by William A. Dembski
1994

Response to this paper.


FIRST LET ME EXPRESS my thanks to the organizers of this symposium for the opportunity to present certain ideas that for some time now have exercised
me. The occasion for this symposium is Phillip Johnson's book Darwin on
Trial. The title would suggest that Johnson's main concern is with
Darwinism and neo-Darwinism proper. Nevertheless, I would claim that
Johnson's book is as much about a philosophical world view used to prop up
Darwinism as it is about Darwinism. Atheism, materialism, scientism, and
secular humanism are a few of the names attached to this world view. Yet
the name I like best and find most descriptive is scientific naturalism.
I want here to examine scientific naturalism. I am going to argue that
this view has a serious defect-it is incomplete. As a consequence of this
defect I shall argue that it is legitimate within scientific discourse to
entertain questions about supernatural design. The backdrop for this
discussion will comprise two areas in mathematics: computational
complexity theory and probability theory.

First let's be clear what we mean by scientific naturalism. The key
ingredient in scientific naturalism is, let me say it, naturalism.
Naturalism as a world view has two components: (1) It is a metaphysical
doctrine about what things exist in the world. These include material
objects and sometimes (as for the philosopher Willard Quine) mathematical
objects such as sets. Excluded are supernatural beings, nonmaterial
interventions, divine meddlings, etc. (2) Naturalism includes an
epistemological doctrine about how the things permitted under this
metaphysical doctrine are to be explained-i.e., they are to be explained
naturalistically. I am not sure that naturalistic explanation is a
perfectly clear notion, but what is clear is that naturalistic explanation
excludes any sort of appeal to nonmaterial intervention, divine meddling,
etc.

Where does the 'scientific' in scientific naturalism come in? As a world
view, scientific naturalism regards itself as continuous with science. It
therefore looks to our scientific understanding of the world for its
justification. This last point distinguishes scientific naturalism from
naturalism simpliciter. It is also this last point that is responsible for
scientific naturalism being incomplete.

To see what is at stake let me quote the last line of Edwin Hubble's The
Realm of the Nebulae: "Not until the empirical resources are exhausted
need we pass on to the dreamy realms of speculation." When Hubble wrote
that line in the 1930s, he clearly believed that the empirical resources
would not be exhausted and that our entrance into the dreamy realms of
speculation could be postponed indefinitely.

Against this I would argue that empirical resources come in limited
supplies and do get exhausted. Moreover, as soon as empirical resources
are exhausted, naturalism can no longer fund its justification in science.
This then is the incompleteness of scientific naturalism, namely, the
incapacity of science to justify naturalism once the empirical resources
wherewith science limits itself get exhausted.

Next I want to focus on two empirical resources, one computational, the
other probabilistic. I want to show how even the possibility of these
resources being exhausted undermines the completeness of scientific
naturalism-the pretension, as far as I'm concerned, that a complete
understanding of the world is possible apart from God. Since this talk is
addressed primarily to non-mathematicians, I'll begin by considering the
words of a well-known American philosopher, Woody Allen.

Woody Allen probably didn't think that God would take him seriously when
he quipped,

If only God would give me some clear sign! Like making a large deposit
in my name at a Swiss bank.{1}

But what if God had taken Allen seriously? Would an unexpected $7,000,000,
say, in Allen's Swiss bank account have convinced him that God was real?
Suppose that a thorough examination of the bank records failed to explain
how the money appeared in Allen's account. Should Allen have inferred that
God had given him a sign?

Since I can't answer for Allen, let me answer for myself. If I were a
famous personality having uttered Allen's remark and subsequently found an
additional $7,000,000 in my Swiss bank account, I would certainly not have
attributed my unexpected good fortune to the largesse of an eccentric
deity. It's not that I don't believe in God. I do. But my theology
constrains me to think it unworthy of God to grant flippant requests like
Allen's and then apparently ignore the urgent requests of so many
suffering people in the world.

I would refuse to acknowledge a miracle for theological reasons, Barring
theological reasons, however, I would still refuse to acknowledge a
miracle. Why? Well, other explanations readily come to mind. If I had
uttered the remark and were as famous as Allen, and if $7,000,000 had
appeared in my account, I would probably have concluded that some
eccentric billionaire with a religious agenda was trying to convert me to
his cause. The strange appearance of the $7,000,000 would have been
fiendishly designed to make me believe in God. But alas, I was too clever
for them.

There is a point to these musings. Allen's remark is clearly funny;
however, if taken seriously it is self-defeating. If God were in fact to
do what Allen requested. Allen and just about anyone else would remain
unconvinced. The question therefore arises whether God can do anything,
either in response to a request like Allen's or otherwise, which would
provide convincing proof that he and no one else had acted.
Let's put it this way: is there anything that has, could, or might happen
in the world from which it would be reasonable to conclude that God had
acted? Are there or could there be any facts in the world for which an
appeal to God is the best explanation? Or to reverse the question, is God
always an easy way out, a lame excuse, a prescientific device that
invariably misses the best explanation?{2}

We are asking a transcendental question in the Kantian sense: What are the
conditions for the possibility of discovering design (i.e., supernatural
intervention, nonmaterial interference, divine meddling, call it what you
will) in the actual world? This question must be answered at the outset,
for if this world is the type of place where anything even in principle
that happens can be adequately explained apart from teleology and design,
then it makes no sense to look for design in what actually happens. Might
the world do something, however quirky, that would convince us of design?
An illustration might help. Imagine a peculiar art studio comprised of
ten-inch by ten-inch canvases, a full range of oil paints, and a robot
that paints the canvases with the paints. In painting the canvases, the
robot divides each canvas into a ten by ten grid of one-inch squares, and
paints each square with precisely one color. Imagine that this robot also
has visual sensors and thus can paint scenes presented to its visual
field, though only crudely, given the coarse-grained approach it adopts to
painting.

Imagine next that Elvis and an Elvis impersonator come to have their
portraits painted by this robot. Will the portraits distinguish Elvis from
his impersonator? Because the representations on canvas are so crude, if
the impersonator is worth his salt, the two portraits will be
indistinguishable. Our imaginary art studio cannot distinguish the real
Elvis from the fake Elvis.

This example indicates what is at stake in determining whether design has
at least the possibility of being detected and empirically grounded.
Putative instances of design abound. But is it possible within this world
to distinguish authentic from spurious design should instances of
authentic design even exist? Or is this world like the art studio? Just as
the portraits painted at the studio cannot distinguish the real from the
fake Elvis, so too is it impossible for our empirical investigations of
the world to distinguish authentic from spurious design?

Scientific naturalism prefers to think just this, namely, that the world
is the kind of place where all objective phenomena can be explained by
purely naturalistic factors. Non-naturalistic factors therefore become not
only redundant but also illegitimate to explanation. As George Gaylord
Simpson put it,

There is neither need nor excuse for postulation of nonmaterial
intervention in the origin of life, the rise of man, or any other part
of the long history of the material cosmos.{3}

Simpson claims that the world is the kind of place where no objective,
empirical funding can ever legitimately lead us to postulate design (what
he calls "nonmaterial intervention").

That is a bold claim. The question remains whether it is true. In the case
of the art studio, it is true that robot portraits of Elvis and his
impersonator will fail to distinguish the two. The paintings produced by
the studio are simply too coarse grained to do any better. From these
paintings there is, to use Simpson's phrase, "neither need nor excuse for
postulation of" two Elvises, the real and the fake. From the portraits
alone we might legitimately infer only one sitter. But is the world so
coarse grained that it cannot even in principle produce events that would
evidence design? That is what Simpson seems to be affirming. A little
reflection, however, indicates that this claim cannot be right.

We consider a thought experiment, one I call "The Incredible Talking
Pulsar." Imagine that astronomers have discovered a pulsar some three
billion light years from the earth. The pulsar is, say, a rotating neutron
star that emits regular pulses of electromagnetic radiation in the radio
frequency range. The astronomers who found the star are at first
unimpressed by their discovery. It's only another star to catalogue. One
of the astronomers, however, is a ham radio operator. Looking over the
pattern of pulses one day, he finds that they are in Morse code. Still
more surprisingly, he finds that the pattern of pulses signals English
messages in Morse code.{4}

Word quickly spreads within the scientific community, and from there to
the world at large. Radio observatories around the globe start monitoring
the "talking" pulsar. The pulsar isn't just transmitting random English
messages, but is instead intelligently communicating with the inhabitants
of earth. In fact, once the pulsar has gained our attention, it identifies
itself. The pulsar informs us that it is the mouthpiece of Yahweh, the God
of both the Old and the New Testaments, the creator of the universe, the
final judge of humankind.

Pretty heady stuff you say. But to confirm this otherwise extravagant
claim, the pulsar agrees to answer any questions we might put to it. The
pulsar specifies the following method of posing and answering questions.
The descendants of Levi are to make an ark like the one originally
constructed under Moses (see Exodus 25). This ark is to be placed on Mount
Zion in Israel. Every hour on the hour a question written in English is to
be placed inside the ark. Ten minutes later the pattern of pulses reaching
earth from the pulsar will answer that question, the answer being framed
as an English message in Morse code.{5}

The information transmitted through the pulsar proves to be nothing short
of fantastic. Medical doctors learn how to cure AIDS, cancer, and a host
of other diseases. Archaeologists learn where to dig for lost
civilizations and how to make sense out of them. Physicists get their
long-sought-after unification of the forces of nature. Meteorologists are
forewarned of natural disasters and weather patterns years before they
occur. Ecologists learn effective methods for cleansing and preserving the
earth. Mathematicians obtain proofs to many long-standing open problems-in
some cases proofs they can check, but proofs they could never have
produced on their own. The list of credits could be continued, but let us
stop here.

What shall we make of the pulsar? Whether the pulsar is in fact the
mouthpiece of Yahweh, the pulsar creates serious difficulties for
scientific naturalism. Not only is there no way to square the pulsar's
behavior with our current scientific understanding of the world, but it is
hard to conceive how any naturalistic explanation will ever account for
the pulsar's behavior. For instance, our curtent scientific understanding
based on Einsteinian special relativity tells us that messages cannot be
relayed at superluminal speeds. Since the pulsar is three billion light
years from the earth, any signal we receive from the pulsar was sent
billions of years ago. Yet the pulsar is "responding" to our questions
within ten minutes of the written questions being placed inside the ark.
The pulsar's answers therefore seem to precede our questions by billions
of years.

To get around this, scientific naturalists might want to postulate reverse
causality or superluminal signaling. Naturalists might find this idea more
congenial than postulating "nonmaterial intervention," but reverse
causality and superluminal signaling do not even begin to address the
questions raised by the pulsar. It is inescapable that in dealing with the
pulsar we are dealing with not just an intelligence, but with a
super-intelligence. Now by a super-intelligence I don't mean an
intelligence that at this time surpasses human capability, but which in
time humans can hope to attain. Nor do I mean a super-human intelligence
that might nevertheless be realized in some finite rational material agent
embedded in the world (say an extraterrestrial intelligence or a conscious
super-computer). By a super-intelligence I mean a supernatural
intelligence, i.e., an intelligence surpassing anything that physical
processes are capable of offering. This intelligence exceeds anything that
humans or finite rational agents in the universe are capable of even in
principle.

How can we see that the pulsar instantiates a super-intelligence? The
place to look is computer science. There are problems in computer science
that can be proven mathematically to require more computational resources
for their solution than are available in the universe. Think of it this
way. There are estimated to be no more than 1080 elementary particles in
the universe. The properties of matter are such that circuits cannot be
switched faster than 1045 times per second.{6} The universe itself is
about a billion times younger than 1025 seconds (assuming that the
universe is at least a billion years old). Given these upper bounds we can
confidently assert that no computation exceeding lO80 x 1045 x 1025 =
10150 elementary steps is possible within the universe. By an elementary
step I mean the switching of a two-state device, conceived abstractly as
the switching of a binary integer (= bit). For a computation of this
complexity therefore to be carried out in the universe, every available
elementary particle in the universe would have to serve as an elementary
storage device (= memory bit) capable of switching at 1045 hertz over a
period of a billion billion years.

1050 is incredibly generous as an upper bound on the complexity of
computations possible in the universe. Here are a few reasons why a much
smaller bound will do: (1) quantum mechanical considerations indicate that
reliable memory storage is unworkable below the atomic level{7} since at
this level quantum indeterminacy will make not only storage, but also
reading and writing of information impossible. Hence each elementary
storage device will have to consist of more than one elementary particle.
(2) The preceding calculation treats the universe as a giant piece of
random access memory that is controlled by a processor outside the
universe operating at 1045 hertz with instant access to any memory
location in RAM. In fact, the processor will itself have to take up part
of the universe. Moreover, its access to memory locations will have in
some cases to be measured in light years and not in 1045 second chunks.
Even with massively parallel processing, computation speeds will fall far
below the 1045 hertz upper bound. (3) Finally, the bound of 1025 seconds
for the maximum running time of a computation is excessive since the heat
death of the universe will probably have occurred by then. Suffice it to
say, even with the entire universe functioning as a computer, no
computation requiring 1050 elementary steps, much less 10150 floating
point operations, is feasible.

Now it is possible to pose problems in computer science for which the
quickest solution requires well beyond this number steps, yet for which
with a solution in hand it is possible even for humans using ordinary
electronic computers to check whether the solution is correct. Factoring
integers into primes is thought to be one such problem. Since the
factorization problem is easy to understand, let me treat it as though it
were one of the "provably hard problems." If at some time in the future a
"quick" algorithm is found for factoring numbers, we shall need to modify
this example; nevertheless, our contention that there are problems whose
solution is beyond the computational resources of the universe, yet
verifiable by humans, will still hold.{8}

What is the factorization into primes of 1961? Solving this requires a bit
of work. But if you are given the prime numbers 37 and 53, it is a simple
matter to check whether these are prime factors of 1961. In fact 37 x 53 =
1961. Factoring is hard, multiplication is easy. We can therefore go to
our pulsar with numbers thousands of digits long and ask it to factor
them. Factoring numbers that long is totally beyond our present
capabilities and in all likelihood exceeds the computational limits
inherent in the universe by many, many orders of magnitude. (When I was
following the literature on factoring a few years back, numbers beyond two
hundred digits in length could not be factored unless they had either
small or special prime factors.) Nevertheless, it is easy enough to check
whether the pulsar is getting the factorizations right, even for numbers
thousands of digits in length.{9}

What lesson can we learn from the pulsar? I claim we should infer that a
designer in the full sense of the word is communicating through the
pulsar, i.e., a designer who is both intelligent and transcendent.
Intelligence is certainly not a problem here. Alan Turing's famous test
for intelligence pitted computer against human in a contest where a human
judge was to decide which was the computer and which was the human.{10} If
the human judge could not distinguish the computer from the human, Turing
wanted intelligence attributed to the computer.

This operationalist approach to intelligence has since been questioned, by
theists on one end and hard-core physicalists on the other. But the basic
idea that there is no better test for intelligence than coherent natural
language communication remains intact. If we cannot legitimately attribute
intelligence to the pulsar, then no attribution of intelligence should
count as legitimate. Transcendence is clear as well, given our discussion
of intractable computational problems. Suffice it to say, a being that
solves problems beyond the computational resources of the material world
is not material. When we can confirm that such problems have in fact been
solved for us, we cannot avoid postulating "nonmaterial intervention."
The pulsar demonstrates that ours is the type of world where design has at
least the possibility of becoming perfectly evident-with the pulsar,
empirical validation for design can be made as good as we like. In the
actual world, design is therefore not only possible but also empirically
knowable. I have belabored this point because it is a point scientific
naturalism would rather not grant. Once, however, it is granted that the
occurrence of certain events might require us to postulate "nonmaterial
intervention," we need to consider whether any events that have actually
occurred require us to postulate such intervention. It is obvious that the
pulsar is an exercise in overkill. No instance of design so crushingly
obvious is known. Science fiction has therefore done its work for us. It
is time to put science fiction to rest, and look at what solid evidence
there is for design in the actual world. We therefore leave computational
resources and turn to probabilistic resources.

I use the term probabilistic resources to describe what I call
replicational resources on the one hand, and specificational resources on
the other. To appreciate what is at stake with these resources let us
consider two examples. The first illustrates replicational resources, the
second specificational resources.

Here is the first example. Imagine that a massive revision of the criminal
justice system has taken place. Henceforward a convicted criminal is
sentenced to serve time in prison until he flips n heads in a row, where n
is selected according to the severity of the offense (we assume that all
coin flips are fair and are duly recorded; no cheating is possible). Thus
for a ten-year prison sentence, if we assume the prisoner can flip a coin
once every five seconds (this seems reasonable), eight hours a day, six
days a week, and given that the average attempt at getting a streak of
heads before tails is 2 (=S18iTi2-i), then he will on average attempt to
get a string of n heads once every 10 seconds, or 6 attempts a minute, or
360 attempts an hour, or 2,880 attempts in an eight-hour work day, or
901,440 attempts a year (assuming a six-day work week), or approximately 9
million attempts in ten years. Nine million is approximately 223. Thus if
we required of a prisoner that he flip 23 heads in a row before being
released, we could expect to see him out in approximately ten years. Of
course specific instances will vary- some prisoners being released after
only a short stay, others never recording the elusive 23 heads!
Now consider the average prisoner's reaction after about ten years when he
finally flips 23 heads in row. Is he shocked? Does he think a miracle has
occurred? Absolutely not. Given his replicational resources, i.e., the
number of opportunities he had for observing 23 heads in a row, he could
expect to get out of prison in about ten years. There is in fact nothing
improbable about his getting out of prison in this span of time. It is
improbable that on any given occasion he will flip 23 heads in a row. But
when all these occasions are considered jointly, it becomes quite probable
that he will be out of prison within the ten years' time. The prisoner's
replicational resources comprise the number of occasions he has to produce
23 heads in a row. If his life expectancy is better than ten years, he has
a good chance of getting out of prison. In short, replicational resources
are adequate for getting out of prison.

If, however, the number of heads a prisoner must flip in a row is
exorbitant, then his replicational resources will be inadequate for
getting out of prison. Consider a prisoner sentenced to flip 100 heads in
a row. The probability of getting 100 heads in a row on a given trial is
so small that he has no practical hope of getting out of prison, even if
his life expectancy was dramatically increased. If he could, for instance,
make 10 billion attempts each year to obtain 100 heads in a row, then he
stands only an even chance of getting out of jail in 1020 years. His
replicational resources are so inadequate for obtaining the desired 100
heads that it's pointless to entertain hopes of freedoms.{11}

With replicational resources the question is how many opportunities exist
for observing a specific event (in the preceding example the event was
flipping n heads in a row). With specificational resources the question is
how many opportunities are there for specifying an as yet undetemmined
event. Lotteries provide the perfect vehicle for illustrating
specificational resources. Indeed, each lottery ticket is a specification.
To illustrate specificational resources, consider now the following
lottery to end all lotteries: In the interest of eliminating the national
deficit, the federal government agrees to hold a national lottery in which
the grand prize is to be dictator of the United States for a single day-
i.e., for twenty-four hours the winner will have full power over every
aspect of government. If a white supremacist wins, he can order the
wholesale execution of nonwhites. If a porn king wins, he can order this
country turned into a giant debauch. If a pacifist wins, he can order the
destruction of all our weapons .... The more moderate elements of the
society will clearly want to prevent the loony fringe from winning, and
will therefore be inclined to invest heavily in this lottery.

This natural inclination, however, is mitigated by the following
consideration: the probability of any one ticket winning is 1 in 2100, or
approximately 1 in 1030. To buy a ticket, the lottery player pays a fixed
price and then records a 0-1 string of length 100-whichever string he
chooses. He is permitted to purchase as many tickets as he wishes, subject
only to his financial resources and the time it takes to record the 0-1
strings of length 100. The lottery is to be drawn at a special meeting of
the United States Senate: By alphabetical order each senator is to flip a
coin once and record the resulting coin toss.

Suppose now that the fateful day has arrived. A trillion tickets have been
sold at ten dollars apiece. To prevent cheating, Congress has enlisted the
services of the National Academy of Sciences. Following the NAS's
recommendation, each ticket holder's name is duly entered onto a secure
data base, together with the tickets purchased and the ticket numbers
(i.e., the bit strings relevant to deciding the winner). All this
information is now in place. After much fanfare the senators start
flipping their coins. As soon as Senator Zygmund has announced his toss,
the data base is consulted to determine whether the lottery had a winner.
Lo and behold, the lottery did indeed have a winner-Joe "Killdozer"
Skinhead, leader of the White Trash Nation. Joe's first act as dictator is
to raise a swastika over the Capitol.

From a probabilist's perspective there is one overriding implausibility to
this example. The implausibility rests not with the federal government's
sponsoring a lottery to eliminate the national debt, nor with the
fascistic prize of being dictator for a day, nor with the way the lottery
is decided at a special meeting of the Senate, nor even with the
fantastically poor odds of winning the lottery. The implausibility rests
with the lottery's having a winner. Indeed, as a probabilist myself, I
would encourage the federal government to institute such a lottery if it
could redress the national debt, for I am convinced that if the lottery is
run fairly, there will be no winner. The odds are simply too much against
it.

Suppose, for instance, that a trillion tickets are sold at ten dollars
apiece (this would cover the deficit as it stands in 1992). What is the
probability that one of those tickets (= specifications) will match the
winning string of 0's and l's drawn by the Senate? An elementary
calculation shows that this probability can be no greater than 1 in 1018.
This is a tiny probability. Even if we increase the number of lottery
tickers sold by several orders of magnitude, there still won't be enough
sold for the lottery to stand a reasonable chance of having a winner.
Since lottery tickets are specifications, this is equivalent to saying
there aren't enough specifications to specify the event in question (i.e.,
the winning of the lottery).

Often it is necessary to consider replicational and specificational
resources in tandem. Suppose for instance in the preceding lottery that
the Senate will hold up to a thousand drawings to determine a winner.
Assume as before that a trillion tickets have been sold. It follows that
for his probabilistic setup the specificational resources include a
trillion specifications and that replicational resources include a
thousand possible repetitions. An elementary calculation now shows that
the probability of this modified lottery having a winner is no greater
than 1 in 10". That too is a tiny probability. The joint replicational and
specifcational resources are so inadequate that it remains exceedingly
unlikely this lottery will have a winner.

In times past it used to be much easier to "inflate" probabilistic
resources than it is now. The question whether the universe is finite or
infinite used to be a philosophical, not an empirical question. Thomas
Aquinas claimed it was only by revelation that we could know that the
universe was finite. Reason, according to him. left open the possibility
of an infinite universe. Spinoza's philosophical system required an
infinite universe, but again on metaphysical, not empirical, grounds. Hume
himself appreciated the benefits that accrue to scientific naturalism when
a universe of infinite duration is presupposed:

A finite number of particles is only susceptible of finite
transpositions: and it must happen, in an eternal duration, that every
possible order or position must be tried an infinite number of times.
This world, therefore, with all its events, even the most minute, has
before been produced and destroyed, and will again be produced and
destroyed without any bounds and limitations. No one, who has a
conception of the power of the infinite, in comparison of the finite,
will ever scruple this detemmination.{12}

In his younger days Einstein had been committed to Spinoza's God. Spinoza
had identified God with Nature and assumed that this God was infinite in
extent and duration. Consistent with Spinoza's conception, Einstein
formulated his field equations to model such an infinite universe. Now
"when in 1927 the Abbé Lemaître derived from Einstein's cosmological
equations the expansion of the universe and correlated that rate with data
on galactic red-shifts already available,"{13} the spatio-temporal extent
of the universe became an empirical question. The "data on galactic
red-shifts already available" was that of Hubble and Humason. When in the
early 1930s Einstein visited Hubble in California and inspected this data,
Einstein came away convinced that the universe was indeed finite.{14} The
inflationary universe of Alan Guth and his successors, much like the
steady state theory of the 1950s, attempts to recapture Spinoza's lost
infinity. In my view, these theories arise solely out of a need to
preserve scientific naturalism, in this case by increasing probabilistic
resources and thereby rendering appeals to chance plausible.
What event exhausts the probabilistic resources inherent in the universe?
The origin of life does so quite nicely. Anyone who grapples with the
improbabilities inherent in life's origin is quickly confounded. Indeed,
the improbabilities are truly staggering. Fred Hoyle, for instance.
computes that a single cell might on the basis of chance be expected every
1040000 years if the entire universe were filled with a prebiotic liquid
(an assumption that is incredibly generous).{15} Bernd-Olaf Küppers, a
pupil of Manfred Eigen, commenting on merely a certain subunit of a virus,
writes:

The RNA sequence that codes for the virus-speciftc subunit of the
replicase complex consists of approximately a thousand nucleotides, . . .
so that it already possess ln = 41000 » 10600 alternative sequences ....
The spontaneous synthesis [of this system] . . . is therefore extremely
improbable.{16}

He concludes that probability theory "does not bring us a single step
further as regards the statistical aspect of the origin of life."{17}
Lecomte du Noüy found similarly wild improbabilities back in the 1940s.{18
} Hubert Yockey and Michael Behe continue to compute them today.{19}
Is this exhausting of probabilistic resources any reason to postulate
nonmaterial intervention, to invoke a supernatural designer, or to believe
in God? I have tried throughout this discussion to be cautious. My sights
have ever been set on scientific naturalism. My aim has been to show that
scientific naturalism is incomplete. I have sketched the beginnings of
such an argument, that science cannot adequately support naturalism and
that nature does things to exhaust the empirical resources determined by
science. One can now try to retain naturalism by introducing a
metaphysical hypothesis that postulates a lot more naturalistic stuff than
science can sanction.

On the other hand, one can dispense with naturalism and introduce an
entirely different son of metaphysical hypothesis-God. These two choices
do not exhaust all possibilities, but they are by far the most common.
Which is to be preferred? Since my aim has not been to pitch metaphysical
hypotheses, but show that one of these metaphysical hypotheses,
naturalism, cannot be redeemed in the coin of science, I shall not argue
this question here. Nevertheless, it must be emphasized that science
regularly has its empirical resources exhausted. Moreover, when its
empirical resources are exhausted, science cannot plead momentary
ignorance which it hopes some day to redress. When its empirical resources
are exhausted, science is in no position to distribute promissory notes.
When its empirical resources are exhausted, science itself closes the door
to naturalistic explanation.

The door therefore remains wide open to a scientiftcally defensible
account of intelligent design.{20}

NOTES

{1} Quoted in Peter's Quotations, s.v. "Doubt."
{2} Richard Dawkins certainly thinks so. Consider his comment on the
origin of the DNA/protein machine: '[To invoke] a supernatural Designer is
to explain precisely nothing, for it leaves unexplained the origin of the
Designer. You have to say something like 'God was always there', and if
you allow yourself that kind of lazy way out, you might as well just say
'DNA was always there', or 'Life was always there', and be done with it"
[Dawkins 1987:141].
{3} Quoted in Johnson [1991:114].
{4} I owe the idea of a talking pulsar to Charles Chastain. The pulsar is
an oracle. Here I am using oracles to investigate the possibility of
design. Oracles, however, illuminate a host of philosophical questions. I
have, for instance, used oracles to investigate the mind-body problem. See
Dembski [1990:203-205].
{5} Perhaps to make this story more convincing, both the questions and the
answers should be in Hebrew. I'm not sure, however, what Hebrew looks like
in Morse code, so I'll stick with English.
{6} This universal bound on computational speed is based on the Planck
time, currently the smallest physically meaningful unit of time. Universal
time bounds for electronic computers involve clock speeds between ten and
twenty magnitudes slower. See Wegener [1987:2].
{7} Even at the atomic level quantum effects make reliable storage
unworkable. Indeed, the smallest scale at which vast, reliable storage is
known to be possible is at the next level up-the molecular level. We can
thank molecular biologists for this insight.
{8} See Balcazár [1990: chapter 11] for the underlying theory.
{9} I've chosen factoring because factoring is easy to understand. There
are problems that are not just thought to be hard, but are provably hard.
{10} See Turing [1950].
{11} This example appeared first in Dembski [1991: 104, note 6].
{12} Hume [1779:67].
{13} Jaki [1989:28].
{14} See Jastrow [1980].
{15} See Hoyle and Wickramasinghe [1981:1-33, 130-141], Hoyle [1982:1-65],
and the appendix by Herman Eckelmann in Montgomery [1991].
{16} Küppers [1990:68]. Küppers is a pupil of Manfred Eigen.
{17} Küppers [1990:68].
{18} See chapter 3 of du Noüy [1947].
{19} See Yockey [1977] and Behe's article in this volume.
{20} Look for the upcoming book on intelligent design by William Dembski,
Stephen Meyer, and Paul Nelson.

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