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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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2/18

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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3/18

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-




4/18

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




5/18

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




6/18

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).




7/18

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


8/18

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

meyer god exists

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