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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 long-standing '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 Hawking2
and Hartle and Hawking3 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[hij,
f] gives the probability amplitude for a
certain three-dimensional space S that has the metric hij
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[hij,
f] |2.
In the case at hand, the probability is for the existence of the
three-dimensional spatial slice S (the "three-geometry S" in
Hartle and Hawking's parlance), from which the probability of the other
states of the universe can be calculated. The three-dimensional 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
hij 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, four-dimensional spacetimes which have a
three-dimensional space S with metric hij and matter
field f as a boundary. The square of
the modulus of the amplitude, | y[hij,
f] |2, gives the probability
that a universe begins to exist with a three-dimensional 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 three-dimensional space S as the
boundary of all merely possible four dimensional, finite
spacetimes, we can calculate the "unconditional probability'' of
the 3-space S, in the sense that we do not need to presuppose some actually
existent earlier 3-space S* as the initial condition from which the
probability of the final condition S is calculated. The probability of
the existence of the 3-space 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 wave-function 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 possible-worlds 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
Hintikka18, 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
above-named ones and I shall call it "the possible-worlds
interpretation"; it consists of the six axioms mentioned below.
I do not mean to say that (what I am calling) "the
possible-worlds 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 possible-worlds interpretation of the probability calculus is
sufficient to make sense of the unconditional probabilities implied by
quantum-gravity 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 possible-worlds interpretation of probability"),
even if unfamiliar, is sufficient to interpret the unconditional
probabilities implied by quantum-gravity cosmologies.
I will say that a possible world is a mind-independent (and Fregean-like) 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 truth-maker of this maximal proposition.
This requires a sort of "platonic realism," but such a
realism is required by quantum-gravity cosmologies in any case (as most
popular books by physicists on these cosmologies have recognized).
Further, Michael Tooley31 has given good
arguments that a Platonic-realist 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
above-specified sense and our second axiom is that there are Tooley-like
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 possible-worlds interpretation of probability
is that probabilities are proportions between possible-worlds (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 aleph-zero 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 aleph-zero worlds in
which a Hartle-Hawking type universe exists (a WH world) and aleph-zero
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 Hartle-Hawking universe):
WO1, WH1, WO2, WH2, WO3, WH3, WO4, WH4 . . .
This gives a 0.5 proportion of WH worlds to the worlds in which the
Hartle-Hawking law obtains. The solution to this problem is to introduce
a fourth axiom that proportionality among aleph-zero sets of worlds is
defined in terms of a suitably ordered sequence of worlds. This means,
in the present case, that there is an aleph-zero 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 aleph-zero 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 aleph-zero 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
aleph-zero 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
aleph-zero). 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 Hartle-Hawking law obtains.
A sixth axiom of the possible worlds interpretation of probability
requires the introduction of Robinson's33
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 Wattenberg34 were the first to
introduce nonstandard reals into probability theory and Brian Skyrms35
and David Lewis36 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 wave-function equation and the possible worlds in which
this functional law obtains. The wave-function 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
wave-function 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 possible-worlds theory of probability are
sufficient for our present purposes of explaining the unconditional
probability of a Hartle-Hawking 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 non-Tooleyian) 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 question-begging 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 self-evident a priori metaphysical truth that implies
the falsity of a science, i.e., an application of inductive logic to
observational evidence? Craig thinks so39
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
quantum-gravity cosmology requires a Platonic-realist 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 quantum-gravity model.43
Pagels says that in Alex Vilenkin's early model, "nothing"
does not refer to a quantum-mechanical 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
time-nothing.'"44 Pagels poetically
grasps the need for a Platonic-realist theory of natural laws in the
Hartle-Hawking model (and the early Vilenkin model) in this passage:
The nothingness "before" the creation of the universe is
the most complete void we can imagine-no space, time or matter
existed. It is a world without place, without duration or eternity,
without number-it is what the mathematicians call "the empty
set." Yet this unthinkable void converts itself into the plenum
of existence-a 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 wave-function equation. The
third sentence needs "probabilist" to be substituted for
"necessary," a phrase that is not pragmatically
self-referentially 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
Platonic-realist theory of laws of nature, since the wave function of
the universe is a functional law of nature.
3. The Inconsistency of the Hartle-Hawking Model with Classical
Theism
The Hartle-Hawking 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 Hartle-Hawking 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 Hartle-Hawking
universe exists follows directly from the natural-mathematical
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 Hartle-Hawking 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 Hartle-Hawking 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 Hartle-Hawking wave function of the
universe.
It may be said that God could will that the Hartle-Hawking wave
function law obtain and leave it to chance, a 99 percent chance, that a
Hartle-Hawking 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 Hartle-Hawking universe. Ned Markosian
has developed such a scenario.46 Imagine
there are 100 possible universes tied for best in intrinsic
value-ranking, and 99 of them are Hartle-Hawking 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 Hartle-Hawking type universe will be created
by God. As it happens, God does will that a Hartle-Hawking
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
natural-mathematical properties of the possible universes make it 99
percent probable that a Hartle-Hawking universe exist uncaused. This
probability statement is not consistent with the classical theist
position that there is 0 percent probability that a Hartle-Hawking
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 Hartle-Hawking universe existing is not 99 percent
but 100 percent.
Oppy says that if the Hartle-Hawking theory is true, the probability
that a Hartle-Hawking 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 Hartle-Hawking 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 Hartle-Hawking 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 Hartle-Hawking 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 three-dimensional slice of spacetime to
appear uncaused out of nothing. But this is a mistake, for the
probability of finding any three-dimensional cross-section of
spacetime in such quantum models is only relative to some other
cross-section 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 Hartle-Hawking theory. What shall we say about Craig's argument? Craig
is wrong both about the Hartle-Hawking 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
four-geometries bounded by a given three-geometry as giving the
amplitude for that three-geometry to arise from a zero
three-dimensional 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 mass-energy) 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 three-geometry in the
Hartle-Hawking 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 three-geometry."57
This predicted fluctuation to a zero three-geometry 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 Hartle-Hawking 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 395-400 in Isham's "Creation as a Quantum
Process."59 On pages 395-97, 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 Hartle-Hawking 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 Hartle-Hawking concept K(c,f
), where K is the probability, c the curvature, and f the matter field
of a certain three-dimensional 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 state-function 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 3-space]: there is no (c1,f1)
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 Hawking-type 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
Guy61 are wrong when they say the Hartle-Hawking 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 H-H wave function]. (Of course the
figure of proportions of possible worlds here is just that-a 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 "possible-worlds" 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 quantum-gravity 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 Hartle-Hawking 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 hij is
.99.
However, if theism is true, p does not entail r. There
must be a theistic proposition q1 that entails r,
since the probability of a universe existing based solely on
natural-mathematical 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 q1,
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 q1. Since the theist cannot allow that
p, in the conjunction p and q1, 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 Hartle-Hawking universe.
e = there obtains the wave function of the universe y[hij,
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 wave-function law is true.
It is part of quantum mechanics that any quantum-mechanical 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 Wheeler-DeWitt 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 Hartle-Hawking "no-boundary" wave function of the
universe.
2a. The probability distribution of the metrical and matter
properties of any given three-dimensional spatial slice of the
universe that has a preceding three-dimensional spatial slice, follow
deterministically from the metrical and matter properties of the
preceding 3-space in accordance with the "no-boundary"
solution of the Wheeler-DeWitt 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 3-spaces of the universe never
evolve in accordance with initial conditions and the
"no-boundary" solution of the Wheeler-DeWitt equation. But if
they never evolve in this way, Hawking's "no-boundary" 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 3-space S1 with the property
F, then there is a subsequent 3-space S2 that is
probabilistically caused by S1 in accordance with the
probability distribution specified by the 'no-boundary' solution of the
Wheeler-DeWitt equation." Now if the 3-space S1
mentioned in the antecedent exists, but the subsequent 3-space S2
is caused by God and is not probabilistically caused by S1 in accordance
with the Hartle-Hawking "no-boundary solution" of the
Wheeler-DeWitt 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 vis-à-vis 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 vis-à-vis 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 3-space S
determines the probabilities for the next 3-space. Suppose the 3-space
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 3-space 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 3-space, so that
the probability of a 3-space, p(h/e & b & G), is 100 percent,
where h is the hypothesis that the 3-space occurs, e is the evidence
that the earlier 3-space 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 wave-function 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 creation-is 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 space-time 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 human-divine 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.
References
1. L. Z. Fang and Z. C. Wu, "An Overview of
Quantum Cosmology," in Quantum Cosmology, ed. L. Z. Fang and
Remo Ruffini (Singapore: World Scientific, 1986), p. 3.
2. Stephen W. Hawking, "The Boundary Conditions
of the Universe," in Astrophysical Cosmology (Vatican City:
Pontifica Academiae Scientarium, 1982) pp. 563-72.
3. J. Hartle and Stephen W. Hawking, "Wave
Function of the Universe," Physical Review D 28 (1983):
2960-75.
4. R. Deltete and R. Guy, "Hartle-Hawking
Cosmology and Unconditional Probabilities," Analysis 57
(1997): 304-15.
5. William Lane Craig, "The Caused Beginning of
the Universe: A Reply to Quentin Smith," British Journal for the
Philosophy of Science 44 (1993): 623-29.
6. William Lane Craig, "Hartle-Hawking Cosmology
and Atheism," Analysis 57 (1997): 291-95.
7. Ned Markosian, "On the Argument from Quantum
Cosmology against Atheism," Analysis 55 (1995): 247-51.
8. Graham Oppy, "Some Questions about 'The
Hartle-Hawking Cosmology,'" Sophia 36 (1997): 84-95.
9. Richard Swinburne, review of Theism, Atheism,
and Big Bang Cosmology, by William Craig and Quentin Smith, Philosophical
Review 104 (1995): 337-39.
10. Oppy, "Some Questions about 'The Hartle-Hawking Cosmology.'"
11. Quentin Smith, "Stephen Hawking's Cosmology
and Theism," Analysis 54 (1994): 263-43.
12. William Lane Craig and Quentin Smith, Theism,
Atheism and Big Bang Cosmology (Oxford: Clarendon Press, 1993), pp.
307-10.
13. Alvin Plantinga, "World and Essence," Philosophical
Review 79 (1970): 461-92.
14. R. Adams, "Theories of Actuality," Nous
8 (1974): 211-31.
15. Rudolph Carnap, "Modalities and
Quantification," Journal of Symbolic Logic 11 (1946): 33-64.
16. Rudolph Carnap, Meaning and Necessity
(Chicago: University of Chicago Press, 1947).
17. Stig Kanger, Provability in Logic
(Stockholm: Almqvist & Wiksell, 1957).
18. Jaakko Hintikka, "Quantifiers in Deontic
Logic," Societa Scientariarum Fennica, Commentationes Human
Litterarum 23 (1957): 3-23.
19. Jaakko Hintikka, "Modality as Referential
Multiplicity," Ajatus 20 (1957): 49-64.
20. Jaakko Hintikka, "Modality and
Quantification," Theoria 27 (1961): 119-28.
21. Jaakko Hintikka, "The Modes of
Modality," Acta Philosophica Fennica 16 (1963): 65-79.
22. Saul Kripke, "A Completeness Theorem in
Modal Logic," Journal of Symbolic Logic 24 (1959): 1-14.
23. Saul Kripke, "Semantical Analysis of Modal
Logic I: Normal Propositional Calculi," Zeitschrift fur
Mathematische Logik 9 (1963): 67-96.
24. Saul Kripke, "Semantical Considerations on
Modal Logic," Acta Philosophica Fennica 16 (1963): 83-94.
25. Quentin Smith, Ethical and Religious Thought
in Analytic Philosophy of Language (New Haven: Yale University
Press, 1997).
26. Quentin Smith, "A More Comprehensive
History of the New Theory of Reference," in The New Theory of
Reference, ed. James Fetzer and Paul Humphreys (Dordrecht: Kluwer
Academic Press, 1998).
27. Rudolph Carnap, Logical Foundations of
Probability (Chicago: University of Chicago Press, 1950).
28. Rudolph Carnap, "The Two Concepts of
Probability," Philosophy and Phenomenological Research 5
(1945): 513-32.
29. Alvin Plantinga, "The Probabilistic
Argument from Evil," Philosophical Studies 35 (1979): 1-53.
30. Arthur Falk, The Joy of Deciding (privately
printed text for a course on decision theory, 1998).
31. Michael Tooley, Causation: A Realist Approach
(Oxford: Clarendon Press, 1987).
32. Storrs McCall, A Model of the Universe
(Oxford: Clarendon Press, 1994), pp. 86-94.
33. Abraham Robinson, Non-Standard Analysis
(Amsterdam: North-Holland Pub. Co., 1966).
34. Allen Bernstein and Frank Wattenberg,
"Nonstandard Measure Theory," in Applications of Model
Theory to Algebra, Analysis and Probability, ed. W. Luxemburg (New
York: Holt, Rinehart and Winston, 1969).
35. Brian Skyrms, Causal Necessity (New
Haven: Yale University Press, 1980).
36. David Lewis, "A Subjectivist's Guide to
Objective Chance," in Studies in Inductive Logic and Probability,
vol. 2, ed. R. Jeffrey (Berkeley: University of California Press, 1980).
37. McCall, A Model of the Universe.
38. Falk, The Joy of Deciding.
39. Craig and Smith, Theism, Atheism and Big Bang
Cosmology.
40. Deltete and Guy, "Hartle-Hawking Cosmology
and Unconditional Probabilities," p. 307.
41. Heinz Pagels, Perfect Symmetry (New York:
Simon and Schuster, 1985).
42. Ibid., p. 347.
43. A. Vilenkin, "Creation of Universes from
Nothing," Physics Letters 117B (1982): 25-28.
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 Hartle-Hawking Cosmology.' "
48. Craig, "The Caused Beginning of the
Universe: A Reply to Quentin Smith."
49. Craig, "Hartle-Hawking Cosmology and
Atheism."
50. R. Deltete and R. Guy, "Emerging from
Imaginary Time," Synthese 108 (1996): 185-203.
51. Deltete and Guy, "Hartle-Hawking 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. 399-400.
61. Deltete and Guy, "Hartle-Hawking Cosmology
and Unconditional Probabilities," p. 306.
62. Ibid.
63. Craig, "Hartle-Hawking 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. 186-87.
Quentin Smith is Professor in the Department of Philosophy at Western
Michigan University
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