by Benny Mattis
In
The God Delusion,
Richard Dawkins argues that the "argument from improbability"
(a type
of argument that infers metaphysical truths from the existence of
high levels of complexity in the world, usually enlisted in the
defense of theism and named the "Argument from Design" or
the "Design Argument"), "properly deployed, comes
close to proving that God does not
exist" (137). "It is indeed a very strong and, I suspect,
unanswerable argument," Dawkins claims, "But in precisely
the opposite direction from the theist's intention" (137).
Christian philosopher Alvin Plantinga, on the other hand, shows in
Where the Conflict
Really Lies that the
Design Argument is actually not very strong, due to the weakness of
its premises, yet still considers it ultimately a case of "concord"
between religion and science (264). Dawkins succeeds in showing that
the argument from improbability best functions as support for
atheism, but Plantinga succeeds in showing that the argument is not
very strong in the first place.
Undercutting
Theism
Before
addressing the strength or weakness of the argument from
improbability, it would be constructive to present the most common
historical instance of it (as the Argument from Design for theism),
and whether it actually supports theism or atheism (in the latter
case as Dawkins' "Ultimate Boeing 747 Gambit"). As for the
former question, Dawkins lays out his interpretation of the argument
with characteristic scorn:
Creationist
'logic' is always the same. Some natural phenomenon is too
statistically improbable, too complex, too beautiful, too
awe-inspiring to have come about by chance. Design is the only
alternative to chance that the [Creationist] authors can imagine.
Therefore a designer must have done it. (146)
This
interpretation of Dawkins' might be put more formally as such:
1)
There exists a being x
such that x
is too complex to have come about by chance.
2)
For any x
such that x
is too complex to have come about by chance, there exists an
explanation y
such that (y
explains how the level of complexity in x
obtained in this world) and (y
posits the existence of a designer for x).
3)
So, there exists an explanation y
such that y
posits the existence of a designer for x.
Dawkins
takes issue with (2); indeed, given (1), (2) directly contradicts
Dawkins' belief that designers in general are not explanatory of
complexity:
(NE)
For any being x,
there does not exist any explanation d
such that (d
posits
a designer of x)
and (d
explains how the level of complexity in x
obtained in this world).
This
is because, as Dawkins states, design "raises an even bigger
problem than it solves: who designed the designer?" (147).
"Design doesn't explain
organized complexity," Plantinga says in summarizing Dawkins'
point; "It presupposes
it, because the designer would have to be as complex as what it
creates" (26). An explanation that presupposes what it explains
is not explanatory at all; hence, Dawkins' assertion that design
hypotheses are not explanatory of high levels of complexity.
Despite
his apparent understanding of Dawkins' undercutting defeater for
design hypotheses, however, Plantinga challenges Dawkins' logic with
an anecdote involving a science fiction scenario:
Suppose
we land on an alien planet...and discover some machine-like objects
that look and work just like a 1941 Allis Chalmers tractor; our
leader says 'there must be intelligent beings on this planet--look at
those tractors.' A sophomore philosophy student on the expedition
objects: 'Hey, hold on a minute! You have explained nothing at all!
Any intelligent life that designed those tractors would have to be at
least as complex as they are!' No doubt we'd tell him a little
learning is a dangerous thing and advise him to take the next rocket
ship home and enroll in another philosophy course or two. (27)
Plantinga
here appears to be likening the Design Argument's proponent's
reasoning with that of the space expedition's team leader, and
Professor Dawkins' reasoning with that of an exceedingly foolish
undergraduate. To make this analogy more complete, we need only
consider the space expedition's resident theologian, who, upon seeing
the tractors, confidently proclaimed that they constituted evidence
for God and, indeed, "concord" between space travel and
theistic religion.
"The
point is we aren't trying to give an ultimate
explanation of organized complexity," explains Plantinga, "and
we aren't trying to explain organized complexity in
general; we are only
trying to explain one particular manifestation of it...it is
perfectly proper to explain one manifestation of organized complexity
in terms of another" (28). Indeed, the expedition leader could
so properly explain the occurrence of those tractors as
such by appealing to a
designer, but Dawkins also allows that the occurrence of particular
complex biological machines we see on earth might be discovered to be
best explained by a designer. "It may even be a superhuman
designer," imagines Dawkins, "but, if so, it will most
certainly not
be a designer who just popped into existence, or who always existed"
(186). Such an unexplained being would in some sense explain the
occurrence of the complex tractor, or a complex biological machine,
but not the occurrence of their particular levels
of complexity as such
(because to posit their existence would require presupposing even
greater levels of complexity, begging the question), and this is "the
problem that any theory of life must solve" (145). We are not
trying to explain tractors as
such in the way the
expedition leader did, or complexity "in general" as
Plantinga suggests, but rather the level of complexity as
such instantiated in
the tractor, i.e., why a particular observed level of complexity has
obtained in this world.
In
another attempt to prevent Dawkins' undercutting defeat of the Design
Argument for theism, Plantinga suggests that God is not, in fact,
complex. Disputing Dawkins' argument in The
God Delusion,
Plantinga digs up Dawkins' definition of complexity from The
Blind Watchmaker:
"Something is complex
if it has parts that are 'arranged in a way that is unlikely to have
arisen by chance alone.' Here he's clearly thinking of material
objects" (29). Plantinga then lays out a clear logical
demonstration of God's simplicity:
1)
"Immaterial objects, e.g. numbers, don't have parts."
2)
"God is...an immaterial spiritual being."
3)
"Hence God has no parts at all."
4)
If something has no parts, then it is not complex, according to
Dawkins' definition of complexity.
5)
So, God is not complex, according to Dawkins' definition of
complexity. (27)
This
argument is simple enough, but any logician will immediately notice
the vagueness of (1); while it is evident that some
immaterial objects don't have parts, Plantinga presumably intends to
claim that all
immaterial objects don't have parts, which is certainly not
sufficiently justified by the single example of numbers (unless, of
course, all immaterial objects are numbers, but this option would be
less than helpful to Plantinga).
Setting
aside the question of whether an immaterial entity could have parts,
it is worth pointing out that Dawkins clearly does not intend for his
definition of complexity (presumably based in biology) in
The Blind Watchmaker
to be applied in The
God Delusion as well;
indeed, Dawkins even refers to theologian Keith Ward's statement that
"It is quite coherent...to suppose that God, while internally
indivisible, is internally complex," indicating a broader
concept of complexity than in his preceding writings on biology
(179). "God may not have a brain made of neurones,"
insists Dawkins, "or a CPU made of silicon, but if he has the
powers attributed to him he must have something far more elaborately
and non-randomly constructed than the largest brain or the largest
computer we know" (184). Even if God is an immaterial substance
(as God presumably is a concrete person, and not an abstract entity
such as a number), as a designer capable of intending the entire
actual world he would have to be (in some
way) more complex than the actual world itself, since his own
intention would be as complex as the world is insofar
as it is designed
(i.e., insofar as God intends it). Even an immaterial God, claims
Dawkins, would not be a legitimate explanation for the levels of
complexity we observe in the world; in this Dawkins brings an
undercutting defeater to theistic belief based on the Argument from
Design for theism.
Rebutting
Theism
It
seems that a designer capable of intending every designed aspect of
the world would have to be at least as complex as the world is
insofar it is designed; this is why positing the existence of such a
designer is not explanatory of the high level
of complexity in the
universe. Dawkins, however, does not stop with this mere
undercutting defeat, but rather continues on to say that "The
argument from improbability, properly deployed, comes close to
proving that God does not
exist" (137). This proper deployment, intended as a rebutting
defeater for theism, is what Dawkins refers to as the Ultimate Boeing
747 Gambit.
Dawkins
credits Fred Hoyle with positing a Boeing 747 as the archetypal
example of organized complexity (138). According to Dawkins'
reasoning, any possible designer of a being as complex as a 747
(let's call the 747-like object Bn,
where Bn+1
is more complex than Bn,
which is more complex than Bn-1,
and so forth) would have to be more complex than the object itself
(that is, it would correspond with Bn+x,
where x
is some number greater than zero). If God existed, then presumably,
God would be the designer of all of the other designers in the
universe; thus, he would quite properly be called the ultimate
designer, or the Ultimate
Boeing 747, as Dawkins
suggests (138). However, the logical end of the Design Argument,
unaided by the possibility of unguided evolution, "presents an
infinite regress from which [God] cannot help us escape" (136).
Dawkins
has shown the incoherence in premise (2) of his Design Argument
(i.e., the failure of intentional explanations to explain complexity
as such), but it can still work if we replace it with
2')
For any x
such that x
is too complex to have come about by chance, there exists an
explanation y
such that (y
explains how x
occurs in this world) and (y
posits the existence of a designer for x).
This
crucial update to the Design Argument might be summed up essentially
in a single premise, where Bn+1
is more complex than Bn,
which is more complex than Bn-1,
and so forth:
DA)
If there is a complex being Bn,
then there is a being Bn+1
that designed Bn.
The
infinite regress only needs a 747 to be put in motion:
B1)
There is a complex being Bn
(for example, a Boeing 747)
B2)
There is a being Bn+1
that designed Bn
(Modus Ponens DA, B1)
B3)
There is a being Bn+2
that designed Bn+1
(MP DA, B2)
B4)
There is a being Bn+3
that designed Bn+2
(MP DA, B3)
...
BU)
There is a being BU
that designed BU-1
(MP DA, B(U-1))
Where
BU is an 'ultimate' designer, i.e. the Ultimate Boeing 747. Of
course, given
(DA) as it is, U
will be a limit towards infinity, rather than a determinate quantity
P.
This can be shown easily enough via reductio
ad absurdum:
A1)
Suppose there is a complex being BP
such that BP
is the ultimate designer.
A2)
There is a being BP+1
that designed BP
(MP DA, A1)
A3)
If (A2), then BP
is not
the ultimate designer.
A3)
So, A1 is false, and there is a complex being BP+1
such that BP+1
is the ultimate designer.
The
existence of an ultimate designer BU
is preserved from (A1) to (A3), but U
continuously increases greater than any finite quantity assigned to
it. Since U
is a limit towards infinity, and BU
would be the ultimate designer, it follows from the necessity of
greater complexity in designers (and the significance of our
subscripts stated above) that BU's
complexity is a limit towards infinity, and thus that an ultimate
designer would be infinitely complex. This is why, as Dawkins claims
with his Ultimate Boeing 747 Gambit, "There almost certainly is
no God" (137).
Given
the reasoning behind the Design Argument, the existence of God would
be infinitely unlikely, as God would be infinitely complex. However,
without the possibility of ultimate designers (which demand
explanation) arising from primeval simplicity (which does not demand
explanation), it also remains utterly mysterious and itself
apparently vastly improbable. This is where evolution comes in: the
theory of evolution reveals how high levels of complexity could arise
in such a universe, because it replaces (2') with
2'')
For any x
such that x
is too complex to have come about by chance, there exists an
explanation y
such that (y
posits a designer for x)
or (y
posits the evolution of x
through evolution by natural selection, explaining its level of
complexity).
and
replaces (DA) with
DA')
If there is a complex being Bn,
then there is a being Bn+1
that designed Bn,
or Bn
evolved out of primeval simplicity.
(DA')
does not lend itself to a necessary infinite regress, but allows for
an ultimate designer BU,
as long as it evolved out of primeval simplicity. The God of theism
would not have evolved out of primeval simplicity, so this still
means that any ultimate designer would not be the God of theism.
Thus, evolution on atheism provides an explanation for high levels of
complexity in the universe, whereas no such explanation can be given
on theism regardless
of its compatibility with science; all else being equal, the argument
from improbability suggests that evolution constitutes evidence for
atheism. Dawkins succeeds in showing that the reasoning behind the
Design Argument best serves atheism, rather than theism.
Deflecting
Dawkins
The
argument from improbability against theism, in the form of Dawkins'
Ultimate Boeing 747 Gambit, suggests that theism is almost certainly
false. Its premises, however, are weak, and Plantinga demonstrates
this in his critique of Dawkins as well as his critique of theistic
applications of the argument. The premises of his Gambit can be
formulated as such:
1)
There exists a being x
such that x
is too complex to have come about by chance.
2'')
For any x
such that x
is too complex to have come about by chance, there exists an
explanation y
such that (y
posits a designer for x)
or (y
posits the evolution of x
through evolution by natural selection, explaining its level of
complexity).
3)
If (1) and (2''), then God's existence is infinitely improbable.
4)
So, God's existence is infinitely improbable.
Dawkins
claims that his Ultimate Boeing 747 Gambit "does not depend on
subjective judgment" (136), but this belief of Dawkins', as
Plantinga demonstrates, is manifestly false.
Premise
(2) and its derivatives (2', 2'', DA, and DA') are where the
subjectivity really lies. Dawkins never justifies the notion that
there simply must be an explanation for the occurrence of a given
level of complexity; he simply assumes that it "is one thing on
which we can all agree" (145). He vaguely motions elsewhere
that "sometimes the language of information theory is used"
in justifying the principle that complexity must have an explanation,
but seems to take the principle as self-evident throughout his
argument (138). Unfortunately, Dawkins' justification for (2'') is
at best inter-subjective, and inter-subjective in a consensus that
does not include a certain prominent Christian philosopher.
"Explanations
come to an end," Plantinga writes, and "for theism they
come to an end in God" (28). So, even given that "mind
would be an outstanding example of organized complexity" (27),
according to theism there is no explanation for the existence of a
mind (28), and so there is no explanation for why that level of
complexity obtained in the world. Plantinga points out that "the
materialist...doesn't have an explanation for the existence of
elementary particles" (28). Dawkins predicts this rebuttal to
(2) by suggesting that "Some kind of multiverse theory could in
principle do for physics the same explanatory work as Darwinism does
for biology" (188). Realizing the unconvincing nature of this
response, Dawkins adds that "the anthropic principle entitles us
to postulate far more luck than our limited human intuition is
comfortable with" (188). Until such a multiverse theory is
explicated, however, Dawkins' justification for the expectation of
explanation of complexity remains a mere 'reason of the gaps.'
Plantinga
also brings up the common notion that "It is not so much as
possible that there is no such person as God...[Dawkins] owes us an
argument...that there is no necessary being with the attributes of
God" (30). Presumably, Plantinga is not suggesting that Dawkins
seriously consider whether God necessarily exists, when the question
of God's existence is what is up for debate in the first place; the
most charitable interpretation of Plantinga here would take this
comment as an objection to (2''). Plantinga might be suggesting that
theism actually offers another way out of the infinite regress
mentioned above, because it actually posits
(2''')
For any x
such that x
is too complex to have come about by chance, there exists an
explanation y
such that (y
posits a designer for x)
or (y
posits the evolution of x
through evolution by natural selection) or (y
posits that x
exists necessarily).
Some
instances of complexity, and thus some high levels of complexity as
such, might not be contingent on designers or evolution; indeed, they
might be necessary occurrences or brute fact.
Plantinga
succeeds in undermining Dawkins' rationales for (2) and its
derivatives, showing them ultimately to be based on little more than
personal opinion. Since Dawkins "can't get excited about
personal opinions" (136), perhaps he should not get too excited
about his argument from the improbability of complexity (the
"Ultimate Boeing 747 Gambit"), either.
Conclusion
The
argument from improbability, historically presented as the theistic
Argument from Design, has been used throughout the ages to convince
skeptics of the existence of God. Richard Dawkins claimed that it is
a strong argument, but rather a strong argument against
theism as the Ultimate Boeing 747 Gambit; Dawkins succeeded in
demonstrating his latter point, but Christian philosopher of religion
Alvin Plantinga showed that the argument from improbability is not
strong in the objective sense that Dawkins intended. A commitment to
impartiality turns the Design Argument against theism, but also
reveals it as ultimately based in subjective intuition.
Sources
Dawkins,
Richard. The God
Delusion. Great
Britain: Bantam, 2006. Print.
Plantinga,
Alvin. Where the
Conflict Really Lies.
Oxford: Oxford University Press, 2011. Print.
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