THE OMEGA POINT THEORY:

A MODEL OF AN EVOLVING GOD

FRANK J. TlPLER, Max-Planck-Institut fur Physik und Astrophysik,

Garching b. Miinchen, and Department of Mathematics and Department

of Physics, Tulane University.

1 . Introduction

Science is now considered by many to have refuted the fundamental

tenets of the Christian religion. Many twentieth century theologians (and

many scientists) have attempted to avoid conflict between science and

religion by claiming that science and religion deal with wholly different

forms of knowledge: the realm of science is the natural world, while the

realm of religion is human morality and religious experience. But this

division must ultimately fail. The starting point of morality is an

understanding of humankind’s place in nature, something that is obviously

a scientific question. Our scientific understanding of our relation to the

natural world must necessarily affect religion. Many important Roman

Catholic authorities have recognized this by actually taking a stand on

cosmological questions. They have claimed that Catholic doctrine requires

the physical universe to have begun a finite time ago.1 Furthermore, it is

obvious that religious experience is truly meaningful only if there really is a

God out there who is the source of this experience; no Christian believes

for a moment that the experience of the presence of God is merely the

subject matter for a specialist in abnormal psychology. Throughout the

whole of human history, religion has been inextricably entwined with the

science of the day, and this will never change.

In this paper I shall discuss two recent developments in physics which

have important implications for religion. The first is the realization that we

humans are present in the Universe at an exceedingly early time in its

history. Almost all of universal history, and possibly almost all of the

history of life, lies in our future. If most of life is in the future, then it is

exceedingly unlikely that Homo sapiens is the most advanced form of life

that will ever evolve in the cosmos; rather, our species should expect to be

replaced one day by another. Traditional religion must come to grips with

the fleeting existence of our species in universal history. It is our relative

insignificance in time, not space, which is the real challenge posed by

modern cosmology for traditional religion.

I shall show that this view leads naturally to a physical theory for an

evolving God, which I term the Omega Point Theory. I shall outline this

theory in Section 3.

The second development is the possibility of a Theory of Everything

(TOE). A TOE might imply that there is only one logically possible

314 FRANK J. TIPLER

universe. This would refute both the Cosmological Argument and, more

importantly, its premise that God had some freedom of choice in creating

the universe. The traditional God would be made superfluous, but an

evolving God might be made necessary. The possibility of a TOE and its

implications for religion will be discussed in Section 4.

2. The Idea of an Evolving God

It is the purpose of this paper to provide an argument for the

existence of a Supreme Being who is also a Person. My analysis will be

carried out entirely within physics itself, and although I shall feel free to

use terminology from religion —- omnipotence, transcendence and

immanence, omniscience, and omnipresence, for example —— I shall regard

these notions as physical concepts, and accordingly define them in physics.

However, the God whose existence I shall claim arises naturally in modern

cosmology is not the traditional unchanging Deity, nor the wholly other

Being of modern 20th century theology, but rather an evolving God

somewhat like the God of Schelling, Alexander, Whitehead, and Teilhard

de Chardin. An evolving God is very much in the world, creates it, and is

created by it. The created and the creator are the same entity seen from

different temporal perspectives, and described in different modes. How this

works will be made clear in Section 3, where I shall outline the Omega

Point Theory. A fuller development of this theory can be found in chapter

l0 of The Anlhropic Cosmological Principle2 (hereafter referred to as

ACP), which I co-authored with John D. Barrow. The theological

implications of the Omega Point Theory were strongly de-emphasized in

the book, however. There, the theory was presented as a purely physical

theory * as in fact it is. But in this paper I shall adopt a theological point

of view and present the Omega Point Theory as a model of an evolving

God. Here I use the word “model” as physicists use it: a simplified picture

expressed in mathematical symbols whose essential features are believed to

correspond to reality. The “standard model” and the “Friedmann model”

are two examples of this use of the word in cosmology. I am sure that my

model of an evolving God is incorrect in its details, but I am also sure that

any fully consistent concept of an evolving God who is a Person must

resemble my model in its essential features. Indeed, I will go further: after I

define “person”, “soul”, and “mind” in Section 3 in terms of modern

computer theory, it will be clear that it is in the basic nature of “persons”

to evolve —~ to change in time —— so that the adjective “evolving” in

“evolving God” is redundant.

My model of an evolving God is, of course, dissimilar in many

respects to the traditional concept of the Supreme Personal Being. Since

my model assumes that at the most basic ontological level there is nothing

but physics and the “stuff” studied by physics, my model can conversely be

regarded as a challenge from physics to the traditional idea of Deity; it is a

claim that not only does the traditional God not exist, He is superfluous.

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MODEL OF AN evowmo 000 315

feel there is much to be said for some version of the cosmological/

ontological argument: there is some entity —~ a Supreme Being — which

necessarily exists in the sense that Its nonexistence would be a logical

contradiction. The existence of such a Being is believed to be the answer to

the questions of “Why is there something rather than nothing?“ and “Why

this universe rather than some other universe?" I shall consider what modern

physics has to say about these two questions — and the cosmological

argument -— in Section 4. The reader is referred to Sections 2.9, 4.7, and

6.14 of ACP for more details. In essence, the answers which many physicists

are giving to these two questions are: (1) that the physical universe in its own

right necessarily exists, and further, (2) there is only one logically possible

universe, for only one solution exists to the equations of physics and there is

only one consistent set of equations. Here is what I regard as the greatest

challenge to traditional theisrn: the possibility that the physical universe

might necessarily exist in its own right. If true, this would mean that God is

at best superfluous unless He is in the world. However, this possibility would

not be a challenge but instead a nice completion to my model of an evolving

God, in which the Deity and the entire physical universe are two aspects of

the same thing, just as a certain collection of atoms acting under blind

physical laws from one point of view is also a human being from another

point of view. Both modes of description of a human being are equally valid,

but epistemologically, neither can be completely reduced to the other,

although ontologically a human being is at the most basic level a collection

of atoms and nothing else. That is, I believe in ontological reductionism but

epistemological anti-reductionism in the sense defined by Ayala.3 I shall

assume the truth of this position in what follows. (See ACP, Section 3.2, for

a defense of this position). My model of an evolving God is most decidedly

not a variant of pantheism. God and the physical universe are not two words

for exactly the same thing.

The postulate from which I shall deduce in Section 3 an evolving God is

fundamentally a moral one: value is something connected with life. and thus.

if value is to remain in the universe, life must persist indefinitely; the laws of

physics must permit forever the continued existence of life. Thus my

argument for an evolving God has a certain family resemblance to Kant’s

moral argument. Furthermore, this continued existence of any sort of life

will imply, as I shall argue in Section 5, not merely a continued existence of

a low form of life, but also progressive evolution without limit in spacetime:

the limit of both cosmological and biological evolution is a point beyond

space and time, the Omega Point. We thus recover a progressive evolution in

the large, something which has been forever banished from evolutionary

biology. Teleology, although removed from terrestrial biology, reappears

when biology is combined with cosmology. I shall develop these ideas,

putting the Omega Point Theory in its historical perspective, in Section 5.

3. The Omega Point Theory

The crucial fact upon which the Omega Point Theory is based is that

we are observing the universe at a very early time in its history. The

316 FRANK J. TIPLER

universe is 10 to 20 billion years old, and our Earth is 4.5 billion years

old. But as large as these numbers are relative to human lifetimes, they

are insignificant in comparison to the length of time the universe will

continue to exist: even if the universe is closed, bounds on the rate of

expansion and the matter density imply at least 100 billion years until the

final singularity, and if the universe is open or flat, then it will continue

to exist forever. Now life has existed on our planet for at least 3.5 billion

years ~— microfossils of what appear to be quite advanced forms of

bacteria have been found which are that old, so life itself must be even

older. Probably life of some form can continue to exist on the Earth for

as least as long as the Sun remains on the main sequence, some 5 billion

years. Thus we would expect life to continue to exist for longer than it

already has existed. This lower bound on life expectancy is much longer

than the mere l00,000 years modern man (Homo sapiens) has existed.‘ It

is also much longer than a typical mammalian species survives, which is

about a million years. So if our species survives as long as does the

average mammalian species, it can expect to continue to exist for only

one five-thousandth of the future of life on this planet. Furthermore, the

future history of life on this planet is itself only a tiny fraction of the

future history of the universe. These numbers put the human race in its

proper perspective in the history of the cosmos.

It is important to emphasize that the above lower bounds on the

length of time the universe will continue to exist are very solid. That the

universe will continue to exist for at least 5 billion more years must be

regarded at least as certain as the fact that it has already existed for at least

5 billion years. There is simply no way our knowledge of physics could be

so wrong as to falsify this prediction of longevity. Thus, any religious

appraisal of the nature and destiny of humankind must take into account

this longevity. Almost all Christian theologians adopt a much shorter

temporal perspective. This is as great an error —— and as great a

misunderstanding of humankind’s place in nature — as believing that the

universe was created a few thousand years ago.

Let us consider the implications of this longevity by assuming that life

will continue to exist as long as the physical universe does. Note that this is

basically a moral postulate. More precisely, the existence of life is the prior

requirement for there to be any morality at all: lifeless and dead matter is

neither good nor had. Furthermore, a universe in which life and intel-

ligence evolved, but in which life (and hence intelligence) and all its works

disappeared forever would in my judgement be ultimately meaningless.

One can of course adopt other definitions of “ultimate meaning” (see Sec-

tion 3.7 of ACP for example; traditional Christian theism is one example).

but I think we can agree that if ultimate meaning is to reside somehow in

the physical universe itself, then a necessary condition is for life of some

sort to continue to exist. Thus, indefinite survival is a necessary condition

for a naturalistic ethics to be possible. If life must die out, then a

naturalistic competitor to Christian ethics is not possible. Furthermore,

whatever one’s views as to the source of ultimate meaning, it is extremely

important to investigate whether it is physically possible for life to exist as

long as the univu'.

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MODEL OF AN EVOLVING GOD 317

long as the universe does, for the answer is central to understanding

humankind’s place in nature.

In order to investigate whether life can continue to exist forever, I

shall need to define “life” in physics language. I claim that life is a form of

information processing (the converse is not true), and that the human mind

—- and the human soul ~ is a very complex computer program. This is not

to say that life is nothing but information processing. This naive

reductionist view I would strongly reject. All I am claiming is that at the

most basic level of physics, life is simply information processing. But there

are higher levels of epistemological description. Human beings love others,

they have emotional needs and deep feelings. These very real aspects of

human life cannot be reduced to simple theorems of information theory

and physics. (In principle, these aspects are equivalent to extremely

complex theorems, but such theorems would be humanly incomprehensible

and effectively undiscoverable. This is ontological reductionism combined

with epistemological irreductionism.) The crucial point is that the higher

levels must be consistent with the physics level; any discussion of human

feelings must be consistent with the general limitations on human minds

deduced from physical information theory which is applied assuming

minds are computer programs. This is in the end no different from the

requirement that a moral philosophy or a work in literary criticism must

not contradict the brute physical fact of people having to eat in order to

live. I find it fascinating -~ and one of the most important ideas I hope to

convey in this paper — that far-reaching and unexpected conclusions

about human destiny can be drawn from the physics level alone.

A complete justification for my claim that the mind is a computer

program would fill a book. A central argument is the Turing Test. I thus

refer the reader to several books on the Turing Test.5 See also Sections 3.2,

3.5, 7.2, and 10.6 of ACP. Instead of reviewing the Turing Test, let me give

here a religious justification for this claim: I shall justify the com-

puter/information processing model of life and mind simply by pointing

out the astonishing similarities between the mind-as-computer-program

idea and the traditional Christian concept of the “soul”. Both are fun-

damentally “immaterial”: a program is a sequence of integers, and an

integer —— 2, say -— exists “abstractly” as the class of all couples. The

symbol “2” written here is a representation of the number 2, and not the

number 2 itself. In fact, Aquinas and Aristotle defined the soul to be “the

form of activity of the body.” In Aristotelian language, the formal cause of

an action is the abstract cause, as opposed to the material and efficient

causes. For a computer, the program is the formal cause, while the

material cause is the properties of the matter of which the computer is

made, and the efficient cause is the opening and closing of electric circuits.

For Aquinas, a human soul needed a body to think and feel, just as a

computer program needs a physical computer to run.

Aquinas thought the soul had two faculties: the agent intellect

(intellectus agens) and the receptive intellect (intellectus possibilis), the latter

being the ability to acquire concepts, and the former being the ability to

retain and use the acquired concepts. Similar distinctions are made in

318 FRANK J. TIPLER

computer theory: general rules concerning the processing of information

coded in the central processor are analogous to the agent intellect; the

programs coded in RAM or on tape are the analogues of the receptive

intellect. (In a Turing machine, the analogues are the general rules of

symbol manipulation coded in the device which prints or erases symbols

on the tape vs. the tape instructions, respectively.) Furthermore, the word

“information” comes from the Aristotle-Aquinas’ notion of “form”: we

are “informed” if new forms are added to the receptive intellect. Even

semantically, the information theory of the soul is the same as the

Aristotle-Aquinas’ theory.

The point I am trying to make is that in a sense the mind-as-a-

program idea is just old wine in a new bottle; it poses no challenge to the

traditional view of the physical nature of man. But thinking of the human

mind as a computer program, and more generally, regarding all thought as

a species of information processing, is a conceptual advance of enormous

significance, for it allows us to turn many philosophical problems about

the scope and limits of human thought (or the thought of any possible

intelligent being, for that matter) into formal problems of mathematical

computer theory. For example, new light is thrown on the old issues of

reductionism vs. irreductionism and determinism vs. indeterminism by

thinking what these mean to a computer (see Section 3.2 of ACP for more

discussion). More importantly, in the language of information processing.

it becomes possible to say precisely what it means for life to continue

forever. I shall say that “life” can continue forever if: (1) information

processing can continue indefinitely along at least one world line 7 all the

way to the future “boundary” of the universe -—— that is, until the end of

time; (2) the amount of information processed between now and this future

boundary is infinite in the region of spacetime with which the world line 7

can communicate; (3) the amount of information stored at any given time

T within this region can go to infinity as T approaches its future limit (this

future limit of T is finite in a closed universe, but infinite in an open one).

The above is a rough outline of the more technical definition given in

Section 10.7 of ACP. But let me ignore details here. What is important is

the physical (and ethical!) reason for imposing each of the above three

conditions. The reason for condition l is obvious; it simply states there

must be at least one history in which life (= information processing) never

ends.

Condition 2 tells us two things. First, that information processed is

“counted” only if it is possible, at least in principle, to communicate the

results of the computation to the history 7. This is important in cosmology.

because in most model universes event horizons abound. In the Friedmann

universe, every comoving observer at some point loses the ability to send

light signals to every other comoving observer, no matter how close. Life

obviously would be impossible if one side of one’s brain became forever

unable to communicate with the other side. Life is organization, and

organization can only be maintained by constant communication between

the different parts of the organization. The second thing condition 2 tells

us is that the amount of information processed between now and the

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MODEL or AN EVOLVING GOD 319

end of time is potentially infinite. I claim that it is meaningful to say that

life exists forever only if the number of thoughts generated between now

and the end of time is actually infinite. But we know that each “thought”

corresponds to a minimum of one bit being processed. In effect, this part

of condition 2 is a claim that time duration is most properly measured by

the thinking rate, rather than by proper time as measured by atomic

clocks. The length of time it takes an intelligent being to process one bit —

to think one thought - is a direct measure of “subjective” time, and hence

is the most important-measure of time from the perspective of life. A

person who has thought ll) times as much, or experienced 10 times as

much (there is no basic physical difference between these options), as the

average person has in a fundamental sense lived 10 times as long as the

average person, even if the chronological age is shorter than the average.

The distinction between proper and subjective time crucial to

condition 2 is strikingly similar to a distinction between two forms of

duration in Thomistic philosophy. Recall that Aquinas distinguished three

types of duration. The first was tempus, which is time measured by change

in relations (positions, for example) between physical bodies on Earth.

Tempus is analogous to proper time; change in both human minds and

atomic clocks is proportional to proper time, and, for Aquinas also, tem-

pus controlled change in corporeal minds. But in Thomistic philosophy,

duration for incorporeal sentient beings ~ angels —~ is controlled not by

matter, but rather by change in the mental states of these beings

themselves. This second type of duration, called aevum by Aquinas, is

clearly analogous to what I have termed “subjective time.” Tempus

becomes aevum as sentience escapes the bonds of matter. Analogously,

condition 2 requires that thinking rates are controlled less and less by

proper time as T approaches its future limit. Tempus gradually becomes

aevum in the future. The third type of Thomistic duration is aeternitas:

duration as experienced by God alone. Aeternitas can be thought of as

“experiencing” all past, present, and future tempus and aevum events in the

universe all at once.

Condition 3 is imposed because, although condition 2 is necessary for

life to exist forever, it is not sufficient. If a computer with a finite amount

of information storage — such a computer is called a finite state machine

~ were to operate forever, it would start to repeat itself over and over.

The psychological cosmos would be that of Nietzsche’s Eternal Return.

Every thought and every sequence of thoughts, every action and every

sequence of actions, would be repeated not once but an infinite number of

times. It is generally agreed (by everyone but Nietzsche) that such a

universe would be morally repugnant or meaningless. Augustine argued

strongly in Book Twelve of The City of God that Christianity explicitly

repudiates such a world view: “Christ died once for our sins, and rising

again, dies no more.”° The Christian cosmos is progressive. Only if

condition 3 holds in addition to condition 2 can a psychological eternal

return be avoided. Also, it seems reasonable to say that “subjectively”, a

finite state machine exists for only a finite time, even though it may exist

for an infinite amount of proper time and process an infinite amount of

320 FRANK J. TIPLER

data. A being (or a sequence of generations) that can be truly said to exist

forever ought to be physically able, at least in principle, to have new

experiences and to think new thoughts.

This raises a fundamental problem for the view of eternal life held by

many Christians. There is no question but that an individual human being

is a finite state machine. His brain is limited in the number of memories it

can store. We are unaware of this because a rough calculation shows we

would have to live at least a thousand years before the limit of capacity

would be reached at the maximum memory storage rate recorded in psy-

chological experiments. However, a thousand years is but an infinitesimal

fraction of eternity (defined as infinite subjective time). It is possible to

have only a finite number of new thoughts and new experiences after being

raised from the dead at the Last Judgement. At normal subjective time

rates, only a thousand years worth of new experiences are possible if the

old memories are retained. It is logically impossible for “eternal” life to be

eternal in an experiential sense, unless we imagine the fundamental

finiteness of humanity is abolished upon resurrection. This is no solution,

for a being which has and uses a potentially infinite memory would be

utterly non-human. Our humanity is defined in part by our basic limita-

tions. A finite memory is one of these.

Implicit in the above argument is the idea that living, feeling, thinking,

etc., necessarily involve a change from one state to another. This is a

definite consequence of the mind-as-a-program concept. But I claim it is a

reasonable consequence. Consider a standard science fiction scenario, that

of placing a person in suspended animation. No mental or any other

changes occur to the person while she is frozen solid. Consistent with this

lack of change, I will suppose that in fact the perSon when revived

remembers nothing of the period while in suspended animation. Question:

was that person “alive” while in suspended animation? Certainly the

program that codes personality was not running during that time. That

person was quite literally in limbo while in suspended animation. I claim

there was no self-awareness during that time, because self-awareness means

analyzing a mental model you have of yourself, and analyzing means

mental change. That person was dead by most current legal definitions

during the suspended animation period, for these definitions are based on

neurological or other bodily activity (i.e., change of some sort). Never-

theless, I would conjecture that most people would be reluctant to consider

her dead, because she was by assumption reanimated. But what if she were

never reanimated? Suppose for some reason we discover we can’t reanimate

her even in principle. Even if the program which coded her personality

were never erased, his self-awareness, by assumption, would never return.

Isn’t this what we mean by death? Isn’t this the actual state — the lack of

self-awareness for all future time — that the legal definitions of death are

attempting to capture? So a program that cannot change, that is forever

static in principle, cannot be a person no matter how complex it is. Nor

can it be “intelligent” in any meaningful sense, because the essense of

intelligence 7 means the ability to learn from experience, and this again is a

species of change, of information processing.

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life/information pri

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MODEL OF AN EVOLVING GOD 321

Let us now consider whether the laws of physics will permit

life/information processing to continue forever. Von Neumann and others

have shown that information processing (more precisely, the irreversible

storage of information) is constrained by the first and second laws of

thermodynamics. Thus the storage of a bit of information requires the

expenditure of a definite minimum amount of available energy, this

amount being inversely proportional to the temperature. (See Section 10.6

of ACP for the exact formula.) This means it is possible to process and

store an infinite amount of energy between now and the final state of the

universe only if the time integral of P/T is infinite, where P is the power

used in the computation, and T is the temperature. Thus the laws of

thermodynamics will permit an infinite amount of information storage in

the future, provided there is sufficient available energy at all future times.

What is “sufficient” depends on the temperature. In the open and flat

ever-expanding universes, the temperature drops to zero in the limit of

infinite time, so less and less energy per bit processed is required with the

passage of time. In fact, in the flat universes, only a finite total amount of

energy suffices to process an infinite number of bits! This finite energy just

has to be used sparingly over infinite future time. On the other hand,

closed universes end in a final singularity of infinite density, and the

temperature diverges to infinity as this final singularity is approached. This

means that an ever increasing amount of energy is required per bit near the

final singularity. The amount of energy required per bit actually diverges

to infinity at the singularity. However, most closed universes undergo

“shear”, when they recollapse, which means they contract at different rates

in different directions (in fact, they spend most of their time expanding in

one direction while contracting in the other two!). This shearing gives rise

to a radiation temperature difference in different directions, and this

temperature difference can be shown to provide sufficient free energy for

an infinite amount of information processing between now and the final

singularity, even though there is only a finite amount of proper time

between now and the end of time in a closed universe. Thus, although a

closed universe exists for only a finite proper time, it nevertheless could

exist for an infinite subjective time.

But although the laws of thermodynamics permit conditions 1

through 3 to be satisfied, this does not mean that the other laws of physics

will so permit. It turns out that, although the energy is available in open

and flat universes, the information processing must be carried out over

larger and larger proper volumes. This fact ultimately makes impossible

any communication between opposite sides of the “living” region, because

the redshift implies that arbitrarily large amounts of energy must be used

to signal (this difficulty was first pointed out by Freeman Dyson). This

gives the first testable prediction of the Omega Point Theory: the universe

must be closed.

However, as I stated earlier, there is a communication problem in

most closed universes ~—~ event horizons typically appear, thereby

preventing communication. However, there is a rare class of closed

universes which doesn’t have event horizons, which means by definition

322 FRANK J. TIPLER

that every world line can- always send light signals to every other world

line. Now Penrose has found a way to precisely define what is meant by

the “boundary” of spacetime, where time ends. In his definition of the

“c-boundary”, world lines are said to end in the same “point” on this

boundary if they can remain in causal contact unto the end of time. If they

eventually fall out of causal contact then they are said to terminate in

different c-boundary points. Thus the c-boundary of these rare closed

universes without event horizons consists of a single point. For reasons

given in Section 10.6 of ACP, it turns out that information processing can

continue only in closed universes which end in a single c-boundary point,

and only if the information processing is ultimately carried out throughout

the entire closed universe.

Thus we have the second testable prediction of the Omega Point

Theory: the future c-boundary of the universe consists of a single point -

call it the Omega Point. (Hence the name of the theory.) It is possible to

obtain other predictions. For example, a more detailed analysis of how the

energy is used to store information leads to the third testable prediction of

the Omega Point Theory: the density of particle states must diverge to

infinity as the energy goes to infinity, but nevertheless this density of states

must diverge no faster than the energy squared.

But these predictions 8 just demonstrate that the Omega Point Theory

is a scientific theory of the future of life in the universe, and it is not my

purpose to discuss the science in detail here. Rather, I am concerned here

with the theological implications of the Omega Point Theory. That the

theory has such implications will be obvious if I restate a number of the

above conclusions in more suggestive words. As I pointed out, in order for

the information processing operations to be carried out arbitrarily near the

Omega Point, life must have extended its operations so as to engulf the

entire physical cosmos. We can say, quite obviously, that life near the

Omega Point is omnipresent. As the Omega Point is approached, survival

dictates that life collectively gain control of all matter and energy sources

available near the final state, with this control becoming total at the

Omega Point. We can say that life becomes omnipotent at the instant the

Omega Point is reached. Since by hypothesis the information stored

becomes infinite at the Omega Point, it is reasonable to say that the Omega

Point is omniscient; it knows whatever it is possible to know about the

physical universe (and hence itself).

The Omega Point has a fourth property. Mathematically, the

c-boundary is a completion of spacetime: it is not actually in spacetime,

but rather just “outside” it. If one looks more closely at the c-boundary

definition, one sees that a c-boundary consisting of a single point is

formally equivalent to the entire collection of spacetime points, and yet

from another point of view, it is outside space and time altogether. It is

natural to say that the Omega Point is “both transcendent to and yet

immanent in” every point of spacetime. When life has completely engulfed

the entire universe, it will incorporate more and more material into itself,

and the distinction between living and non-living matter will lose its

meaning.

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MODEL or AN avowmo 000 323

There is another way to view this formal equivalence of all spacetime

and the Omega Point. In effect, all the different instants of universal his-

tory are collapsed into the Omega Point; “duration” for the Omega Point

can be regarded as equivalent to the collection of all experiences of all life

that has. does. and will exist in the whole of universal history, together

with all non-living instants. This “duration” is very close to the idea of

aeternitas of Thomistie philosophy. We could say that aetemitas is

equivalent to the union of all aevum and tempus. If we accept my earlier

argument that life and personhood involve change by their very nature,

then this identification appears to be the only way to have a Person who is-

omniscient, and hence whose knowledge cannot change: omniscience is a

property of the necessarily unchanging, not-in-time, final state, a state

nevertheless equivalent to the collection of all earlier, non~omniscient

changing states.

Thus the indefinitely continued existence of life is not only physically

possible; it also leads naturally to a model of an evolving God.

4. Is There Only One Possible Physical Universe?

The idea that there may be only one logically possible actually existing

universe is an old idea. Hume (or perhaps I should say, Philo) briefly toyed

with it in his Dialogues on Natural Religion. Einstein often said that he

became a physicist in order to find out “if the dear Lord had any choice

when he created the universe.” But it is only in the last few years, with the

advent of the superstring theories, that the possibility of universal unique-

ness began to be seriously discussed.

Now any philosopher of science can tell you that this idea is complete

nonsense. Any scientific theory, indeed any logical system, is based on

axioms which are themselves unjustified. Thus further scientific advance is

always possible, for the axioms of the present day science can always be

found to be consequences of even more fundamental axioms, and so on ad

infinitum. A philosopher will tell you that one can always find alternatives

to the present day theories which will account for the observations we

have, just as well as the theories which are generally accepted by scientists.

In other words, the axioms used to describe current observations are far

from unique, if for no other reason than that we know very well the

observations are not absolutely precise. Unavoidable experimental errors

allow alternative theories, since many theories will be consistent with the

data. The philosopher might also point out that physicists have

occasionally claimed in the past they had the ultimate theory, only to see

their world view collapse like a house of cards. So why do we find many

famous contemporary physicists proclaiming that a unique physical theory

is not only possible, but just around the corner?

The basic reason is that it is easy to say one can always find an

alternative theory. It is extraordinarily hard to actually go out and find one.

The database of observations‘ is now so enormous that it is exceedingly

difficult to construct a mathematical theory which is even roughly in

agreement with experiment and which is fully self—consistent and universal.

324 FRANK J. TIPLER

The self-consistency problem is the most suggestive. It manifests itself

primarily in the problem of infinities in quantum field theory. Almost all

quantum field theories one can write down are simply nonsensical, for they

assert that most (or all) observable quantities are infinite. Only two very

tiny classes of quantum field theories do not have this difficulty: finite

quantum field theories and renorrnalizable quantum field theories. Even

before superstring theories became a major area of study, Steven Weinberg

stressed how exceedingly restrictive the requirement of renormalization

really is. It is really the renormalizability of Yang-Mills quantum fields

that caused particle theorists to concentrate attention on this class of

theories almost exclusively when attempting to model matter. But there is a

countable infinity of possible renormalizable Yang-Mills theories. Any

compact Lie group defines one. The Lie group SU(2)>< U(l) gives the

Weinberg-Salam unified theory of the weak and electromagnetic inter-

actions, and SU(3) correctly describes the color force which binds nuclei.

But these Lie groups were picked out of the pack by experiment, not by

logic. Still, this is considerable progress. We now have consistent theories

for three of the four known forces. Unfortunately, general relativity, which

is the standard theory of gravity, the fourth force, gives a non-re-

normalizable theory. Furthermore, even the renormalizable field theories

have not completely eliminated the nonsensical infinities; they have really

only succeeded in hiding them from view.

This is where superstrings come in. Green and Schwarz were able to

show in 1985 that, in the context of the standard way of adding Yang-

Mills fields to superstring theories, only two Lie groups, EsxEg and

SU(32), would give a consistent theory. And as a bonus, these theories

were not merely renormalizable, they were actually finite! (to first order,

anyway; there are pious hopes that the theories are finite to all orders). It

also appears that gravity and the other three forces are present in the low

energy limit of superstring theories. Now this is real progress! Full

mathematical self-consistency has reduced the range of possible theories

from the countable infinity of the possible Yang-Mills theories to a mere

two candidates.9 Self-consistency is also important in other ways in super-

strings.

The trend is clear. The more forces and phenomena we try to include

in a single theory, the less freedom we have to construct one. And, side by

side with this shrinking range of possible consistent theories, there are

fewer and fewer phenomena not included in the theory. There are actually

physical arguments to show that we may have seen most of the funda-

mental phenomena, in contrast to the situation at the end of the nineteenth

century. For example, all known elementary particles (fermions) can be

grouped into what are called “families”. if there were more than about 4

families, the synthesis of elements in the Big Bang would be different from

what it is observed to be. And we have already observed 3 families.

Is it any wonder many physicists have come to believe that this

process of fitting a larger and larger set of possible data points to a smaller

and smaller number of self-consistent theories will converge on a single

unique physical theory, a Theory of Everything (TOE)?

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MODEL OF AN EVOLVING 001) 325

A number of people have claimed that the Godel incompleteness

theorem shows a TOE cannot be true necessarily and a priori.10 I think

this claim is incorrect. Godel has indeed proven that any theory which is

sufficiently complex to contain all of arithmetic cannot be proven

consistent by arguments inside the theory itself. But this just means that a

self-justifying TOE must be simpler than the full theory of arithmetic.

There are in fact branches of mathematics which can be proven decidable

and consistent by reference to the branch itself. For examples, Euclidean

geometry was proven decidable by Tarski and hyperbolic geometry was

proven decidable by Schwabhauser.“ Nagel and Newman have given a

proof of consistency of an important part of logic, the sentential calculus,

or logic of propositions, in their popular-level book Gb'del’s Proof.12

Even arithmetic with addition only can be proven decidable. It is quite

possible that the TOE could lie in one of the decidable branches of

mathematics. 1 3

The important role self~consistency has played in the search for the

TOE is one reason for believing that the TOE, if found, will be the only

one logically possible. But it is not the only reason. After all, the TOE is so

hard to find because it has to account for so many things. Why couldn’t

the universe have been much simpler? There are two answers to this

question, both involving the Anthropic Principle. I shall give only one

answer here,“ the answer which involves an analysis of what the word

“existence” means.

A thing can be said to exist only if it or its effects can be detected in

some way. But the word “detected” itself presupposes the existence of

something to do the detecting. Now an analysis of just what detecting or

measuring means in physics shows that a measurement is carried out only

if some piece of information is recorded. This in turn implies that a

universe must be complex enough to permit the recording of information

before it can have observers of any sort. In the ACP, Barrow and I devote

some 400 pages to showing just how enormously complex this apparently

simple requirement that observers exist within it makes the universe. In a

nutshell, the universe must be as complex as it actually is in order to have

observers of our complexity. Since we humans are not really that complex,

this suggest it must be almost as complex as it is in order to have observers

of any sort.

This brings us to the age-old philosophical problem of whether a

universe which has no observers in it ~— and which has no detectable effect

on a universe which does contain observers ~—- can possibly be said to exist.

My own inclination would be to say no, because there is no way I can say

that anything inside such a universe exists; it is not possible to give

meaning to the word “existence” in such a context. So with this under-

standing of the word “existence”, it is quite plausible that only one

Universe is logically possible —~ i.e., capable of existence -~ and we’re in it.

It is interesting that from this view of what existence means, it is the

observers, or rather the possibility of observers and their observations, that

permit the universe to exist. In a sense, the creatures inside the universe

create both the universe and themselves.

326 FRANK J. TlPLER

Even if only one universe is logically possible, this does not mean that

this unique universe actually exists. It would seem that a further

assumption is required: the assumption that something exists. A reasonable

assumption, to be sure, but nevertheless an additional assumption. How-

ever, it is not clear to me this additional assumption is actually required.

Barrow and I develop at some length in Section 3.5 of ACP the fascinating

idea that a perfect computer simulation of a universe would be indis-

tinguishable from the real universe it simulates.15 Now a simulation is just

a sequence of natural numbers, and all sequences of natural numbers have

mathematical existence, even though they may never have achieved the

privilege of an actual physical representation in our actually existing

physical universe. But if one of these corresponds to a perfect simulation of

our physical universe, then as far as the humans simulated in the program

can tell, it is real. Our copies behave no differently than we ourselves. Thus

the existence (in the mathematical sense of the word) of these sequences of

numbers is ultimately indistinguishable from existence in a physical sense,

and mathematical existence comes ultimately from the laws of logic

themselves!

In other words, the universe may very well be, in John Wheeler’s

phrase, a self-excited circuit. It may necessarily exist in its own right. If it

does so exist - and I emphasize the word “if”, because there are many

gaps in the above argument ——- then the God whose existence is asserted by

the cosmological/ontological argument, the wholly other God of Barth,

and more generally any God who does not need the universe as much as

the universe needs him, is quite superfluous. And further, this sort of God

is superfluous in answering the very question for which his existence is

invoked: why is there something rather than nothing; why this universe

rather than some other universe?

5. The Implications of the Omega Point Theory

My favorite definition of “religion” appeared in an article by Miller

and Fowler published in the C TNS Bulletin: “ ‘Religion’ and ‘theology’ are

taken to refer to the following: anything is religious which is concerned

with the meaning of personal place; and theology is interpretative

reflection on and explicit articulation of the meaning of personal place.” 1°

Perhaps I like this definition because it turns the paper you are now

reading, the ACP, and even Darwin’s The Origin of the Species into

religious tracts! But is this definition really that different from Tillich’s

view 17 that religion, in the widest sense of the word,18 is that which deals

with questions of “ultimate concern"?

Certainly “personal place” was the central focus of the preceeding two

sections: in Section 3 the existence of an evolving God was inferred from

the naturalistic ethical postulate that it must be possible for life never to

die out in the universe, while in Section 4, it was argued that perhaps this

never-dying life was, is, and shall be collectively responsible for the

necessary existence of the universe itself (including the life within it). If the

argument of Section 4 is accepted, then the ethical postulate of Section 3 is

unnecessary: bot

the necessarily :

the collectivit) oi

living things as

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MODEL OF AN EVOLVING GOD 327

unnecessary; both it and the evolving God can be inferred as properties of

the necessarily existing universe —— but this universe owes its existence to

the collectivity of (past, present, future) living things, and the collectivity of

living things is the evolving God! The created and the Creator are

inextricably bound up in one another.

Humankind’s place in the scheme of things is that of an intermediate

link; we cannot expect our species, Homo sapiens, to live forever. We could

not possibly survive the great cold and great heat that await life in the far

future. The history of life on the Earth to date is a preview of what will be

the total history of life in the universe: all individual living species that

evolve on Earth eventually become extinct, but life itself goes back in an

unbroken chain, more than 3.5 billion years long, to the early youth of our

planet. As we humans are descended from simpler one-celled organisms,

long since extinct, so beings more complex than Homo sapiens will descend

from us. And beings still more complex will in turn descend from them, up

to the Omega Point.

This picture of the chain of life is strikingly similar to the medieval

and Enlightenment view of life, which the famous historian of ideas Arthur

0. Lovejoy termed “The Great Chain of Being.” ‘9 In this view, all living

things were arranged in a vast static hierarchy, with inorganic materials at

the bottom, followed by plants and animals, mankind in the center, the

angels higher still, and with God at the top. The Omega Point Theory is

essentially a temporalized version of The Great Chain of Being. Not

surprising, because as I emphasized in Section 3, life is fundamentally a

temporal phenomena; this same insight is what underlies Darwin’s Origin

of the Species. “Origin” is itself a temporal word.

This temporally progressive Chain of Being, with one species being

ultimately replaced by another coding more information (this is what is

meant by “more complex” or “more advanced”) is a consequence of the

assumption of “progress” which is built into conditions 1 through 3 of

Section 3. Our own species has limits; there is a limit to the knowledge that

can be coded in a human brain. So if knowledge is to continue to increase,

indeed to increase without limit, it must one day be coded in other than

human brains. Judging from the present rapid development of computers, I

would guess that our successor species will be quite literally “information

processing machines,” machines with minds superior to ours. Perhaps the

molecular biologist Manfred Eigen is correct in saying that DNA reaches

with Homo Sapiens the limit of the complexity it can code. If so, if life is to

gain in complexity and knowledge is to increase, then the leading shoot of

life must move from one substrate - DNA - to another. Certainly this

move must occur at some point in the future, because DNA-based life

cannot survive in the high temperature environment near the final

singularity. The extinction of our species is required both by the laws of

physics and the inherent logic of eternal progress. But this should not

horrify us. All religions agree that what is ultimately important is the eternal

continuation of intelligent personality (ultimately God’s), not the particular

racial form it happens to take. If the Omega Point Theory is true, life shall

not perish from the Cosmos, but shall grow into the Omega Point.

328 FRANK J. TJPLER

Acknowledgements

I should like to thank Professor Jiirgen Ehlers for the hospitality at

the Institut ftir Astrophysik of the Max-Planck~lnstitut fiir Physik und

Astrophysik, where this paper was written, and to the Max Planck Society

for financial support. I am grateful to Professor Frank Birtel for replacing

books and papers lost by various airline carriers. Finally, I am extremely

grateful to the participants of the Vatican Conference, particularly Michael

Heller, John Leslie, Ernan McMullin, Bob Russell, and Bill Stoeger, for

their valuable criticisms of an earlier version of this paper.

‘ In l909 the

universe at the bcpt

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MODEL OF AN EVOLVING GOD 329

NOTES

1 In I909 the Pontifical Biblical Commission listed the creation of the entire

universe at the beginning of time as one of the “fundamental truths" of the Genesis

creation story. Pope Pius Xll claimed in a major address delivered in 1951 that the

Big Bang theory supported Catholic doctrine See I. G. Barbour, Issues in Science

and Religion (New York: Harper Row, 1971) 373-375, for a discussion of this view

of the Roman Catholic position. it should be emphasized, however, that this

position, although held by many influential Catholics, cannot be considered

Catholic dogma. Although this position on the beginning of the Universe is not

Catholic dogma, there are scientific-historical statements, such as the Resurrection

of Christ, which definitely are. See Anthony Kenny, A Path from Rome (Oxford:

Oxford University Press, 1986). And the Resurrection is the scientific foundation of

Christianity: as St. Paul himself emphasized, if Christ did not rise from the dead,

belief in any Christian tenet is in vain. Christianity rests, as do the natural sciences,

on a matter of fact; Christianity requires that at least one “gap’” in the natural

order ~—- the Resurrection ~ occurred in the past. I personally do not believe in the

Resurrection, for reasons succinctly stated by David Hume in his work On

Miracles, and also because I am an ontological reductionist: there are no gaps in

the natural order. Furthermore, I think eternal life for an individual human being

would be a bad thing, for reasons stated in Section 3. As Hume said to one of his

biographers, individual eternal life would just lead to an accumulation of garbage

in the Cosmos: errors and crimes made by individuals would never be forgotten.

But collective eternal life can lead to unlimited progress.

St. Augustine recognized that the Resurrection, qua scientific fact, had

far-reaching implications for scientific cosmology. The second half of the twelfth

book of The City of God, devoted to showing the uniqueness of the Resurrection,

implied that one of the central assumptions of Greek science, namely the Eternal

Return, could not possibly be true: “For Christ died once for our sins, and rising

again, dies no more." Thus, although Augustine was willing to allow natural

science to tell us that some unimportant (for redemption) Biblical passages must be

re-interpreted metaphorically, the Resurrection was definitely not open to such

re-interpretation; rather, for Augustine, the Resurrection was an uncloseable “gap”

in the natural order, and any acceptable scientific theory must be consistent with it.

See McMullin’s essay in this volume.

2 John D. Barrow and Frank J. Tipler, The Ant/tropic Cosmological Principle

(Oxford: Oxford University Press, 1986); hereafter referred to as ACP.See also

Frank J. Tipler, Essays in General Relativity (New York: Academic Press, 1980)

2137.

3 Francisco J. Ayala, “Introduction,” in Studies in the Philosophy of Biology,

by Francisco J. Ayala and Theodosius Dobzhansky (Berkeley: University of

Chicago Press, 1974).

“ Eric Delson, “One Source, Not Many,” Nature 325 (1988) 206.

5 D. R. Hofstadter and DC. Dennet, The Minds I (New York: Basic Books,

1981), is the best and most complete defense of the Turing Test as a test for the

presence of a mind. This book provoked an exchange between the philosopher

John Searle and Dennett in the pages of New York Review of Books over the

validity of the Turing Test. 1 recommend reading this exchange, although I think

Dennett won hands down. Searle simply cannot understand the enormous effective

computer power of the human brain (1010 to 1015 bits of memory and a

330 FRANK J. TIPLER

computation speed between 10 and l,000 gigaflops; see Section 3.2 of ACP. For

comparison, the Cray-XMP has a memory of about l0‘° bits and a speed of l

gigaflop. The Cray crawls in comparison to the human brain). Scarle’s “Chinese

room" thought experiment could not possibly work because it would be absolutely

impossible for a human inside to move paper fast enough for the room to pass the

Turing Test (in Chinese).

6 See Note I.

7 l. G. Barbour, l97l, op. Cil., regards “intelligence” as one of the two most

essential properties of God, if God is to be thought of as a Person. (The other

essential property is “purpose”.)

8 An explicit assumption made in this analysis is that the Second Law of

Thermodynamics holds in the large at all times, and more generally, that time

direction is always defined, even arbitrarily close to the final singularity. (A time

direction arising from the spacetime metric is not absolutely required, but a time

direction defined by the Second Law is necessary.) Recent work in quantum

cosmology has challenged both assumptions. Hawking has pointed out that his

boundary condition on the wave function of the universe requires the universe to

be spatially closed, but it also requires the entropy to decrease after the time of

maximal expansion. This would make the continued progression of life impossible;

knowledge could increase only to a finite maximum at the time of maximal

expansion. In Hawking’s universe, the history of the contracting phase would be

identical to the history of the expanding phase, only run in reverse. Thus life would

never continue to the end of time, for the end of time is really the same as the

beginning. If the Omega Point Theory is to hold, Hawking’s boundary condition

must be incorrect. This is a fourth prediction of the Omega Point Theory, but not a

significant one, because very few believe Hawking’s cosmological model. A

universal reversal of entropy seems too improbable.

A far more fundamental challenge to the Omega Point Theory is the

possibility that time direction may not be defined when the spacetime metric is

quantized. [sham discusses this possibility in his paper in this volume.

Furthermore, Penrose‘s c-boundary is a classical concept, and it is not clear that an

analogue of the c-boundary exists in quantum cosmology. An analogue of the

singularity exists ~ a place where the radius of the universe is zero is still there

even in quantum cosmology -— but if time direction is not defined, we cannot

distinguish between the initial and final singularities. Nevertheless, I think the

Omega Point Theory can survive this challenge. Quantum cosmology is built on the

Many-World Interpretation of quantum mechanics, and all the Omega Point

Theory really requires is that a time direction based on entropy be defined in one

branch universe, where conditions 1, 2, and 3 can hold. A time direction arising

from the metric is not essential, as I said above, nor is it necessary for time to be

globally defined for the entire collection of branch universes.

9 Unfortunately, this reduction to a mere two theories is spoiled by the

non-uniqueness of the vacuum state in superstring theories. Different vacua give

different physics, and as yet there is no good reason to pick one vacua over

another.

1" See, for example, Stanley L. Jaki, “Teaching of Transcendence in Physics,"

American Journal of Physics 55 (1987) 884-888.

‘1 J. Donald Monk, Mathematical Logic (New York: Springer-Verlag, 1976)

234.

‘1 Ernest Nagel and James R. Newman, Go'del’s Proof (London: Routledge

and Kegan, I971).

13 My method of avoiding the limitations for a TOE of the Godel

lncompleteness Theorem is similar to Nobel laureate economist Paul Samuelson's

proposal for avoadmg

Impossibility Theorm

procedure for deciding

leaders, among religion

satisfies four 855W

welfare function canm

this person decide ultra

of irrelevant alternaaw

preferred to altername

change any one indzwti

choice of A over B H

individual switches m i

start to prefer A to l.

opposite direction F

(transitive): If A now

over C. See Paul »\

Values and ECOIIOHEK' 1

Press, l967) 4l-5l F-t

Price Theory (Cmczm

Arrow IMPOSSlbillU Ti

1" The other we

was invented by John

quantum mechanics. in

exhibit are determined

logic of this interprets:

particles in the umw

observer-participamjt

collectively bring man

also, the creatures ml

themselves. But in the

used in a sense close: I

Participatory Anthea]

Determinism," IBM .

points out that the Putt

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future can interact an

existence.

‘5 See also Dmgi

York: Basic Books. 1‘!

1° James 8. Mi

Creation/Evolution Ct

1’ Paul Tillidr. T

‘8 See I. Barbom

‘9 Arthur 0. Lo!

University Press. WM!

Section 3.2 of ACP. For

M bits and a speed of 1

brain). Searle’s “Chinese

a: it would be absolutely

for the room to pass the

' as one of the two most

as a Person. (The other

that the Second Law of

more generally, that time

ha] singularity. (A time

Id) required, but a time

went work in quantum

has pointed out that his

: requires the universe to

nerease after the time of

union of life impossible;

Ill the time of maximal

lracting phase would be

rreverse. Thus life would

5 really the same as the

ng's boundary condition

I Point Theory, but not a

cosmological model. A

1 Point Theory is the

. the spacetime metric is

pper in this volume.

and it is not clear that an

g3. An analogue of the

terse is zero is still there

not defined, we cannot

ievertheless, I think the

mology is built on the

d all the Omega Point

mopy be defined in one

A time direction arising

merry for time to be

as.

series is spoiled by the

:5. Different vacua give

to pick one vacua over

mscendence in Physics,"

L Springer-Verlag, 1976)

uqf (London: Routledge

a TOE of the Godel

mist Paul Samuelson‘s

MODEL OF AN EVOLVING GOD 331

proposal for avoiding the democracy-is-impossible implications of the Arrow

Impossibility Theorem. According to this Theorem, no social welfare function A a

procedure for deciding which alternatives (among economic goods, among political

leaders, among religions, etc.) society as a whole should choose m exists which

satisfies four assumptions. The first assumption is nondictatorship: the social

welfare function cannot consist of picking a single person (the dictator) and letting

this person decide what the whole society will choose. The second is independence

of irrelevant alternatives: if the social welfare function implies alternative A is

preferred to alternative B, then a change in individual preferences which does not

change any one individual‘s preferences between A and B cannot change the social

choice of A over B. The third is that society cannot switch from A to B if a single

individual switches in the other direction from B to A. That is. if more individuals

start to prefer A to B, then the choice of society as a whole cannot switch in the

opposite direction. Finally, the social welfare function must be consistent

(transitive): If A would be chosen over B. and B over C, then A must be chosen

over C. See Paul A. Samuelson, “Arrow’s Mathematical Politics," in Human

Values and Economic Policy, by Sidney Hook (New York: New York University

Press. 1967) 4l-51. For the Arrow Impossibility Theorem see David Friedman.

Price Theory (Cincinnati: South-Western Publishing, 1986) and Jerry S. Kelley,

Arrow Impossibility Theorems (New York: Academic Press, 1978).

1‘ The other answer involves the Participatory Anthropic Principle, which

was invented by John A. Wheeler. It draws on the Copenhagen Interpretation of

quantum mechanics, which holds that many of the properties subatomic particles

exhibit are determined by the observer’s choice of what to measure. Following the

logic of this interpretation, Wheeler conjectures that all the properties of all the

particles in the universe are determined by the collection of all the acts of

observer-participancy in the past, present. and future. In particular, these acts

collectively bring into existence all the observers themselves. Thus in this answer

also, the creatures collectively are responsible for creating the entire universe and

themselves. But in this answer, the creation is more direct; the word "creation" is

used in a sense closer to its everyday usage. See the ACP index for references to the

Participatory Anthropic Principle. See also John Wheeler, “Probability And

Determinism,” IBM Journal of Research and Development 32 (1988) 4-15. He

points out that the Participatory Anthropic Principle presupposes the Omega Point

Theory, for only the enormously more powerful observer-participators of the far

future can interact on the scale necessary to bring our enormous universe into

existence.

‘5 See also Douglas R. Hofstadter and Daniel C. Dennett, The M ind’s I (New

York: Basic Books, 1981).

‘6 James B. Miller and Dean R. Fowler, “What’s Wrong With the

Creation/Evolution Controversy?” CTNS Bulletin 4 (Autumn 1984) 1-13.

‘7 Paul Tillich, The Dynamics of Faith (New York: Harper and Row, 1957).

‘5 See I. Barbour, 1971, op. cit., 219, for a detailed discussion.

‘9 Arthur 0. Lovejoy, The Great Chain of Being (Cambridge, Mass: Harvard

University Press, 1936).