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God Exists!
Author(s): Robert K. MeyerSource: Nos, Vol. 21, No. 3 (Sep., 1987), pp. 345-361Published by: WileyStable URL: http://www.jstor.org/stable/2215186Accessed: 08-08-2014 05:49 UTC
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God Exists
ROBERT K. MEYER
AUSTRALIAN ATIONAL NIVERSITY
Everything has a cause. And the cause of everything has a cause.
So metaphysics
teaches.
Project any
of
these causal
sequences
in-
definitely back,
without
limit,
and the mind
boggles.
Whence there
is a First Cause. That all men call God.
The reader, we trust, has heard this argument before.
With its
variants
(for example,
from
motion),
it
is
the
Cosmological
Argu-
ment for
the
Existence of God.
Aquinas
devised it
(with
hints from
Aristotle) and pronounced it valid. Later philosophers have not been
so sure. In
Kant,
the
argument
finds
an
equal
and
opposite
one-
that things go back and back and back and back-and gets under-
mined in the resulting antilogism. Other philosophers-Hume, for
example-may be taken to have pronounced it simply
invalid. And
this, perhaps, is today the ruling opinion.
But is this ruling opinion correct? Oddly, the Cosmological
Argu-
ment
these days gets a boost from Cosmology. Trace back
the Ac-
tual
History
of the
Universe-not
what
it could
or
might
have
been,
but what it
was-and its outset, on today's common opinion,
came
with a
Big Bang. Physicists, not wishing to delve further
into
Theology than that, do not report Who, if Anybody, said "Let there
be
Light." But,
if
they
are to be
believed,
all of
a
sudden Light
there was,
in
a mighty rush.
So
it
is
at
least ironic
that,
at
a
time
when
empirical
scientists
are
putting
some
physical teeth back into this
old
argument,
philosophers (by
and
large, and Thomists not counting)
have
given
it up. There is nothing particularly unusual about this.
Philosophy
is rarely out of tune with the Science of the last century,
and has
NOUS
21 (1987):
345-361
?
1987 by Nou's Publications
345
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346
NOUS
been
known on
occasion to
pronounce
it
Ineluctable. It does take
a while to decide
why things must
be the
way
that
Scientists
have
told us that they are, and it would be comforting if they would take
a
hundred years
off
(or at
least
fifty,
given
that a
good many
con-
temporary
philosophers
have
by
now
caught up
with
Relativity
and
Quantum Theory) so that philosophers could catch
up.
But,
if
the
Cosmological Argument
is now
pronounced invalid,
what is
wrong
with
it?
Various
things, according to various
people.'
Any argument that has been around
that long has had more than
sufficient time for
minute
examination
by philosophical
counsel for
any
one of several hundred
positions
on these
questions (and,
more
relevantly, for two), and it is not surprising that, it is alleged, various
loopholes
have
been found. The most
persistent
has
to do with the
character of the backwards causal
sequences. Aquinas, living
at
a
time when the natural
numbers
only
went
forward,
the
negative
integers not
yet having
been
invented,
did
not
think
of the infinite
descending sequence,
0,
-
1,
-2,
....
(And,
presumptively,
it
did not occur
to
him to
think
of the
positive integers
as
analogous
to a
descending
causal
sequence,
with
item
n + 1
identified as the
cause of item
n, forever.)
Was Aquinas that dumb? We leave that question to scholarly
exhumation and examination of his old
math homework. But there
is no need or
reason to think that the Cosmological
Argument is
itself that
dumb (whence, granting Aquinas the benefit of the
doubt,
the
present
argument
should be ascribed to
him,
not
to
us).
For
consider some
homely
causal
sequence-the rolling
of a
ball across
the floor
by
a
child,
for
example.
If we view
this situation from
the
viewpoint
of the most casual physics, the ball occupies a
succes-
sion of
points
,
. . .
,
,
. . . on an appropriate
plane, where the xi and y, are real numbers. The ball's occupy-
ing any
of
these points is,
presumptively,
an
item
in a
causal
se-
quence. Yet the
ordering
is
not
of the
1, 2,
3
variety.
To
the
con-
trary,
since the real
numbers
are
densely ordered,
there
is
between
any
two
distinct
pairs
and
a third
pair
.
So this causal
sequence,
at least on
the
most casual
physics, is already deeply infinitistic
in
character. The picture is
not of one item
in
the sequence
causing
the
next (since there
is
no
next), but of
the
causal relation
just
rolling along (so to speak)
as the ball works its way through continuum many spots on the
floor,
some of
them
mighty
close
together.
While the title of this
paper
has
(somewhat
rashly)
asserted
the
truth
of
the conclusion of the
Cosmological Argument,
we
are
(naturally) concerned here
only
with its
validity. So the premiss-
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GOD EXISTS 347
that everything has
a cause-is
assumed,
since we are not here
query-
ing what Metaphysics teaches. (Quantum or other Indeterminism
might, of course, but this is not our present concern.) But we are
entitled to ask what the premiss means. For our homely example,
though it surely dealt with causally related tems, hardly enabled us
to speak of the cause
of a
particular
item
in
the sequence.
The Mechanistic Ideal, at least, has been that, given a particular
item in the sequence, and sufficient information pertaining thereto,
the
subsequent
items are
thereupon determined.
This
suggests that
what "Everything
has
a cause" ought perhaps
to
mean is that, for
every item
J,
there is some causal sequence C and some item
I
such that, in the sequence C, I is causally anterior to
J.
And it is
not hard to see that, if that is what "Everything has a cause" means,
we
are back
in
the
old
soup. Beginning
with
J,
we can
go causally
back and back and back
and
back,
forever.
Well,
so
perhaps
we can.
But what
happens
after "forever"?
Consider again
the infinite
sequence
of
ball-rolling
items.
Beginning anywhere in medias res, it does go back forever,
in
the
sense that any item
in
the
sequence
has an infinite number of causal
antecedents. But it
is
not
just
the
case,
in
our
homely example,
that every element of the sequence of ball-rolling items has some
causal antecedent,
in
this sequence.
The
child, remember, rolled
the
ball
across the floor.
That
is,
there
was an
item,
in a
larger
causal
sequence, causally
anterior to
every
item
in
the
ball-rolling
subse-
quence: namely,
the
impetus
that the child
provided
to the
ball,
that made it roll.
This suggests that our first
try
at
"Everything
has a cause"
(and, perhaps,
the Mechanistic
Ideal on
which
it
rested)
is a
bit
naive. It is not simply particular items
in
a causal sequence that
require causal antecedents. If we are to make causal sense of even
the most mundane and
ordinary
items
of
our
experience (at
least
if
we use the real
numbers-or,
these
days, perhaps
even
Leibniz's,
and
Robinson's, infinitesimals),
it is whole
causal
sequences
that
require such antecedents.
This leads us
to
formulate
the Causal
Prin-
ciple (henceforth, CP)
in the
following
manner:
(CP)
For
every
causal
sequence C,
there is some item
I
which
is
causally
anterior to
every
item
J
in
C.
A few words are in order about CP. In the first place, it subsumes
our earlier version
of
"Everything
has
a
cause".
For,
where
J
is
any item,
we
may
form the one-element causal
sequence consisting
of
J
alone.
By CP,
there is
some
element
I
causally
anterior to
every
member
of this
sequence: namely,
in
this
case,
to
J.
But
first-order
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348
NOUS
functional calculus fans will note immediately that, on a
point of
quantifier interchange, CP is strictly stronger than the
subsumed
principle. In prenex form, its quantifiers would read '(C)(HIJ)(J)'.
The weaker
principle, were we to state it analogously,
would come
out with prenex quantifiers '(C)(J)(HIJ)'. That is, roughly
speaking,
CP
stands to its weak analogue as uniform continuity does to
continuity.
Some to whom
we
have communicated
this
argument
have
ob-
jected at this point that the question has
been
begged. Since CP
does
in
fact suffice
for
the existence
of
God, it is
at
least begged
in
the sense that every valid argument begs the question: namely,
if you believe its premisses, you cannot but believe its conclusion,
since it is
already
contained
in
the
premisses.
In
this
case,
the claim
is simply that if everything has a cause, then God
exists,
which
is the traditional content of the Cosmological Argument. Since some
have found
this claim
startling,
while others have found
it
false,
the
question
is
at
least not
begged
in
a
psychological
sense. But
the idea
behind
the
friendly objections
seemed
to be somewhat
simpler.
If
every
time we
try
to
project
a
causal
sequence
backward
without
limit,
we strike
something causally
anterior
to
every
member
of the sequence, does not this mean that every causal sequence has
a
First
element? Whence
every
causal
sequence
that
is
long enough
has
a
first
element, namely
God.
While what follows the 'whence'
is true
enough,
a delicate mathematical
point
is still involved. For
it
is
not
true,
at
any rate,
that
every
causal
sequence
has
a
First
element,
even
after
CP is
granted.
Let us
go
back
to
the
ball-rolling,
fixing items
and
,
with
the former
causally
anterior, and let us
consider
now
all
the items
in
between. This
is a causal sequence, but it does not have a first element. What
it has, by CP, is an element of a larger sequence which is causally
anterior to
all
members of
the
given sequence. (In
this
case, clearly
the
item will
do.) So,
at least
intuitively,
it would seem
that the
path
to a First Cause is
still
blocked. We
take a causal
sequence,
and
apply
CP
to find an
item anterior to all members
thereof. But this
item
is
just part
of
a
larger
causal
sequence,
whence,
again applying CP,
we
find
an item anterior to all members
of
the
larger sequence. This too, it would seem,
is on its
way
to
going
on
forever. And our task is to
show
that,
this
time,
a sufficient
number of iterations (perhaps infinitely many) will, no fooling, yield
a First
Cause.
The
way
to do
this,
we shall
see,
is
to
make use of a renowned
mathematical
principle-the
famous Axiom
of
Choice. We shall first
apply
this axiom
informally,
to
get the ideas down.
And then we
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GOD EXISTS
349
shall set out the requisites for a formal
proof.
The
idea,
in
fact,
is the one that we have
just been through.
Pick
any item I. If
I
is not already a First Cause (that is, if we did not pick God to
start with), there
will
be some II
causally
anterior to
I, by
CP. Pick
an
II
with this property,
and find
by
CP a
causal anterior
I2
to
both
of
IlI.
Pick an
I2.
If
we continue
in this
way,
we
may get
a
causal sequence (.
. .
Ii+1
J0
.
. .
Jo=I),
where each
natural
number
i
appears
among
the indices. Let us
not
be discouraged
by this,
as
those
who
faint-heartedly pronounce
the
Cosmological
Argument invalid are prone to do. For there is, by CP, a
causal
antecedent
I.
to all
these
Ii,
where
X
is
(as usual)
the
first
transfinite ordinal. Picking I,,, we are off again. But we have by
now made an infinite number of
arbitrary
choices
(we
had
already,
in
fact), which is what the Axiom of Choice licenses. And we
simply
continue the process until
we
have either exhausted
Absolutely
Everything-in which case
we
have
found a
First Cause,
since
there
is nothing left to choose-or can
quit
because we have
already
found
a
First Cause.
In
any
event,
there
is
a First Cause. That
all
call God.
In
this informal version, the
argument may
be no more convinc-
ing than previous versions
of the
Cosmological Argument.
For one
thing, there are still various gaps in the argument. (The famous
question,
"Who made God?" is one of
them.)
For
another,
as we
have described
the
"picking" process,
there is still
something
mind-
boggling
about it.
To fill these
gaps,
and to
unboggle
the
mind,
it is necessary to be a little
more
careful. Let us
begin by returning
to CP.
In
stating it,
we made use of the notion
of a
causal
sequence,
and of a
relation,
"is
causally
anterior to".
But,
aside from
trading
on
the reader's
intuitions,
we didn't
really say
what these
things
were; or, more important
for our
immediate
purposes,
what formal
properties they were supposed to have.
Let us
begin with,
"is
causally anterior to", which we shall
henceforth abbreviate
simply by
'A'.
A
is
evidently
a
binary rela-
tion.
And,
since we don't want to
presuppose
what the
Universe
is made up
of
(events, atoms, souls,
or
whatever) we
have been
using
the
relatively
colourless
word "item" to
describe what it is
that
A
relates.
Items,
intuitively,
are
what is real in the
Universe.
Balls and falls, shirts
and
dirt, lights
and
fights, sinkings
and drink-
ings and thinkings we presume either to be
items,
or to
be con-
stituted from items in ways not here to be explained. We make
no
such
presupposition
about what is
more
evidently
conceptual
or
abstract.
For
example,
sets and
numbers,
whatever their
ontological
status,
do not
obviously
stand
in
causal
relations to each
other
(esoteric
efforts at
shuffling
the
furniture
of
the
Universe
aside).
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350
NOUS
This enables us to assume
that the collection V of all items is in
fact a set,
in
the mathematical sense, and that A is
a binary rela-
tion
on that set. This enables us to invoke the ordinary apparatus
of set theory. (If this is
displeasing, either because the
assumptions
are
already
felt
to
be too restrictive
or
because
the reader prefers
to do his
or
her mathematics
on some
other basis than,
say, ZF
set
theory,
we note that these assumptions are readily
transferable
to related
contexts; e.g.,
in
set theories
that
admit them,
V could
be
a
proper class, provided
that
other
assumptions
are
adjusted
to
suit.)
What else do we
expect
of
"is
causally
anterior
to"?
Since we
have given up (here, anyway)
on
the thought that
A is a
next-to-
next
relation, relating
a cause to
an
immediate effect,
it makes sense
to
think
of
A
as transitive.
If
I is
causally
anterior
to
J,
and
J
bears
the same relation
to
K,
then
I
is
causally
anterior to
K
as well.
If, nonetheless,
we
wish
to have some primitive idea
of a causal
relation
C
that relates
causes to their unique, immediate effects,
a relation that would not sensibly be transitive,
then we
may simply
identify
A
as
the
ancestral of C; that is,
in
this case,
A
bears
the
same relation to
C
that
"ancestor" bears to
"parent";
or,
near
enough, that a
bears to successor
as a relation
on
natural
numbers.,
This observation, perhaps,
relates our work here to some more
tradi-
tional
metaphysical analyses
of
causality; whence, given
CP,
it will
apply
to
these analyses
also.
But,
for
reasons
in
part
adduced above,
our concern here
is
with
A,
not
C,
and we
do
not
think
of
A
as
"cooked
up"
from
any
other relation.
Let us now
turn
to the question, "Who made God?"
The only
reasonable answer, after all, is "God",
if
we want
to speak that
way.
If
not,
the
First Cause is itself to be viewed as uncaused. So
far
as
the formal
properties
of
A
are
concerned,
this leaves us two
choices that seem plausible. Either
we
can
make
A
irreflexive,
allow-
ing nothing to be its own cause;
or
we
can
make
it reflexive, count-
ing any
item
I
(by
courtesy, so
to
speak) among
its
own
causes.
The
former, perhaps, is
closer to the usual intuitions about
these
things.
The
idea
then
would be
that a First Cause
(and only
a First
Cause)
would
be
itself
uncaused. But,
so
far as
formal
analysis
is
concerned,
it doesn't make much difference.
(Roughly
speaking,
we
can
think
of "is
causally
anterior to" either
as an
analogue
of
arithmetical
8/11/2019 Meyer God Exists
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GOD
EXISTS 351
It will be convenient, accordingly,
to take A as reflexive, extend-
ing to every item
I
the above courtesy of being counted among its
own causal antecedents. A corresponding
relation
PA, meaning
"I
is properlycausally anterior to
J,
" may then be defined as just sug-
gested by (I
A
J) & (I
*
J). PA,
of course, is also taken to be
transitive, whence, since it
is
evidently
irreflexive, it
follows im-
mediately that it is also asymmetric:
f I PA
J then not J
PA
I. The
corresponding property
to
be imposed
on
A
is that of anti-symmetry:
if
I
A
J and J
A
I, then
I
=
J.
This corresponds, in either case,
to the thought
that the causal relation has a direction,
without
loops.
One
does not start from an item
I, proceed
through
a
change
of ef-
fects
II,
I2,
etc.,
and
get
back
to I.
(More sharply, one does not,
some years hence, run into one's younger self on the street.) These
assumptions, though they certainly are traditional, rule out
some
esoteric
possibilities
that
physicists,
science fiction writers, and other
partisans of the imagination have wished to entertain. Since our
purpose here is to be traditional
in
all
things,
we
shall,
in
the
pre-
sent
context,
rule
them
out as well.
We can sum
up
our
assumptions
with some familiar
mathematical
terminology. Any transitive,
reflexive,
antisymmetric
relation R is called a partial order. Given
such a relation R defined
on a set S, S is called a partially ordered et, under the relation R.
So our
assumptions
on
the "causal
anterior" relation
A
amount
to the
following.
(PO) The set
V
of all items is partially
ordered under
A.
We need now
merely
to
spell
out what
we
mean
by
a
causal
sequence.
But,
in
the light
of
the assumptions
that we have made
on A, all
that
is
required
for some set
S
of items to be
a
causal
sequence
is that, when confined to
S,
the relation
A
be total; i.e., a subset
S of V is a causal sequenceprovided that, for all I,
J
in S, we have
either
I A
J
or
J
A
I. Such
a
subset
of a
partially ordered set
X
is called a chain in X. And so the causal sequences are just the chains
in V,
under the partial order
A.
We
introduce
some further
familiar
terminology (at
least it
will
be familiar to
those who are familiar
with
it)
to restate
our
Causal
Principle
CP. Let
X
be
a
partially
ordered set, under a relation
R.
A
member
J
of
X
is minimal
provided
that,
if
I
R
J
then
I
=
J. (Less formally, thinking
of R as a
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