 
Why Steven Hawking's Cosmology Precludes a Creator
by Quentin Smith
The following article is from Philo,
Volume 1, Number 1.
Abstract: Atheists have tacitly conceded the field to theists in the
area of philosophical cosmology, specifically, in the enterprise of explaining
why the universe exists. The theistic hypothesis is that the reason the
universe exists lies in God's creative choice, but atheists have not proposed
any reason why the universe exists. I argue that quantum cosmology proposes
such an atheistic reason, namely, that the universe exists because it has an
unconditional probability of existing based on a functional law of nature.
This law of nature ("the wave function of the universe") is
inconsistent with theism and implies that God does not exist. I criticize the
claims of Alston, Craig, Deltete and Guy, Oppy and Plantinga that theism is
consistent with quantum cosmology.
1. Explaining the Universe
Atheists have traditionally conceded in advance the theoretical arena in
cosmology to the theists. Atheists have offered no explanation of why the
universe exists, and theists have offered an explanation. It can be argued that
since theism has greater explanatory power, it is preferable according to this
theoretical criterion. Atheists have traditionally taken a merely negative
route, arguing that the theistic explanation is false, disconfirmed, or
meaningless. But this seems to be a tacit admission that theism is prima facie
theoretically superior to atheism, since theism at least purports to explain
something that atheism does not even attempt to explain.
But I think this prima facie superiority of theism to atheism can be
countered by showing that atheism offers an explanation of the universe, and a
better explanation, than theism. I believe that contemporary physical cosmology
can explain (in principle and in simplified models) the universe's existence.
Quantum gravity cosmology, I believe, does show how the universe can be
explained in atheistic terms.
In Fang and Wu's introduction to the book Quantum Cosmology, which collects
the major technical papers by Stephen Hawking, James Hartle, John Wheeler, and
others, they say quantum cosmology implies that "in principle, one can
predict everything in the universe solely from physical laws. Thus, the
longstanding 'first cause' problem intrinsic in cosmology has been finally
dispelled."^{1} This cosmology has eliminated the need to postulate (or even
the possibility of postulating) a first cause (originating cause) of the
universe's beginning. Stephen Hawking has famously said "there is no place
for a Creator." However, there is little or no actual arguments to be found
either in their technical or popular writings to support such
"atheistic" claims. Apparently they want to leave to philosophers the
task of figuring out how their mathematical equations both imply that there is
no First Cause and that there is an atheistic explanation of the universe's
existence. Some attempts to carry out this task in partial form will be made in
this paper. I will also show that the very explanation of the universe offered
by quantum cosmology implies that quantum cosmology is logically incompatible
with theism, that is, implies that God does not exist.
2. The Unconditional Probability of the Existence of a Universe
I shall concentrate on the cosmology developed by Hawking^{2} and Hartle and
Hawking^{3} and later elaborated upon by Hawking and other coauthors. The wave
function of the universe in Hartle and Hawking's paper gives a probabilistic and
noncausal explanation of why our universe exists. More precisely, it provides an
unconditional probability for the existence of a universe of our sort (i.e., an
expanding [and later contracting] universe with an early inflationary era and
with matter that is evenly distributed on large scales). Given only their
functional law of nature, there is a high probability that a universe of this
sort begins to exist uncaused.
This can be explained more exactly. In their formalism, y[h_{ij},
f] gives the
probability amplitude for a certain threedimensional space S that has the
metric h_{ij} and matter field f.
A probability amplitude y gives a number that, when squared, is the
probability that something exists. This is often put by saying that the square
of the modulus of the amplitude gives the probability. The square of the modulus
of the amplitude is  y[h_{ij},
f] ^{2}.
In the case at hand, the probability is for the existence of the
threedimensional spatial slice S (the "threegeometry S" in Hartle
and Hawking's parlance), from which the probability of the other states of the
universe can be calculated. The threedimensional space S is the first state of
the temporally evolving universe, i.e., the earliest state of the temporal
length 10^{43} second (the Planck length). S is the state of the universe that may
be called the "big bang"; it precedes the inflationary epoch and gives
rise to inflation.
The metric is the degree of curvature of spacetime; the metric h_{ij}
Hartle and
Hawking derive is that of an approximately smooth sphere (like the earth) that
is much smaller than the head of a pin.
The matter field f is equivalent to an approximately homogeneous distribution
of elementary particles throughout the small sphere S.
Hartle and Hawking derive the probability amplitude by adding up or summing
over all the possible metrics and matter fields of all the possible, finite,
fourdimensional spacetimes which have a threedimensional space S with metric h_{ij}
and matter field f as a boundary. The square of the modulus of the
amplitude,  y[h_{ij},
f] ^{2}, gives the probability that a universe begins to
exist with a threedimensional space S that possesses this metric and matter
field. The probabilities for the history of the rest of the universe can be
calculated once we know the metric and matter field of the initial state S.
Since the wave function includes the threedimensional space S as the
boundary of all merely possible four dimensional, finite spacetimes, we can
calculate the "unconditional probability'' of the 3space S, in the sense
that we do not need to presuppose some actually existent earlier 3space S* as
the initial condition from which the probability of the final condition S is
calculated. The probability of the existence of the 3space S is not conditional
upon the existence of any concrete object (body or mind) or concrete event
(state of a body or mind) or even upon the existence of any quantum vacuum,
empty space or time; the probability follows only from the mathematical
properties of possible universes. The probability of S is conditional only upon
certain abstract objects, numbers, operations, functions, matrices, and other
mathematical entities, that comprise the wavefunction equation. This gives us a
probabilistic explanation of the universe's existence that is based solely on
laws of nature, specifically the functional law of nature called "the wave
function of the universe."
Robert Deltete and Reed Guy,^{4} William Lane Craig,^{5},^{6} Ned
Markosian,^{7} Graham Oppy,^{8} Richard
Swinburne,^{9} and others have commented that my earlier explanation
of this notion of "the unconditional probability" of a universe
existing has no apparent sense and that this atheistic explanation of the
universe's existence is therefore unviable. Their criticisms, however, can be
shown to be unwarranted.
Oppy has successfully argued that a propensity or objective chance
interpretation of the probability calculus does not provide a sensible
conception of the relevant unconditional probability.^{10} However, he mistakenly
assumes I am adopting this "objective chance'' interpretation in my paper
"Stephen Hawking's Cosmology and Theism."^{11} Oppy's misinterpretation
may be due to the fact that he does not recognize that the configuration space
and state space of quantum gravity cosmology are timeless abstract objects
("mathematical spaces") rather than physical existents.^{12}
Other critics of my notion of unconditional probability have not provided
much by way of argument. It seems to me there is a straightforward way to
understand such probabilities. We do not appeal to the propensity (objective
chance) interpretation of probability, the personalist interpretation, the
logical interpretation, the actual finite frequency interpretation, or the
limiting relative frequency interpretation. Rather, we need a possibleworlds
interpretation, where possible worlds are understood as abstract objects (along
the lines originally developed by Alvin Plantinga,^{13} R.
Adams,^{14} and others);
these theories are metaphysical interpretations of some version of the semantics
for modal logic developed by Rudolph Carnap,^{15}, ^{ 16} Stig
Kanger,^{17} and especially
Jaakko Hintikka^{18}, ^{19},
^{20}, ^{ 21} and Saul
Kripke.^{22}, ^{23}, ^{ 24} (I give more details in
my Ethical and Religious Thought in Analytic Philosophy of Language and in an
article in The New Theory of Reference.^{25}, ^{26}) Carnap used possible worlds in
his logical interpretation of probability.^{27}, ^{ 28} Plantinga has shown how
possible worlds can be used in the frequency interpretation of probabilities and
there have been other uses of possible worlds.^{29}, ^{ 30} However, there is a
different interpretation of probability than the abovenamed ones and I shall
call it "the possibleworlds interpretation"; it consists of the six
axioms mentioned below.
I do not mean to say that (what I am calling) "the possibleworlds
interpretation" of the probability calculus is the only valid one. I see no
reason to deny that there are actual finite frequencies, limiting relativity
frequencies, propensities, subjective probabilities, or even logical
probabilities. My claim is merely that the possibleworlds interpretation of the
probability calculus is sufficient to make sense of the unconditional
probabilities implied by quantumgravity cosmologies, whereas the familiar
interpretations are insufficient and thus "outdated" in terms of the
most recent advances in the physical sciences. Specifically, my thesis is not
that each or any one of the following six axioms, taken by itself, is a new
idea; rather, my thesis is that the conjunction of these six axioms ("the
possibleworlds interpretation of probability"), even if unfamiliar, is
sufficient to interpret the unconditional probabilities implied by
quantumgravity cosmologies.
I will say that a possible world is a mindindependent (and Fregeanlike)
maximal proposition W, such that for each proposition p, W entails p or W
entails ~p. The one and only actual world is the one and only maximal
proposition W' that is true. The concrete, physical universe belongs to the
truthmaker of this maximal proposition.
This requires a sort of "platonic realism," but such a realism is
required by quantumgravity cosmologies in any case (as most popular books by
physicists on these cosmologies have recognized). Further, Michael Tooley^{31} has
given good arguments that a Platonicrealist theory of laws of nature is
required by science in general; Tooley's natural laws are relations among
universals and these universals need not be instantiated by anything. Our first
axiom is thus that there are possible worlds in the abovespecified sense and
our second axiom is that there are Tooleylike laws of nature. (I do not mean to
commit myself to all the specifics of Tooley's, Plantinga's, Adams's, etc.,
theories.)
The third axiom of our possibleworlds interpretation of probability is that
probabilities are proportions between possibleworlds (or classes of possible
worlds). Given our third axiom, if the functional law of nature provides a 0.99
probability that a universe of our sort begins to exist uncaused, this means
that in 99 percent of the possible worlds in which this wave function is a law
of nature, there exists a universe of our sort that begins to exist uncaused.
Since there are at least alephzero possible worlds in which this functional
law obtains, we need to address Cantor's argument that there are no unique
proportions (such as 99/100) among infinite sets. Cantor's line of thinking
would suggest that since there are alephzero worlds in which a HartleHawking
type universe exists (a WH world) and alephzero worlds in which the wave
function obtains, then there is no fixed .99 proportion between them since the
worlds can be ordered as follows (where a WO world is a world in which the law
obtains but in which there is no HartleHawking universe):
WO1, WH1, WO2, WH2, WO3, WH3, WO4, WH4 . . .
This gives a 0.5 proportion of WH worlds to the worlds in which the HartleHawking
law obtains. The solution to this problem is to introduce a fourth axiom that
proportionality among alephzero sets of worlds is defined in terms of a
suitably ordered sequence of worlds. This means, in the present case, that there
is an alephzero number of mutually exclusive, exhaustive, and finite sets of
worlds in which the wave function obtains, such that each of these finite sets
contains only 99 WH worlds and one WO world. (There are infinitely many
logically possible worlds in which the wave function does not obtain, and all of
these worlds are not included in our infinite set of worlds.)
However, there are more than alephzero worlds in which the wave function of
the universe obtains and thus we need to characterize proportionality among
worlds in terms of nondenumerable infinities. This requires a fifth axiom that
proportionality can be defined in these cases in terms of a proportionally
preserving, branching, treelike topological structure. This "tree"
branches finitely and equally at each of an alephzero number of levels. Storrs
McCall has worked out a convenient model in terms of a decennary tree (a tree
that branches in ten at each level).^{32} But we differ from McCall in that we do
not regard possibilities as existent, concrete items but as abstract objects,
propositions, and in that we do not view the treelike structure as a temporally
evolving branching of the future possibilities of concrete particulars but as an
abstract structural relation among possible worlds. We borrow from McCall his
idea of a decennary tree, suitably redefined for our purposes. As I conceive it,
a decennary tree is an abstract topological structure that branches in ten, such
that each of these ten branches itself branches in ten branches, each of which
in turn branches in ten, for each of an alephzero number of discrete nodes. (A
node is a point where a tenfold branching occurs.) Such a decennary tree will
contain a nondenumerable infinity of branches, specifically, 10 0 (ten to the
power of alephzero). On our abstract tree, each world is represented by a
branch of the tree; the branches are WH or WO worlds except that at each level
of ten branches, one branch is "unlabeled." The unlabeled branch has a
successor fan of branches that are labeled (as WO or WH worlds) at the next
level. Let us suppose the 0.99 probability is a nonterminating and nonrepeating
decimal, e.g., 0.99372 . . . and that the 0.1 probability of a WO world is the
decimal 0.00627. . . . The proportion between these two sets of worlds is
specified by 9 of the branches on the first level being WH worlds and none being
WO worlds. On the second level, 9 sets of branches (with each set having 10
members) are WH worlds and no set contains WO worlds; on the third level 3 sets
of branches contain WH worlds and 6 sets contain WO worlds, on the fourth level
there are 7 sets compared to 2 sets, and so on. This delineates the precise
decimal value of the proportion of WH worlds to WO worlds and thus the
proportion of WH worlds to all the worlds in which the HartleHawking law
obtains.
A sixth axiom of the possible worlds interpretation of probability requires
the introduction of Robinson's^{33} nonstandard real numbers to solve the problem
that classical measure theory (which uses only standard real numbers) poses,
viz., that there is a probability of zero for each particular WH or WO world.
Bernstein and Wattenberg^{34} were the first to introduce nonstandard reals into
probability theory and Brian Skyrms^{35} and David
Lewis^{36} were the first
philosophers to do this; since this time Falk and others have also used
nonstandard reals.^{37}, ^{ 38} Some nonstandard real numbers are infinitesimals; an
infinitesimal is smaller than any real number but larger than zero. Others are
hyperreals, which is a number that differs from a real number by an
infinitesimal. The probability of each particular WH or WO world is not zero but
is a standard or nonstandard real number. For example, if we suppose that the
Lebesque measure of the unit set consisting of our world WH' is zero, we may
say that the infinitesimally small probability of WH' existing is infinitely
close to the Lebesque measure of the set {WH'}.
Note that the introduction of decennary trees and nonstandard reals allows
there to be a definite probability for a particular world and we are thus not
confined to probability densities when dealing with infinite worlds.
We need to emphasize at this juncture the distinction between the parts of
the wavefunction equation and the possible worlds in which this functional law
obtains. The wavefunction equation involves a summation over all the possible
histories of finite universes that have the state S as a boundary. These
possible histories are a part of the wavefunction equation. Since this equation
exists in each WH or WO possible world, the parts of this equation (and thus the
possible histories summed over) also exist in each WH or WO world. If we
consider the wave function of the universe to be a complex mathematical
proposition p, then p will be a conjunct of each maximal proposition (possible
world) WH or WO. The possible histories summed over are neither possible worlds
(maximal propositions) nor physically existent histories. Rather, they are
complex counterfactual propositions that are parts of the mathematical
proposition p, which is itself a conjunct of each maximal proposition WH or WO.
These six axioms of the possibleworlds theory of probability are sufficient
for our present purposes of explaining the unconditional probability of a HartleHawking
type of universe. If Oppy, Deltete and Guy, Swinburne, Markosian, and others
have problems with this theory of probability, they cannot refute it by assuming
without argument that nominalism is true, that a regularity (or nonTooleyian)
theory of natural laws is true, or that only a propensity (objective chance),
actual frequency, or personalist theory of probability is true, for this would
amount at best to a questionbegging argument. Furthermore, these arguments
would rule out a priori (as impossibly true) an entire branch of contemporary
science, quantum gravity cosmology. Could there really be a selfevident a
priori metaphysical truth that implies the falsity of a science, i.e., an
application of inductive logic to observational evidence? Craig thinks so^{39} but
I doubt Oppy, Markosian, Swinburne, Deltete and Guy would want to go so far as
to reject the application of inductive logic to observations in favor of an a
priori "metaphysical intuition."
The extant arguments offered against the unconditional probability theory I
stated are invalid. For example, Deltete and Guy endorse an invalid argument
given by Drees, namely that: "A mathematical probability of getting a
universe from [literally] nothing does not give a physical universe, but only
the idea of a physical universe."^{40} Contra these authors, what gives the
(probable existence of an) idea of a universe is the mathematical probability of
there existing an idea of a universe. But the mathematical probability of there
existing a universe gives us (to a certain degree of probability) a
universe.
This is tautologically true and it is surprising that Deltete and Guy could
endorse Drees's tautologically false statements as "plausible."
As I mentioned, some writers of popular physics books are aware that
quantumgravity cosmology requires a Platonicrealist theory of probabilistic
laws of nature. (I exclude Hawking, whose philosophical musings in his popular
writings have been widely and correctly criticized as confused and
inconsistent.) One example is Heinz Pagels, who poetically grasps the relevant
ideas in Perfect Symmetry.^{41} He says Hawking and Hartle "calculate the
probability for the universe to emerge from a state of 'nothing,' as in Alex
Vilenkin's model, to the state of 'something.'"42 Pagels earlier recounts
Alex Vilenkin's account of "nothing" in Vilenkin's first
quantumgravity model.^{43} Pagels says that in Alex Vilenkin's early model,
"nothing" does not refer to a quantummechanical vacuum or empty
space. "'Space is still something,' Alex once remarked to me, 'and I think
the universe should really begin as nothing. No space, no timenothing.'"^{44}
Pagels poetically grasps the need for a Platonicrealist theory of natural laws
in the HartleHawking model (and the early Vilenkin model) in this passage:
The nothingness "before" the creation of the universe is the most
complete void we can imagineno space, time or matter existed. It is a world
without place, without duration or eternity, without numberit is what the
mathematicians call "the empty set." Yet this unthinkable void
converts itself into the plenum of existencea necessary consequence of physical
laws. What are these laws written into that void? What "tells" the
void that it is pregnant with a possible universe? It would seem that even the
void is subject to law, a logic that exists prior to space and time.^{45}
There is no constructive point in analytic philosophers engaging in the task
of tearing apart Pagel's passage or his earlier quoted sentences as logically
incoherent if taken literally. If we treat it as poetry, we can translate it
into a precise philosophical passage. Like most other physicists, Pagels uses
"creation" to mean the beginning to exist of something; he does not
use this word in a theological sense. The first sentence (translated or
conceptually transformed into literal and coherent philosophical language) means
that it is not the case that there is space, time, or matter except at or after
the beginning of the universe. The second sentence, apart from its exclusion of
eternity and thus tacitly of an eternal god, is best ignored, if only for the
reason that independently of the universe there timelessly exist numbers that
belong to the wavefunction equation. The third sentence needs "probabilist"
to be substituted for "necessary," a phrase that is not pragmatically
selfreferentially incoherent to be substituted for "unthinkable void"
and a noncausal term substituted for "converts," among other changes.
Apart from the usage of "void," the last three sentences convey with a
relative poetic clearness the fact that Vilenkin's, and Hartle and Hawking's,
cosmologies require a Platonicrealist theory of laws of nature, since the wave
function of the universe is a functional law of nature.
3. The Inconsistency of the HartleHawking Model with Classical Theism
The HartleHawking derivation of the unconditional probability of the
existence of a universe of our sort is inconsistent with classical theism. The
unconditional probability is very high, near to 1. For purposes of
simplification, we are saying the probability is 99 percent; there is a 99
percent probability that a universe of our sort—I will call it a HartleHawking
universe—exists uncaused.
The universe exists uncaused since the probability amplitude is determined by
a summation or path integral over all possible histories of a finite universe.
That is, the probability that a HartleHawking universe exists follows directly
from the naturalmathematical properties of possible finite universes; there is
no need for a cause, probabilistic or otherwise, for there to be a 99 percent
probability that a HartleHawking universe will exist.
This is not consistent with classical theism. According to classical theism,
if a universe is to have any probability of existing, this probability is
dependent on God's dispositions, beliefs, or choices. But the HartleHawking
probability is not dependent on any supernatural states or acts; Hartle and
Hawking do not sum over anything supernatural in their path integral derivation
of the probability amplitude.
Furthermore, according to classical theism, the probability that a universe
exist without divine causation is 0, and the probability that if a universe
exists, it is divinely caused, is 1. Thus, the probabilities that are implied by
classical theism are inconsistent with the probabilities implied by the HartleHawking
wave function of the universe.
It may be said that God could will that the HartleHawking wave function law
obtain and leave it to chance, a 99 percent chance, that a HartleHawking
universe begin to exist uncaused. But then God is not the creator of the
universe, and we no longer have the god of classical theism. According to
traditional theism, it is a contradiction to suppose that the universe exists
without being created by God.
Some may suggest a scenario where there is a 99 percent probability that God
shall create a HartleHawking universe. Ned Markosian has developed such a
scenario.^{46} Imagine there are 100 possible universes tied for best in intrinsic
valueranking, and 99 of them are HartleHawking type universes. According to
Markosian, since God is omnipotent, God could see to it that, for each of these
universes, there is a 1 percent chance that she will create (on a whimsy) that
universe. It follows, that there is a 99 percent probability that a HartleHawking
type universe will be created by God. As it happens, God does will that a HartleHawking
universe exist. Markosian thinks this scenario makes classical theism consistent
with Hartle's and Hawking's cosmology.
But it does not, for the wave function states that the naturalmathematical
properties of the possible universes make it 99 percent probable that a HartleHawking
universe exist uncaused. This probability statement is not consistent with the
classical theist position that there is 0 percent probability that a HartleHawking
universe exist uncaused or with Markosian's scenario where the 99 percent
probability obtains only because it is derived from supernatural considerations.
Further, since God is omniscient, she knows by middle knowledge or foreknowledge
which universe she will create and thus the probability of the HartleHawking
universe existing is not 99 percent but 100 percent.
Oppy says that if the HartleHawking theory is true, the probability that a
HartleHawking universe exists is 100 percent since such a universe does exist.^{47} But this
conditional probability is not the one I am talking about.
Given the condition that a HartleHawking universe exists, the probability of
its existing is 100 percent. But the unconditional probability of such a
universe, i.e., its probability not conditional upon anything but the wave
function of the universe, is 99 percent. It is this latter probability that
allows for an atheistic and acausal explanation of why the universe exists.
4. William Craig's Claim that the HartleHawking Probability Is Merely
Conditional
William Lane Craig and many others (e.g., Deltete and Guy) argue that the
probability implied by the wave function of the universe is not unconditional
and is conditional in a way that allows for a divine creation of the universe ex
nihilo. Their claim is that I have misunderstood the HartleHawking model.^{48},
^{49}, ^{50}, ^{ 51} According to Craig, the only probabilities that follow from their
model are conditional in the sense that they are transition probabilities for
one state of the universe to follow another state. He writes:
Smith interprets Hawking's model as establishing a certain probability for
the first threedimensional slice of spacetime to appear uncaused out of
nothing. But this is a mistake, for the probability of finding any
threedimensional crosssection of spacetime in such quantum models is only
relative to some other crosssection given as one's point of departure.^{52}
Craig does not refer to Hawking's articles in support of this claim, but to
the quantum cosmologist Christopher Isham's article on the HartleHawking
theory. What shall we say about Craig's argument? Craig is wrong both about the
HartleHawking theory and about Isham's interpretation of it.
First, Hawking and Hartle do say the probability is unconditional; in their
1983 article, they write about an unconditional probability amplitude, a
probability "amplitude for the Universe to appear from nothing."^{53
}More fully, they say:
One can interpret the functional integral over all compact fourgeometries
bounded by a given threegeometry as giving the amplitude for that
threegeometry to arise from a zero threedimensional geometry, i.e., a single
point. In other words, the ground state is the amplitude for the Universe to
appear from nothing.^{54}
Hartle has written to GrŸnbaum about the odd statement he and Hawking made
that nothing is a "single point" and has rejected this identification;
Hartle writes: "the 'nothing' is not realized as a physical state in the
formalism"^{55} and thus that the misleading statement about nothing being a
physical state, a "single point," should be omitted.
Hawking also recently emphasizes that the universe "would quite
literally be created out of nothing: not just out of the vacuum, but out of
absolutely nothing at all, because there is nothing outside the
universe."^{56} By "be created" Hawking, like other physicists,
means began to exist. The statement that universe is "created out of
nothing" means (in the familiar terms of analytic philosophy) that the
universe (a maximal spacetime containing massenergy) began to exist and that it
is not that the case that the universe is caused to exist or consists of
anything that exists temporally prior to the universe or that there is time
prior to the universe.
The only "single point" or zero threegeometry in the HartleHawking
model is one predicted with a certain degree of (unconditional) probability by
the wave function, and thus is not an unexplained given or brute fact. Hartle
and Hawking write in their original paper: "In the case of the Universe we
would interpret the fact that the wave function [the probability amplitude] can
be finite and nonzero at the zero three geometry as allowing the possibility of
topological fluctuations of the threegeometry."^{57} This predicted
fluctuation to a zero threegeometry is not the referent of "nothing"
in the "appear from nothing" phrase, since "nothing" has no
referent (or, in Hartle's words, "the 'nothing' is not realized as a
physical state in the formalism."^{58}
As I said, Craig does not refer to the HartleHawking article to support his
contention about the probabilities being conditional, but to Christopher Isham's
article. Did Isham get it wrong, or did Craig misread Isham?
Craig refers to pages 395400 in Isham's "Creation as a Quantum
Process."^{59} On pages 39597, Isham is talking about how the probability of
one state of the universe can be predicted from another state. But on page 398
he starts talking about the HartleHawking theory of the uncaused beginning of
the universe and says the wave function that gives the probability amplitude for
the beginning of the universe does not make reference to, or depend upon, any
earlier configuration or time from which the first physical state has evolved.
Isham writes about the HartleHawking concept K(c,f ), where K is the
probability, c the curvature, and f the matter field of a certain
threedimensional space. Isham writes:
Note that the "transition" probability [Isham puts
"transition" in scare quotes, since there is no transition from
anything else] associated with this statefunction is K(c,f ) =  y(c,f )
^{2}. .
. . Hence, K(c,f ) is a function of just a single configuration point (c,f )
[i.e., a single point in superspace, where each point represents a 3space]:
there is no (c_{1},f_{1}) corresponding to an earlier configuration and time from
which the system has "evolved." This is the precise sense in which the
theory is said to predict the probability that the universe is created in
various configurations "from nothing."^{60}
So Craig misinterprets both Isham and Hawking; Hawking's theory does give us
an unconditional probability that a Hawkingtype universe begins to exist
uncaused and Isham correctly recognizes and states this fact in his
interpretation of Hawking's theory. This also shows that Deltete and Guy^{61} are
wrong when they say the HartleHawking theory is analogous to ordinary quantum
mechanics in that it is about merely "a transition between two real
states" and thus that the "probability amplitude is
conditional."^{62}
5. Plantinga's Criticism of the Atheist Argument from Quantum Cosmology
Craig asserts that "Plantinga pointed out to Smith that since according
to classical theism God exists in all possible worlds, the probability of the
universe on the wave function cannot differ from its probability on the wave
function plus theism."^{63} Exactly what did Plantinga point out and how
should we evaluate his argument? Plantinga states that the relevant
unconditional probability is (to quote Plantinga's own words):
the proportion of possible worlds in which the universe has the
characteristics [specified by the HH wave function]. (Of course the figure of
proportions of possible worlds here is just thata figure; we have no reason to
think possible worlds occupy something like a space, and no reason to think that
there are at most continuum many possible worlds.) So the absolute probability
of there being such a universe is, say, .95. But according to theism, God's
existence is a necessary truth; so the probability that there be such a universe
on the existence of God is the same as its probability on any necessary truth,
which is just its absolute probability. So where's the inconsistency [that Smith
alleges]? Of course the probability that there is such a world, given that God
wills that there be such a world, is 1. But that's not an absolute probability,
but a probability conditional on the (contingent) truth that God wills there be
such a world.^{64}
I am sympathetic with the "possibleworlds" approach to probability
sketched (but not endorsed) by Plantinga in this passage and I think Plantinga's
ideas are more nearly in line with the probability theory required by
quantumgravity cosmology than are Deltete's and Guy's or Oppy's. However, I
believe there are several ways to respond to Plantinga's argument that there is
no inconsistency between classical theism and quantum cosmology.
To begin with, the argument that theism and quantum cosmology are consistent
is invalid in relevance logic. Let p be the complex proposition that states the
HartleHawking theory. For any conjunction of p with any necessary truth
q, p by
itself will entail (in the sense of relevance logic) the statement r of the
probability value. The proposition r is:
(r) The probability that a universe begins to exist with the matter field f
and metric h_{ij} is .99.
However, if theism is true, p does not entail r. There must be a theistic
proposition q_{1} that entails r, since the probability of a universe existing
based solely on naturalmathematical truths and without divine causation is
zero. Thus, quantum gravity cosmology and theism will differ as regards to which
conjunct in the conjunctive proposition, p and q_{1}, entails r, which prevents the
two theories from being consistent in relevance logic.
Another problem is that there is no candidate for the theistic necessary
truth q_{1}. Since the theist cannot allow that p, in the conjunction
p and q_{1},
entails r, the theist must find some necessary truth of theism that entails
r.
Plantinga's proposition, God exists, does not entail r; nor does the theistic
necessary proposition whatever universe that exists is created by God.
Contingent propositions about God's decision to create a universe are not
candidates, precisely because they are not necessary truths.
In fact, there is even an inconsistency in standard propositional logic
between theism and quantum cosmology. I have been using "conditional
probability" to mean a probability that is dependent on the existence of
some concrete things or events (bodies, minds, or events involving bodies or
minds). I will now use "conditional probability" to refer instead to
any probability of the form c(h/e & b), where c is the probability value,
h
a contingent hypothesis, e a contingent evidence statement, and b the
"background knowledge" of necessary truths. An "unconditional
probability" now refers to probabilities of the form c(h/b), which can be
abbreviated as c(h) to highlight their unconditional nature (they are not
conditional on any contingent proposition). I will assign the following values
to these letters:
h = there exists a HartleHawking universe.
e = there obtains the wave function of the universe y[h_{ij},
f].
b = small houses are houses, and . . . , etc. (the conjunction of all
necessary truths).
The proposition c(h/e & b) = .99 is true if Hawking's quantum cosmology
is true and it is no part of Plantinga's argument to argue this cosmology is
false. But if classical theism is true, b will include some truths that are
incompatible with c(h/e & b) = .99, since it is a necessary truth of
classical theism that for any possible universe U, the conditional probability
that U exists is zero unless the conditions include some positive, contingent
truths about divine dispositions, states or acts. A positive, contingent truth
about divine acts is any truth of the form, God exists and contingently performs
the act A. If theism is true, c(h/e & b) = 0, since e includes no positive,
contingent truths about divine dispositions, states, or acts. Thus if quantum
cosmology and theism are both true, it follows both that c(h/e & b) = .99
and that it is not the case that c(h/e & b) = .99. This shows that we need
not rely on relevance logic to show that quantum cosmology and theism are
logically inconsistent.
6. William Alston and the Problem of Conserving a Quantum Universe
God cannot conserve (in the sense of continuous creation) the successive
states of the universe if the wavefunction law is true.
It is part of quantum mechanics that any quantummechanical system Q is
governed by a wave function, and that the wave function evolves in accordance
with the Schrodinger equation unless interfered with by an outside influence.
Now the evolution of the quantum mechanical system Q in quantum cosmology is
governed by the gravitational Schrodinger equation (the WheelerDeWitt
equation). Since the system Q that is the subject of quantum cosmology involves
a physically closed system, the entire universe, there can be no outside
influences. The evolution of the probabilities of the metric and matter field of
the universe cannot be due to divine influence.
This argument can be presented more formally.
1a. The universe is a physically closed system that is described by the
HartleHawking "noboundary" wave function of the universe.
2a. The probability distribution of the metrical and matter properties of any
given threedimensional spatial slice of the universe that has a preceding
threedimensional spatial slice, follow deterministically from the metrical and
matter properties of the preceding 3space in accordance with the
"noboundary" solution of the WheelerDeWitt equation.
Therefore,
3a. There are always sufficient conditions for the probabilistic evolution of
the universe that are physical.
Therefore,
4a. There is no causal role for the god of classical theism to play in
determining the probabilistic evolution of the universe.
Note that if we introduce at this point a theological ceteris paribus clause
about divine conservation, we are introducing an argument that science is false,
and are not showing how science is consistent with theism. Note, first, that
there cannot be a theological ceteris paribus clause about divine conservation
that is logically consistent with quantum cosmology, for such a clause would
entail that the probabilities of the successive 3spaces of the universe never
evolve in accordance with initial conditions and the "noboundary"
solution of the WheelerDeWitt equation. But if they never evolve in this way,
Hawking's "noboundary" quantum cosmology is false.
If an alleged natural law L is never instantiated, despite the fact that its
antecedent is instantiated (the antecedent referring to the initial conditions),
then the alleged law is false. Consider this alleged law: "If there is a
3space S_{1} with the property F, then there is a subsequent 3space S_{2} that is
probabilistically caused by S_{1} in accordance with the probability distribution
specified by the 'noboundary' solution of the WheelerDeWitt equation."
Now if the 3space S_{1} mentioned in the antecedent exists, but the subsequent
3space S_{2} is caused by God and is not probabilistically caused by S1 in
accordance with the HartleHawking "noboundary solution" of the
WheelerDeWitt equation, then the quantum cosmological law is false.
William Alston states that quantum mechanics allows for divine intervention.^{65} Divine intervention would be ruled out, Alston says, if
"the universe as a whole [is] a closed system visàvis our body of
physical laws. That, in effect, is what envisaged by the Laplacean formulation
of determinism."^{66} If the universe is a closed system visàvis our body
of physical laws, then "the total state of the universe at one moment is a
determinate function of its state at any other moment."^{67
} Alston regards
quantum mechanics as refuting this view and allowing that "God designed the
universe to operate in accordance with probabilistic laws so as to give room for
God to enter the process as an agent."^{68}
Thus, we would have it that the wave function of the 3space S determines the
probabilities for the next 3space. Suppose the 3space that actually occurs
after S is S1. We may suppose that the probability of S1, conditional upon S and
the wave function, is 85 percent. But God wants to bring about a different
3space S2. Thus the probability of S1 conditional upon S, the wave function,
and God's volition that S2 occur, is 0 percent. Let us suppose that this is true
for each 3space, so that the probability of a 3space, p(h/e & b & G),
is 100 percent, where h is the hypothesis that the 3space occurs, e is the
evidence that the earlier 3space occurred, b is the relevant background
knowledge (in this case, the wave function), and G is God's willing that h be
true.
But in this case quantum cosmology would be false. It never succeeds in
giving us the correct probability for any hypothesis h. Quantum cosmology is
false since it includes among its conditions e + b, and omits G. It is not the
mere omission of G that renders quantum cosmology a false theory; it is the
inclusion of probabilistically irrelevant conditions e and b as the conditions
for h. Since p(h/e & b & G) = p(h/G), it follows that e and b are
probabilistically irrelevant. Quantum cosmology is thus false for two reasons;
it omits a relevant condition of p(h), and it includes only irrelevant
conditions of p(h).
The theist may respond to this that "science is true since it is only
about the natural universe, and does not take into account supernatural
activity." But this response is offered as a panacea to disguise the
implication of theism, namely, that science is false. Theism implies that
science gives us a false theory of the natural universe, since science asserts
that probabilistically irrelevant conditions of natural occurrences are the only
probabilistically relevant conditions. The reason the theist cannot admit this,
I submit, is sociological. Anybody who says "science is false and religion
is true" immediately puts themselves beyond the pale of academic
respectability and is dismissed as a "religious kook." I submit the
theist ought to brave this negative peer pressure and "come out of the
closet" about the implications of her theism.
Thus, Alston is mistaken that quantum mechanics can allow divine activity in
a way that classical determinism cannot. But Alston puts forth another line of
argument, that no scientific law specifies "unqualifiedly'' conditions for
a natural occurrence, be these conditions sufficient or probabilistic. Alston
writes: "The most we are ever justified in accepting is a law that
specifies what will be the outcome of certain conditions in the absence of any
relevant factor other than those specified in the law."^{69} "None of our
laws take account of all possible influences."^{70} Thus, "it can hardly
be claimed that such a law will be violated if a divine outside force
intervenes."^{71} But this does not solve the problem, since, if theism is
true, the conditions mentioned in the law are probabilistically irrelevant to
the outcome, and the law is false. If the law is true, then the conditions are
probabilistically relevant; but in that case, God cannot intervene since his
intervention, being omnipotent, makes any other conditions probabilistically
irrelevant.
Now, does quantum cosmology bring any new twist to this argument? This
argument holds for ordinary quantum mechanics as well as quantum cosmology, but
what quantum cosmology adds to this is that the wave function of the universe is
a unique sort of law in that it does take account of all possible influences and
does offer unqualified conditions for occurrences of states of the universe and
of the universe as a whole. The qualified laws are those that purport to
describe some part of the universe, since they allow that some other part may be
influential and thus change the outcome specified by the law. But the wave
function of the universe is about the whole universe. It is the one law that
incorporates the clause that there are no other possible outside influences. If
it did not incorporate this clause, it would not be a wave function of the
universe but a wave function of a subsystem of the universe.
The response that the law means no other "natural influences" is
unsuccessful, since the law, as a universal generalization, does not have for
its domain only some of the things that exist—God's creatures. The variable
ranges over everything. The natural/supernatural distinction is not made by the
wave function, but is invented by the theist, limiting the actually unlimited
domain of quantification of the variables in the wavefunction law. But this law
in fact has no limits to its domain of quantification. For the theist to
stipulate that it does not range over everything, but only some things—the
things belonging to God's creationis to change the law—or more exactly, is to
say the law is false since it ranges over everything and thus over God and thus
fails to account for God's activities in what it mentions.
This fact is illustrated by one point. As Hawking says in A Brief History of
Time,^{72} the wave function gives in principle the probabilities of the histories
of intelligent organisms: "Each history in the sum over histories will
describe not only the spacetime but everything in it as well, including any
complicated organisms like human beings who can observe the history of the
universe." Some of these histories include, to borrow Alston's phrase,
"the many occasions on which human beings take themselves to be in
communication with God, receiving messages from God and speaking to God in turn,
being aware of God's activity towards them. . . these events involve's God's
doing something at a particular time and place to bring something about."^{73}
The histories of intelligent organisms not only include their interactions with
other intelligent organisms, but also their interactions with God (or what they
believe is a god). If they receive a message from God, the description of this
event involves the description of the organism receiving the message from God
and (as a part of this complex event) God giving the message. A complete wave
function of the universe would thus include these humandivine interactions;
otherwise, it would not be complete. Thus, the universal variables in the
complete wave function do range over all events (which include, if theism is
true, creaturely events and the Creator's events). Accordingly, a theist has to
say that if a complete wave function does not incorporate reference to divine
activity, it is not true. It is not a wave function that describes the complete
histories of intelligent organisms; it has gaps in it, gaps at every moment when
someone stoops to prayer or hears a message from God. But the complete wave
function purports to have no gaps, and thus the theist must say that this
complete wave function is false.
The moral of this story is that quantum cosmology and classical theism cannot
both be true. One has two choices: become an atheist or else argue that science,
in the form of quantum cosmology, is false. However, since Copernicus and
Galileo, any time that religion has opposed science, religion has lost.
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38. Falk, The Joy of Deciding.
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41. Heinz Pagels, Perfect Symmetry (New York: Simon and Schuster, 1985).
42. Ibid., p. 347.
43. A. Vilenkin, "Creation of Universes from Nothing,"
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44. Pagels, Perfect Symmetry, p. 343.
45. Ibid., p. 347.
46. Markosian, "On the Arguments from Quantum Cosmology against
Atheism."
47. Oppy, "Some Questions about 'The HartleHawking Cosmology.' "
48. Craig, "The Caused Beginning of the Universe: A Reply to Quentin
Smith."
49. Craig, "HartleHawking Cosmology and Atheism."
50. R. Deltete and R. Guy, "Emerging from Imaginary Time,"
Synthese
108 (1996): 185203.
51. Deltete and Guy, "HartleHawking Cosmology and Unconditional
Probabilities."
52. Craig, "The Caused Beginning of the Universe: A Reply to Quentin
Smith," p. 637.
53. Hartle and Hawking, "Wave Function of the Universe," p. 2961.
54. Ibid.
55. Hartle, letter to Adolf GrŸnbaum, 1990.
56. Stephen Hawking and Roger Penrose, The Nature of Space and Time
(Princeton, N.J.: Princeton University Press, 1996).
57. Hartle and Hawking, ''Wave Function of the Universe," p. 2962.
58. Hartle, letter to Adolf Grünbaum.
59. Christopher Isham, "Creation of the Universe as a Quantum Tunneling
Process," in Physics, Philosophy and Theology, ed. R. J. Russell et al.
(Vatican City: Vatican Observatory, 1988).
60. Ibid., pp. 399400.
61. Deltete and Guy, "HartleHawking Cosmology and Unconditional
Probabilities," p. 306.
62. Ibid.
63. Craig, "HartleHawking Cosmology and Atheism," p. 292 n. 2.
64. Alvin Plantinga, quoted with permission from a private communication to
Quentin Smith about quantum cosmology and theism, 1996.
65. William Alston, "Divine Action, Human Freedom, and the Laws of
Nature," in Quantum Cosmology and the Laws of Nature, ed. R. Russell, N.
Murphy, and C. Isham (Vatican City: Vatican Observatory, 1993).
66. Ibid., p. 190.
67. Ibid., p. 188.
68. Ibid., p. 189.
69. Ibid., p. 190.
70. Ibid.
71. Ibid.
72. Stephen W. Hawking, A Brief History of Time (New York: Bantam Books,
1988), p. 137.
73. Alston, "Divine Action, Human Freedom, and the Laws of Nature,"
pp. 18687.
Quentin Smith is Professor in the Department of Philosophy at Western
Michigan University.
