion: therefore,
a begin-
ningless
series of events in time cannot exist. We have seen
that an
actual infinite cannot exist in reality.
Since a be-
ginningless
series of events in time is an actual infinite,
such a
series cannot exist. That means the
series of all past
events must
be finite and have a beginning. But
because
the universe
is the series of all events, this means that the
universe
must have had a beginning.
Let me give a few examples to make the
point clear. We
have seen
that if an actual infinite could exist in reality, it
would be
impossible to add to it. But the series
of events in
time is
being added to every day. Or at least so
it appears.
If the
series were actually infinite, then the number of
events that
have occurred up to the present moment is no
greater than
the number of events up to, say, 1789.
In fact,
you can pick
any point in the past. The number of
events
that have
occurred up to the present moment would be no
greater than
the number of events up to that point, no
matter how
long ago it might be.
Or take another example. Suppose Earth and Jupiter
CREATIO EX NIHILO 7d
have been
orbiting the sun from eternity. Suppose
that it
takes the
Earth one year to complete one orbit, and that it
takes
Jupiter three years to complete one orbit.
Thus for
every one
orbit Jupiter completes, Earth completes three.
Now here is
the question: if they have been orbiting
from
eternity,
which has completed more orbits? The
answer is:
they are
equal. But this seems absurd, since the
longer they
went, the
farther and farther Jupiter got behind, since every
time Jupiter
went around the sun once, Earth went around
three
times. How then could they possibly be
equal?
WILLIAM LANE CRAIG 8a
Or, finally, suppose we meet a man who
claims to have
been
counting from eternity, and now he is finishing: -5, -4,
-3, -2, -1,
0. Now this is impossible. For, we may ask, why
didn't he
finish counting yesterday or the day before or the
year
before? By then an infinity of time had
already
elapsed, so
that he should have finished. The fact
is we
could never
find anyone completing such a task because at
any previous
point he would have already finished.
But
what this
means is that there could never be a point in the
past at
which he finished counting. In fact we
could never
find him
counting at all. For he would have
already fin-
ished. But if no matter how far back in time we go,
we
never find
him counting, then it cannot be true that he has
been
counting from eternity. This shows once
more that
the series
of past events cannot be beginningless.
For if
you could
not count numbers from eternity, neither could
you have
events from eternity.
These examples underline the absurdity of a
beginning-
less series
of events in time. Because such a series
is an
actual
infinite, and an actual infinite cannot exist, a begin-
ningless
series of events in time cannot exist.
This means
that the
universe began to exist, which is the point that we
set out to
prove.
The second
philosophical argument:
1. The
series of events in time is a collection formed by adding one
member after another.
2. A
collection formed by adding one member after another can-
not be actually infinite.
3.
Therefore, the series of events in time cannot be actually in-
finite.
This
argument does not argue that an actual infinite cannot
exist. But it does argue that an actual infinite
cannot come
to exist by
the members of a collection being added one
after the
other.
The series of events in time is a
collection formed by
WILLIAM LANE CRAIG 8b
adding one
member after another. This point is pretty
obvious. When we consider the collection of all past
events, it
is obvious that those events did not exist simul-
taneously--all
at once--but they existed one after another
in
time: we have one event, then another
after that, then
another,
then another, and so on. So when we talk
about
the
collection of "all past events," we are talking about a
collection
that has been formed by adding one member
after
another.
The second step is the crucial one: a
collection formed
by adding
one member after another cannot be actually
infinite.
Why?--because no matter how many members a
person added
to the collection, he could always add one
more. Therefore, he would never arrive at
infinity. Some-
times this
is called the impossibility of counting to infinity.
For no
matter how many numbers you had counted, you
could always
count one more. You would never arrive
at
infinity. Or sometimes this is called the impossibility
of
traversing
the infinite. For you could never cross
an infin-
ite
distance. Imagine a man running up a
flight of stairs.
Suppose
every time his foot strikes the top step, another
step appears
above it. It is clear that the man could
run for-
ever, but he
would never cross all the steps because you
could always
add one more step.
Now notice that this impossibility has
nothing to do with
the amount
of time available. It is of the very
nature of the
infinite
that it cannot be formed by adding one member
after
another, regardless of the amount of time available.
Thus, the
only way an infinite collection could come to
exist in the
real world would be by having all the members
created
simultaneously. For example, if our library
of in-
finite books
were to exist in the real world, it would have
to be
created instantaneously by God. God
would say:
"Let
there be. . . !" and the library would come into exis-
tence all at
once. But it would be impossible to form
the
library by
adding one book at a time, for you would never
arrive at
infinity.
WILLIAM LANE CRAIG 8c
Therefore, our conclusion must be: the series of events
in time
cannot be actually infinite. Suppose there were, for
example, an
infinite number of days prior to today.
Then
today would
never arrive. For it is impossible to
cross an
infinite
number of days to reach today. But
obviously,
today has
arrived. Therefore, we know that prior to today
there cannot
have been an infinite number of days.
That
means that
the number of days is finite and therefore the
universe had
a beginning. Contemporary philosophers
have shown
themselves to be impotent to refute this
reasoning.9 Thus, one of them asks,
If an infinite series of events has
preceded the present moment,
how did we get to the present moment? How could we get to the
present moment--where we obviously are
now--if the present
moment was preceded by an infinite series
of events?10
Concluding that this difficulty has not
been overcome and
that the
issue is still in dispute, Hospers passes on to an-
other
subject, leaving the argument unrefuted.
Similarly
another
philosopher comments rather weakly, "It is dif-
ficult to
show exactly what is wrong with this argument,"
and with that
remark moves on without further ado.11
Therefore, since the series of events in
time is a collec-
tion formed
by adding one member after another, and
since such a
collection cannot be actually infinite, the
series of
events in time cannot be actually infinite.
And
once more,
since the universe is nothing else than the series
of events,
the universe must have had a beginning, which
is precisely
the point we wanted to prove.
The first scientific confirmation: the evidence from the
expansion of
the universe. Prior to the 1920's,
scientists
assumed that
the universe as a whole was a stationary ob-
ject--it was
not going anywhere. But in 1929 an
astrono-
mer named
Edwin Hubble contended that this was not
true. Hubble observed that the light from distant
galaxies
appeared to
be redder than it should be. He
explained this
WILLIAM LANE CRAIG 8d
by proposing
that the universe is expanding.
Therefore,
the light
from the stars is affected since they are moving
away from
us. But this is the interesting
part: Hubble not
only showed
that the universe is expanding, but that it is
expanding
the same in all directions. To get a picture of
this,
imagine a balloon with dots painted on it.
As you
blow up the
balloon, the dots get further and further apart.
Now those
dots are just like the galaxies in space.
Every-
thing in the
universe is expanding outward. Thus, the
rela-
tions in the
universe do not change, only the distances.
Now the staggering implication of this is
that this means