Summary of Paper: In around 50,000 words, this paper
provides a scientifically and philosophically careful treatment of the
fine-tuning argument for divine creation of the cosmos, addressing most of the
major criticisms of the argument in the process. [See section 1.1 below for
overview].
This is an early version of the paper before it went through
the editing process at Blackwell; thus some typos, etc., are still
present. For the final version of the
paper, see the Blackwell Companion in
Natural Theology, or you might be able to find it posted on a website
somewhere.
This essay is a highly abridged
version of an in-process book-length project in which I argue for the existence
of God based on this fine-tuning of the cosmos for life along with the beauty
and intelligibility of the laws of nature.
The main purpose of the book is to put this argument on as rigorous as
possible scientific and philosophical foundation. Although this essay has the same purpose, it
will focus solely on the argument based on the fine-tuning for life, though in
my judgment the argument based on beauty and intelligibility is as strong.
The
sections of this essay are arranged as follows.
In section 1.2, I present some key terms and definitions for easy
reference. In section 1.3, I present the basic form of what I call the core fine-tuning argument for the
existence of God. This argument is explicated terms of what I call the restricted version of the likelihood principle.
In section 1.4, I present an alternative way of formulating the argument using
what I call the method of probabilistic
tension. In sections 2.1 - 2.6, I present the evidence for fine-tuning and
consider some of the main criticisms of this evidence.
Since
I shall formulate the argument in sections 1.3 and 1.4 in terms of certain conditional epistemic probabilities, I
need to develop an account of conditional epistemic probability and a general
method for determining the degree of conditional epistemic probability that one
proposition has on another. I do this in sections 3.1 - 3.3. In sections 4.1 -
4.5, I address some further critical issues for my formulation of the
fine-tuning argument, namely the appropriate background information to use in the
argument and the appropriate comparison range of values for the constants of
physics. In sections 5.1 - 5.2, I
complete the core fine-tuning argument by using the results of the previous
sections to derive the premises of the main argument presented in sections 1.3
-1.4.
In
section 6.1- 6.3, I address the so-called multiverse hypothesis as an
alternative explanation of the fine-tuning, or at least as a way of undermining
the fine-tuning argument for theism. The multiverse hypothesis is widely
considered the leading alternative to a theistic explanation. In sections 7.1- 7.5, I reply to various
miscellaneous objections to the fine-tuning argument, such as the so-called
“Who Designed God?” objection. Finally, in section 8, I conclude the entire
argument.
My
overall approach will be to present a version of the fine-tuning argument that
is more rigorous than its predecessors by presenting the argument in a
step-by-step fashion and then justifying each step, using widely used
principles of reasoning. This way of
developing the argument will not only show that the argument can be made
philosophically rigorous, but it automatically will answer many of the
criticisms that have been raised against it; it also will help us go beyond a
mere “battle of intuitions” between advocates and critics of the argument.
Further, as much as possible I shall avoid using theories of confirmation that
attempt to account for everyday and scientific forms of reasoning but whose
claims go significantly beyond what these forms of reasoning demand. Thus, for instance, I will avoid appealing to
prior probabilities and to
notions of purely logical probability that claim that relations of probability
exist completely independently of human cognizers. (For example, see sections
1.3 and 3.2).
In
this section, I shall define some key terminology and abbreviations that are
used in more than one section. This will help the reader keep track of my terms
and symbolisms.
2. The existence of a
Life-Permitting Universe (LPU).
This will always mean the existence of a material spatio-temporal
reality that can support embodied moral agents, not merely life of some
sort. Indeed, in every case where I use
the word “life,” I shall have in mind embodied moral agents as the relevant
kind of life. The reason that embodied moral agents are the relevant kind of
life will become clear in section 5.2, where I argue that LPU is not improbable
under theism. Throughout, it will be
assumed that the existence of such beings requires a high degree of material
complexity, such as we find in the brains of higher-order animals.
C of physics (see sections 2.3 and
4.2), I shall use the term “fine-tuning” specifically to refer to the claim
that the life-permitting range of C – that is, the range of values that allows
for life – is very small compared to the some properly chosen “comparison
range” for that constant. (For how to choose this comparison range, see
sections 4.3 - 4.4). The “fine-tuning”
of a constant will never be used to include the claim that it has life-permitting
values.
My basic argument first claims that, given
the fine-tuning evidence, the existence of a life-permitting universe (LPU)
strongly supports theism over the naturalistic single-universe hypothesis
(NSU). I call this the core fine-tuning argument. After
developing this argument in sections 2 through 5, I then present arguments for
preferring theism over the multiverse hypothesis (section 6). Finally, in section 8, I shall briefly
consider other possible alternative explanations of the fine-tuning.
The core fine-tuning argument relies on a
standard principle of confirmation theory, the so-called likelihood principle. This principle can be stated as follows.
Let h1 and h2
be two competing hypotheses. According
to the likelihood principle, an observation e counts as evidence in favor of
hypothesis h1 over h2 if the observation is more probable
under h1 than h2.
Put symbolically, e counts in favor of h1 over h2
if P(e| h1) > P(e| h2), where P(e| h1)
and P(e| h2) represent the conditional probability of e on h1
and h2, respectively. Moreover, the degree to which the evidence
counts in favor of one hypothesis over another is proportional to the degree to
which e is more probable under h1 than h2: specifically,
it is proportional to P(e| h1)/P(e| h2).
The likelihood principle appears to be
sound under all interpretations of probability. The type of probability that we
shall be concerned with is what is called conditional epistemic probability. The conditional epistemic probability of a
proposition A on a proposition B can be defined roughly as the degree to which
proposition B, in and of itself, supports or leads us to expect A to be
true. In section 3.2, I shall explicate
this notion of probability in much more detail.
Put in terms of epistemic probability, the likelihood principle can be
reworded in terms of degrees of expectation instead of probability, in which
case it becomes what I call the expectation
principle. According to the expectation principle, if an event or state of
affairs e is more to be expected under one hypothesis h1 than
another h2, it counts as evidence in favor of h1 over h2--that
is, in favor of the hypothesis under which it has the highest expectation. The
strength of the evidence is proportional to the relative degree to which it is
more to be expected under h1 than h2. Re-wording the
likelihood principle in terms of expectation is particularly helpful for those
trained in the sciences, who are not familiar with epistemic probability and
therefore tend to confuse it with other kinds of probability, even when they
are aware of the distinction.
Because
of certain potential counterexamples, I shall use what I call the restricted version of the likelihood
principle, although I shall often refer to it simply as the likelihood
principle. The restricted version limits
the applicability of the likelihood principle to cases in which the hypothesis
being confirmed is non-ad hoc. A sufficient condition for a hypothesis being
non-ad hoc is that there are
independent motivations for believing the hypothesis apart from the confirming
data e, or for the hypothesis to have been widely advocated prior to the
confirming evidence. To illustrate the need for the restricted version, suppose
that I roll a die twenty times and it comes up some apparently random sequence
of numbers B say 2,
6, 4, 3, 1, 5, 6, 4, 3, 2, 1, 6, 2, 4, 4, 1, 3, 6, 6, 1. The probability of its coming up in this
sequence is one in 3.6 x 1015, or about one in a million
billion. To explain this occurrence,
suppose I invented the hypothesis that there is a demon whose favorite number
is just the above sequence of numbers (i.e., 26431564321624413661), and that
this demon had a strong desire for that sequence to turn up when I rolled the
die. Now, if this demon hypothesis were
true, then the fact that the die came up in this sequence would be expected B that is, the sequence would not be
epistemically improbable. Consequently,
by the standard likelihood principle, the occurrence of this sequence would
strongly confirm the demon hypothesis over the chance hypothesis. But this seems counterintuitive: given a sort
of common-sense notion of confirmation, it does not seem that the demon
hypothesis is confirmed.
Finally,
given that we can establish the conclusion, what is its significance? Even if
LPU counts as strong evidence in favor of theism over NSU, that does not itself
establish that theism is likely to be true, or even more likely to be true than
NSU. In this way, LPU is much like fingerprints found on the gun. Via the likelihood principle, the defendant’s
fingerprints’ matching those on a murder weapon typically provide strong
evidence for guilt because the jury correctly judges that it is very unlikely
for this matching to occur if the defendant is not guilty (and claims to have
never seen the murder weapon), whereas it is not unexpected if the defendant
actually used the murder weapon.
Although such a match can provide strong evidence that the defendant is
guilty, one could not conclude merely from this alone that the defendant is
guilty; one would also have to look at all the other evidence offered. Perhaps, for instance, ten reliable
witnesses claimed to see the defendant at a party at the time of the
shooting. In that case, by the
restricted version of the likelihood principle, the matching would still count
as significant evidence of guilt, but this evidence would be counterbalanced by
the testimony of the witnesses.
Similarly we shall claim that the evidence of fine-tuning significantly
supports theism over NSU; this, however, neither shows that, everything
considered, theism is probably true, nor that it is the most plausible
explanation of existence of the universe, nor even that it is more probable
than NSU. In order to show that any
hypothesis is likely to be true using a likelihood approach, we would have
assess the prior epistemic probability of the hypothesis, something I shall not
attempt to do for theism.
Our
more limited conclusion is nonetheless highly relevant to the rationality of
and justification for belief in God, even though it does not itself establish
that, all things considered, theism is more probable than NSU. One could argue,
for example, that in everyday life and science we speak of evidence for and
against various views, but seldom of prior probabilities. For example, if one
were to ask most physicists why they
(tentatively) believe in general relativity's approximate truth (or at least
its future empirical fruitfulness), they probably would cite the evidence in
favor of it, along with some of Einstein’s motivations. They probably would not cast these
considerations – such as Einstein’s motivations – into talk of prior
probability, either epistemic or otherwise.
Of course, at the end of the day, some might say things like,
“Einstein’s theory is likely to be true,” which is a notion of epistemic
probability. But, I can imagine them
saying, “I have no idea what the prior probability of Einstein’s theory is; all
I will say is that Einstein had motivations for considering it and there are at
least three strong pieces of empirical evidence in its favor.” Indeed, I think it would be very difficult to
estimate the prior probability of general relativity's approximate truth (or
future empirical fruitfulness) in any objective manner, since we should have to
weigh incommensurable factors against each other – the simplicity of the
mathematical framework of general relativity against such things as the
philosophically puzzling character of the idea of a four-dimensional
space-time’s being curved. Arguably, this is analogous to the case of theism.
One
way of putting my approach in perspective is to note that one of the most
common philosophical objections to theism is an updated version of one offered
by Kant, in which the methods of reason are restricted to justifying only the
existence of natural causes. Unlike
Kant, however, modern atheistic philosophers often reject God as a necessary
hypothesis of practical reasoning. Typically, these philosophers claim that by
analyzing the notion of explanation, particularly as exemplified in natural
science, we find that to explain something involves citing overarching laws,
mechanical causes, and the like; thus, they assert, the very notion of
explanation involves a restriction to purely naturalistic explanations. The
idea of God as providing a complete explanation of all contingent reality is
therefore rejected as being empty, an improper extension of “explain” to places
where it cannot apply. Another attack is
to argue that even if God could be said to explain contingent reality, God's
own existence would be as much in need of explanation.
Richard
Swinburne (2004, Chaps. 2 - 4) has responded to these critics by offering an
alternative analysis of ordinary explanation.
He claims that these critics have neglected the notion of personal
explanation and then goes on to claim that God provides the best personal explanation
of everything we know about the universe.
His argument rests on the dual claim that the simplicity of an
explanation is the ultimate criterion of its adequacy and that God provides the
simplest explanation of the universe.
There are many places one might object to Swinburne's project, particularly
these two claims about simplicity. Further, by basing his project on the notion
of explanation used in everyday life, Swinburne leaves God's own existence
entirely unexplained. Indeed, Swinburne
claims that God is the ultimate contingent brute fact and could be said to
necessarily exist only in the limited sense that God is without beginning and
that, in principle, nothing could explain God's existence.
The
approach I am taking avoids this question of how best to analyze the notion of
explanation or whether God ultimately provides the best explanation of the
universe. Rather, it simply attempts to
establish the more limited claim that various features of the universe offer
strong evidence in favor of theism over its major naturalistic alternatives. I believe that establishing this more limited
claim in a careful, principled way would alone be a great accomplishment. In section 7.1, however, I address how this
more limited claim fits into an overall argument for the existence of God. In that section I also briefly address the
issue of God's providing an ultimate explanation and respond to the claim that
God is as much in need of a designer as the universe itself. A fuller
discussion of this issue, however, is beyond the scope of this chapter.
One problem with using simply the
likelihood principle is that whether or not a hypothesis is confirmed or
disconfirmed depends on what one builds into the hypothesis. For example, single-universe naturalists
could prevent disconfirmation of their hypotheses by advocating the elaborated
naturalistic-single universe hypothesis (NSUe), defined as NSU conjoined
with the claim that the universe that exists is life-permitting: that is, NSUe
= NSU & LPU. Similarly, theists
could avoid any question about whether LPU is probable on theism by
constructing an elaborated theistic hypothesis, Te, which builds in the claim
that God desired to create such a universe: Te = T & God desires to create
a life-permitting universe.
One could attempt to deal with these sorts
of moves by finding some principled way of restricting what can be built into
the theistic and naturalistic hypotheses -- e.g., by requiring that the
theistic and naturalistic hypotheses be some sort of “bare” theism and “bare”
single-universe naturalism, respectively.
This, however, is likely to run into difficulties not only in justifying
the principle, but in defining what “bare” theism and “bare” single-universe
naturalism are supposed to be. A simpler way of addressing the issue is by
means of a concept I call
probabilistic
tension. A hypothesis h suffers from probabilistic tension if and only if h
is logically equivalent to some conjunctive hypothesis, h
1& h
2,
such that either P(h
1| h
2) << 1 or P(h
2|
h
1) << 1: that is, one conjunct of the hypothesis is very
unlikely, conditioned on the other conjunct.
Among other things, a hypothesis h that suffers from probabilistic
tension will be very unlikely: since P(h) = P(h
1& h
2)
= P(h
1| h
2) x P(h
2) = P(h
2| h
1)
x P(h
1), it follows that if P(h
1| h
2) <<
1 or P(h
2| h
1) <<1 1.="" h="" p="" then="">
I claim that significant probabilistic
tension is an epistemic black mark against a hypothesis, and thus offers us a
reason to reject it. To see this, consider the fingerprint example discussed
above. We noted that based on the
likelihood principle, the matching of a defendant's fingerprints with those on
a murder weapon often strongly confirm the guilt hypothesis over the innocence
hypothesis. Such matching, however, does not confirm the guilt hypothesis over
what could be called an “elaborated innocence hypothesis” -- that is, an
innocence hypothesis constructed in such a way that the matching of the
fingerprints is implied by the hypothesis.
An example of such a hypothesis is that the defendant did not touch the
murder weapon conjoined with the hypothesis that someone else with almost
identical fingerprints touched the weapon. This latter hypothesis entails that
the fingerprints will appear to match, and hence by the likelihood principle
the matching could not be more surprising under this hypothesis than under the
guilt hypothesis.
Nonetheless, this elaborated innocence
hypothesis suffers from severe probabilistic tension: one conjunct of the
hypothesis (that some other person with almost identical fingerprints touched
the weapon) is very improbable on the other conjunct (that the defendant is
innocent), since it is extremely rare for two people to happen to have almost
identical fingerprints. Given that the guilt hypothesis does not suffer from a
corresponding probabilistic tension, the high degree of probabilistic tension
of the elaborated innocence hypothesis gives us strong reason to reject it over
the guilt hypothesis, even though this elaborated hypothesis is not itself
disconfirmed by the matching of the fingerprints.
This idea of probabilistic tension allows
us to eliminate any arbitrariness with regard to how we choose the theistic and
naturalistic hypotheses that we are confirming or disconfirming.
For example, both the theist and the naturalist can build into their respective
hypotheses whatever is necessary for them to entail the relevant data. Then one
can apply the method of probabilistic tension to these elaborated hypotheses. Consider, for instance, the
elaborated NSU hypothesis (NSUe) and the
elaborated theistic hypothesis (Te)
defined above: That is, NSUe = NSU & LPU and Te = T & God desires to
create a life-permitting universe. Both of these hypotheses entail LPU, and
hence neither is confirmed (via the likelihood principle) with respect to the
other by LPU.
Now, given the truth of premise (1) of our
main argument in section 1.3, NSUe clearly exhibits a high degree of
probabilistic tension relative to background information k´, since one
conjunction of the hypothesis, LPU, is very improbable conditioned on the other
conjunct, NSU: that is, P(LPU|NSU &k´) << 1.
Given the truth of premise (2), elaborated theism will not suffer any
corresponding probabilistic tension. The
reason is that according to premise (2), it is not the case that P(LPU|T &
k´) << 1, and hence it follows
that it is
not unlikely that the God
of “bare theism” would desire to create a life-permitting universe. This means there will be no probabilistic
tension between “bare” theism and the claim that God desires to create such a
universe. This will be true even if the probability of P(LPU|T & k') is
merely indeterminate, since such a probabilistic tension would exist only if
P(LPU|T & k') << 1. Thus, the
fine-tuning evidence causes the elaborated naturalistic hypothesis to suffer
from a severe probabilistic tension without causing a corresponding
probabilistic tension in the elaborated theistic hypothesis. Thus, because it creates this probabilistic
tension, we could say that the fine-tuning evidence (but not LPU itself) gives
us strong reason to reject NSU over the theistic hypothesis.
In
practice, any sufficiently elaborated hypothesis will suffer from severe
probabilistic tension somewhere. For
instance, the elaborated guilt hypothesis mentioned above could include that
the knife used in the murder was green, had a certain shaped scratch mark on
its handle, had a weight of 0.15679876675876 kg, and the like. The
corresponding elaborated innocence hypothesis would include the same data. Both would suffer from severe probabilistic
tension with respect to each piece of data -- e.g., the murder knife having a
weight of 0.15679876675876 kg is very improbable under both the “bare” guilt
and “bare” innocence hypothesis. The lesson
here is that only the probabilistic tension which one hypothesis has and which
another lacks relative to some particular domain can be used as evidence in
favor of one hypothesis over another. In
our case, the particular domain of probabilistic tension is that arising from
the fine-tuning data. Elaborated
naturalism might do better in other areas with regard to probabilistic tension,
but to say that the fine-tuning data counts against elaborated naturalism with
respect to theism, all we have to show is that fine-tuning creates a
probabilistic tension within elaborated naturalism without creating a
corresponding tension within elaborated theism.
The evidence for fine-tuning of the
universe for life falls into three categories:
(i)
The fine-tuning of the laws of nature
(ii)
The fine-tuning of the constants of nature
(iii)
The fine-tuning of the initial conditions of the universe
We shall present examples of each
type of fine-tuning below. Before we
begin, we should note that each of the above types of fine-tuning presupposes
that a necessary requirement for the evolution of embodied moral agents is that
there exist material systems that can sustain a high level of self-reproducing
complexity--something comparable to that of a human brain. Given what we know of life on earth, this
seems a reasonable assumption.
The
first major type of fine-tuning is that of the laws of nature. The laws and
principles of nature themselves have just the right form to allow for the
existence embodied moral agents. To
illustrate this, we shall consider the following five laws or principles (or
causal powers) and show that if any one of them did not exist, self-reproducing,
highly-complex material systems could not exist: (1) a universal attractive
force, such as gravity; (2) a force relevantly similar to that of the strong
nuclear force, which binds protons and neutrons together in the nucleus; (3) a
force relevantly similar to that of the electromagnetic force; (4) Bohr's
Quantization Rule or something similar; (5) the Pauli-exclusion principle.
If
any one of these laws or principles did not exist (and were not replaced by a
law or principle that served the same or similar role), complex self-reproducing
material systems could not evolve. First, consider gravity. Gravity is a long-range attractive force
between all material objects, whose strength increases in proportion to the
masses of the objects and falls off with the inverse square of the distance
between them. In classical physics, the amount of force is given by Newton's
law, F= Gm1m2/r2, where F is the force of
attraction between two masses, m1 and m2, separated by a
distance r is apart, and G is the gravitational constant (which is simply a number
with a value of 6.672 × 10-11 N.m2/kg2). Now
consider what would happen if there were no universal, long-range attractive
force between material objects, but all the other fundamental laws remained (as
much as possible) the same. If no such
force existed, then there would be no stars, since the force of gravity is what
holds the matter in stars together against the outward forces caused by the
high internal temperatures inside the stars. This means that there would be no
long-term energy sources to sustain the evolution (or even existence) of highly
complex life. Moreover, there probably
would be no planets, since there would be nothing to bring material particles
together, and even if there were planets (say because planet-sized objects
always existed in the universe and were held together by cohesion), any beings
of significant size could not move around without floating off the planet with
no way of returning. This means that
embodied moral agents could not evolve, since the development of the brain of
such beings would require significant mobility.
For all these reasons, a universal attractive force such as gravity is
required for embodied moral agents.
Second,
consider the strong nuclear force. The
strong nuclear force is the force that binds nucleons (i.e., protons and
neutrons) together in the nucleus of an atom.
Without this force, the nucleons would not stay together. This force is actually a result of a deeper force,
the “gluonic force,” between the quark constituents of the neutrons and
protons, a force described by the theory of quantum chromodynamics. This force must be strong enough to overcome
the repulsive electromagnetic force between the protons and the quantum
zero-point energy of the nucleons.
Because of this, it must be considerably stronger than the
electromagnetic force; otherwise the nucleus would come apart. Further, to keep atoms of limited size, it
must be very short-range – which means its strength must fall off much, much
more rapidly than the inverse square law characteristic of the electromagnetic
force and gravity. Since it is a purely
attractive force (except at extraordinarily small distances), if it fell off by
an inverse square law like gravity or electromagnetism, it would act just like
gravity and pull all the protons and neutrons in the entire universe
together. In fact, given its current
strength, around 1040 stronger than the force of gravity between the
nucleons in a nucleus, the universe would most likely consist of a giant black
hole.
Thus,
to have atoms with an atomic number greater than that of hydrogen, there must
be a force that plays the same role as the strong nuclear force – that is, one
that is much stronger than the electromagnetic force but only acts over a very
short range. It should be clear that
embodied moral agents couldn’t be formed from mere hydrogen, contrary to what
one might see on science fiction shows like “Star Trek.” One cannot obtain enough self-reproducing,
stable complexity. Furthermore, in a universe in which no other atoms but
hydrogen could exist, stars could not be powered by nuclear fusion, but only by
gravitational collapse, which means they would not last long enough for the
evolution of embodied moral agents.
Third,
consider electromagnetism. Without electromagnetism, there would be no atoms
since there would be nothing to hold the electrons in orbit. Further, there
would be no means of transmission of energy from stars for the existence of
life on planets. It is doubtful whether
enough stable complexity could arise in such a universe for even the simplest
forms of life to exist.
Fourth,
consider Bohr's rule of quantization, first proposed in 1913, which requires
that electrons occupy only fixed orbitals (energy levels) in atoms. It was only with the development of quantum
mechanics in the 1920s and 1930s that Bohr’s proposal was given an adequate
theoretical foundation. If we view the
atom from the perspective of classical Newtonian mechanics, an electron should
be able to go in any orbit around the nucleus.
The reason is the same as why planets in the solar system can be any
distance from the sun – e.g., the earth could have been 150 million miles from
the sun instead of its present 93 million miles. Now the laws of electromagnetism – i.e.,
Maxwell’s equations – require that any charged particle that is accelerating
will emit radiation. Because electrons
orbiting the nucleus are accelerating--since their direction of motion is
changing-- they will emit radiation. This radiation will cause the electron to
lose energy, causing its orbit to decay so rapidly that atoms could not exist
for more than a few moments. This was a
major problem confronting Rutherford’s model
of the atom – in which the atom had a nucleus with electrons around the nucleus
– until Niels Bohr proposed his ad hoc
rule of quantization in 1913, which required that electrons occupy fixed
orbitals. Thus, without the existence of this rule of quantization -- or
something relevantly similar -- atoms could not exist, and hence there would be
no life.
Finally,
consider the Pauli exclusion principle, which dictates that no two fermions
(spin ½ particles) can occupy the same quantum state. This arises from a deep principle in quantum
mechanics which requires that the joint wave function of a system of fermions
must be anti-symmetric. This implies that not more than two electrons can
occupy the same orbital in an atom, since a single orbital consists of two
possible quantum states (or more precisely, eigenstates) corresponding to the
spin pointing in one direction and the spin pointing in the opposite direction.
This allows for complex chemistry, since without this principle, all electrons
would occupy the lowest atomic orbital. Thus, without this principle, no
complex life would be possible.
The constants of physics are fundamental
numbers that, when plugged into the laws of physics, determine the basic
structure of the universe. An example of
a fundamental constant is
Newton’s gravitational
constant G, which determines the strength of gravity via
Newton’s law F = Gm
1m
2/r
2. We will say that a constant is fine-tuned if
the width of its life-permitting range, W
r, is very small in
comparison to the width, W
R, of some properly chosen comparison
range: that is, W
r/W
R << 1. A more philosophically rigorous way of
determining this comparison range will be presented in sections 4.4. Here we shall simply use certain standard
comparison ranges that naturally arise in physics and hence are used by
physicists when they speak of cases of anthropic fine-tuning.
There are many examples of the anthropic
fine-tuning of the fundamental constants of physics. Elsewhere I have more thoroughly examined six
of what I considered the most well-established cases, carefully articulating
the physical lines of evidence offered in support of these cases along with
correcting some incorrect and often-repeated claims regarding fine-tuning
(Collins, 2003). For purposes of
illustration, here I shall explicate in some detail only two constants of
physics--the strength of gravity and the cosmological constant.
Using a standard measure of force
strengths – which turns out to be roughly the relative strength of the various
forces between two protons in a nucleus -- gravity is the weakest of the
forces, and the strong nuclear force is the strongest, being a factor of 1040
– or ten thousand billion, billion, billion, billion – times stronger than
gravity (Barrow and Tipler, 1986, pp. 293 - 295). Now if we increased the
strength of gravity a billion-fold, for instance, the force of gravity on a
planet with the mass and size of the earth would be so great that organisms
anywhere near the size of human beings, whether land-based or aquatic, would be
crushed. (The strength of materials depends on the electromagnetic force via
the fine-structure constant, which would not be affected by a change in
gravity.) Even a much smaller planet of only 40 feet in diameter – which is not
large enough to sustain organisms of our size – would have a gravitational pull
of one thousand times that of earth, still too strong for organisms with brains
of our size to exist. As astrophysicist
Martin Rees notes, “In an imaginary strong gravity world, even insects would
need thick legs to support them, and no animals could get much larger” (2000,
p. 30). Based on the evidence from
earth, only organisms with brains of a size comparable to our own have
significant moral agency. Consequently, such an increase in the strength of
gravity would render the existence of embodied moral agents virtually
impossible and thus would not be life-permitting in the sense that we
defined.
Of course, a billion-fold increase in the
strength of gravity is a lot, but compared to the total range of the strengths
of the forces in nature (which span a range of 1040 as we saw
above), it is very small, being one part in ten thousand, billion, billion,
billion. Indeed, other calculations show
that stars with life-times of more than a billion years, as compared to our sun’s
life-time of ten billion years, could not exist if gravity were increased by
more than a factor of 3000 (Collins, 2003). This would significantly inhibit
the occurrence of embodied moral agents.
The case of fine-tuning of gravity
described above is relative to the strength of the electromagnetic force, since
it is this force that determines the strength of materials – e.g., how much
weight an insect leg can hold; it is also indirectly relative to other
constants – such as the speed of light, the electron and proton mass, and the
like – which help determine the properties of matter. There is, however, a fine-tuning of gravity
relative to other parameters. One of these is the fine tuning of gravity
relative to the density of matter in the early universe and those factors
driving the big bang explosion – that is, the combination of the density of
radiation as compared to normal baryonic matter (e.g., protons and neutrons)
and possibly a positive cosmological constant.
Holding these other parameters constant, if the strength of gravity were
smaller or larger by an estimated one part in 10
60 of its current
value, the universe would have either exploded too quickly for galaxies and
stars to form, or collapsed back on itself too quickly for life to evolve.
The lesson here is that a single
parameter, such as gravity, participates in several different fine-tunings
relative to other parameters.
Probably
the most widely discussed case of fine-tuning for life is that of the cosmological
constant. The cosmological constant, Λ, is a term in Einstein’s equation of
general relativity that, when positive, acts as a repulsive force, causing
space to expand and, when negative, acts as an attractive force, causing space
to contract. Einstein's equation implies
that if the vacuum -- that is, space-time devoid of normal matter -- has an
energy density, then that energy density must act in a mathematically, and
hence physically, equivalent way to a cosmological constant. The seeming need for fine-tuning of the
cosmological constant arises from the fact that almost every field within
modern physics -- the electromagnetic field, the Higgs fields associated with
the weak force, the inflaton field
hypothesized by inflationary cosmology, the dilaton
field hypothesized by superstring theory, and the fields associated with
elementary particles – each contributes to the vacuum energy far in excess of
the maximum life-permitting amount.
These contributions to the vacuum energy can be either negative or
positive. If the total effective cosmological constant is positive and larger
than some positive value Λ+max, or negative and smaller than some
negative value Λ-max, then the universe would have expanded (if
positive), or collapsed (if negative), too quickly for stars or galaxies to
form. Thus, for life to occur, the
cosmological constant must be between Λ-max, and Λ+max. I shall let Λmax designate the
larger of the two absolute values of Λ-max and Λ+max. Since the absolute values of Λ-max
and Λ+max are within one or two orders of magnitude of each other, I
shall explain the cosmological constant problem for the case in which Λ is
assumed to be positive, but the same analysis will apply for the case in which
Λ is negative.
Einstein
originally hypothesized the existence of the cosmological constant so that his theory
would imply a static universe. Thus, the original cosmological constant that
Einstein postulated was not associated with contributions to the vacuum energy
of the various fields of physics. If we
let Λvac represent the contribution to the cosmological constant
from the vacuum energy of all the fields combined, and Λbare
represent the intrinsic value of the cosmological constant apart from any
contribution from these fields, then the total value, Λ tot, of the
cosmological constant is Λ tot = Λvac + Λbare.
The contributions to Λvac can be further divided into those
contributions arising from various forms of potential energy, V, as the
universe passes through different phases along with those arising from the
zero-point energies of the vacuum fluctuations of the quantum fields of the
fundamental forces and elementary particles.
Finally,
there have been various proposals for a new and highly speculative type of
energy, called quintessence, whose
defining feature is that it acts like a cosmological constant in the way it
causes space to expand or contract, but unlike the cosmological constant it can
change with time as the universe evolves from the big bang onwards.
Consequently, we can define the total effective
cosmological constant as the sum of all these contributions that function in
the same way as the cosmological constant with regard to causing space to
expand or contract: that is, Λeff = Λvac + Λbare
+ Λq, where Λq designates the contribution resulting from
quintessence. The fine-tuning problem can now be stated as follows: without
fine-tuning or some new principle of physics, Λeff is expected to be at least 1053 to
10120 times larger than the maximum life permitting value Λmax.
The smallness of the cosmological constant compared to its non-fine-tuned,
theoretically expected value is widely regarded as the single greatest problem
confronting current physics and cosmology.
To understand this fine-tuning problem
more fully, it will be helpful to consider the three major types of
contribution to the vacuum energy term, Λ
vac, of the cosmological
constant in modern cosmology. Following standard terminology, we will let ρ
vac
designate the vacuum energy density, and ρ
max the maximum vacuum
energy density compatible with the existence of life, given that the vacuum
energy is the only contribution to the cosmological constant.
The
first contribution we shall consider arises from the Higgs field postulated as
part of the widely accepted Weinberg‑Salem‑Glashow electroweak theory.
According to this theory, the electromagnetic force and the weak force acted as
one force prior to symmetry breaking of the Higgs field in the very early
universe when temperatures were still extremely high. Before symmetry breaking,
the vacuum energy of the Higgs field had its maximum value V
0. This
value was approximately 10
53 ρ
max. After symmetry
breaking, the Higgs field fell into some local minimum of its possible energy
density, a minimum which theoretically could be anywhere from zero to 10
53
ρ
max, being solely determined by V
0 and other free
parameters of the electroweak theory.
Now either this local minimum is less than
ρmax, or it is greater than ρmax and the other
contributions to the cosmological constant offset its contribution to Λ
eff so that Λ eff << Λmax. In either case, the fine-tuning would have to
be in one part in 1053. In the former case, for instance, the local
minimum of energy would have to be between zero and ρmax , which
would be one part in 1053 of its possible range of values.
The second contribution to the vacuum
energy is the postulated inflaton field of inflationary cosmology. Inflationary
universe models hypothesize that the inflaton field had an enormously high
energy density in the first 10
‑35 to 10
‑37 seconds of our
universe, resulting in an effective cosmological constant that caused space to
expand by a factor of around 10
60 (Guth, 1997, P.185). By around 10
‑35 seconds or so,
however, the value of the inflaton field fell to a relatively small value
corresponding to a
local minimum of
its energy.
Now, in order to start inflation, the initial
energy density of the inflaton field, ρ
i, must have been enormously
larger than ρ
max: ρ
i >> ρ
max. Theoretically, however, the local minimum of
the inflaton field could be anything from zero to ρ
i. (See Sahni and
Starobinsky 1999: section 7.0; Rees 2000, p.154).
The fact that
the effective cosmological constant after inflation is less than ρ
max requires
an enormous degree of fine-tuning, for the same reason as the Higgs field above
– e.g., neglecting other contributions to the cosmological constant, the local
minimum of energy into which the inflaton field fell must be between 0 and ρ
max,
a tiny portion of the its possible range, 0 to ρ
i.
The
final contribution results from the so-called zero-point energies of the fields associated with forces and
elementary particles, such as the electromagnetic force and electrons and
protons. If we calculate this
contribution using quantum field theory and assume that space is a continuum,
the contribution turns out to be infinite.
Physicists, however, typically assume that quantum field theory is valid
only up to a certain very large cut-off energy (see section 4.5), in which case
the contribution turns out to be extraordinarily large, but finite, with the
actual value depending on the cut-off energy below which quantum field theory
is taken as valid. The so-called Plank
energy is often assumed to be the energy scale that quantum field theory breaks
down, in which case the energy contribution of the zero-point energy for the
various fields would be expected to be 10120 ρmax. (See
Sahni and Starobinsky, 1999, p. 44.) To
reduce this contribution to within an order of magnitude of the life-permitting
range (thus eliminating any significant fine-tuning) would require an extremely
low cut-off energy, which most physicists consider very unlikely (Donoghue,
2007, p. 236).
One
solution to the cosmological problem is to claim that God, or some other
intelligence, fine-tuned the various contributions to the cosmological
constant, Λvac + Λbare + Λq, in such a way
that Λeff << Λmax. Another much discussed solution is an appeal
to multiple universes and some anthropic selection effect, which we shall
discuss in section 6. Is there a
non-divine, non-anthropic solution to the fine-tuning of the cosmological
constant? Physicist Victor Stenger, the leading critic of the data appealed to
by advocates of the fine-tuning argument, claims that there is. According to
Stenger,
. . . recent
theoretical work has offered a plausible non-divine solution to the
cosmological constant problem. Theoretical physicists have proposed models in
which the dark energy is not identified with the energy of curved space-time
but rather with a dynamical, material energy field called quintessence. In these models, the cosmological constant is exactly
0, as suggested by a symmetry principle called supersymmetry. Since 0 multiplied by 10120 is still 0,
we have no cosmological constant problem in this case. The energy density of
quintessence is not constant but evolves along with the other matter/energy
fields of the universe. Unlike the cosmological constant, quintessence energy
density need not be fine-tuned (2004, p. 182).
Although in a later publication
(2007, pp. 151-153), Stenger does not mention supersymmetry, he still claims
that a hypothesized new form of energy, quintessence, could solve the
cosmological constant problem and that it “requires no fine-tuning.” (2007, p.
152).
Stenger's
proposal can be summarized in three steps. (1) Postulate some natural symmetry
or principle that requires that the cosmological constant, Λ
tot = Λ
vac
+ Λ
bare, be zero. (2) Postulate some additional quintessential field
to account for what appears to be a small positive value of the
effective cosmological constant today.
(3)
Postulate that there is some natural equation that implies that Λ
q
< Λ
max in the early universe, an equation which itself does not
require fine-tuning. Since Λ
eff
= Λ
vac + Λ
bare + Λ
q, the three steps above
would guarantee in a natural way that Λ
eff << Λ
max.
A
well-known proposal that would go part way to making Λtot = 0 is the
appeal to the speculative hypothesis of supersymmetry. Supersymmetry requires that for each bosonic
field there exist a corresponding fermionic field, where bosonic fields are
those associated with spin 1 particles, such as the photon, and fermionic
fields are those associated with spin ½ particles, such as electrons and
protons. It further requires that the positive zero-point energy contribution
associated with each bosonic field is exactly cancelled by the negative zero-point
energy contribution associated with the corresponding fermionic field. Consequently, it requires that the total
zero-point energies associated with the various fields of physics sum to zero,
resulting in a net contribution of zero to the total cosmological constant.
This solution faces a major difficulty: even if supersymmetry exists, it is
presently a broken symmetry and thus cannot solve the cosmological constant
problem. As astrophysicist John Peacock notes, “supersymmetry, if it exists at
all, is clearly a broken symmetry at present day energies; there is no natural
way of achieving this breaking while retaining the attractive consequence of a
zero cosmological constant, and so the Λ problem remains as puzzling as ever”
(1999, p. 268).
Further,
even if some other symmetry could be discovered that would force the
contributions of the bosonic or fermionic fields to cancel each other out, the
first two contributions to the cosmological constant mentioned above would
remain -- i.e., those arising from the Higgs field and the inflaton field. In order to get a zero cosmological constant,
one would have to postulate some law, symmetry, or other mechanism that forced
the sum of all contributions to the
cosmological constant to be zero. In
order to get this suggestion to work, physicists would have to either (a)
abandon inflationary cosmology, which requires that the effective cosmological
constant be initially very large and then fall off to near zero or (b) invoke
some special law, symmetry, or “mechanism” that selectively requires that the
cosmological constant be zero at the end of the inflationary period. If options (a) and (b) are both rejected, one
will be left with the fine-tuning problem generated by a large effective
cosmological constant required for inflation that must drop off to near zero
after inflation in order for life to exist.
Further,
supposing that option (a) or (b) are chosen, steps (2) and (3) are still
required to account for the small, non-zero effective cosmological constant
today. In typical models of quintessence, Λ
q “tracks” the matter and
radiation density of the universe -- that is, Λ
q is some function of
these densities. One problem here is that unless the function is both natural
and simple, without any adjustable parameters needed to make Λ
q <
Λ
max, the problem of fine-tuning will simply re-arise: if that
function is not simple or natural, or such a parameter is needed, then the
question will arise as to why that function or parameter is such that the value
of the effective cosmological constant is within the life-permitting range
instead of falling outside the life-permitting range. So far, no such natural
function has been found, and it is widely argued that current models of
quintessence require fine-tuning, especially when combined with inflationary
cosmology.
Further, quintessential energy must have special characteristics to act as an
effective cosmological constant. As
noted by physicists Robert R. Caldwell and Paul J. Steinhardt,
“The simplest model proposes that the
quintessence is a quantum field with a very long wavelength, approximately the
size of the observable universe” (2001).
The long wavelength of the field means that its energy is dominated by
potential energy, which in turn allows for it to act as an effective
cosmological constant.
In sum, it is conceivable that by
postulating the right set of laws-symmetries-mechanisms, physicists will be
able to explain the fine-tuning of the effective cosmological constant in a non-ad-hoc way. Nonetheless, two points should be made. First, any such explanation will require the
hypothesis of just the right set of laws. At best, this will merely transfer
the fine-tuning of the cosmological constant to that of the laws of nature;
even if those laws of nature are deemed “natural,” one would still have to have
the right set of laws to eliminate the fine-tuning of the cosmological
constant. Consequently, other than eliminating the ability to quantify the
degree of fine-tuning, it is unclear how much such a move undercuts the need
for some anthropic explanation. Second,
it is unclear at what point we should continue searching for such an
explanation in terms of physical laws when no plausible candidates have been
forthcoming in the last twenty years.
Atheists like Stenger claim that we should continue searching until we
can be absolutely sure that no scientific explanation can be found. In section 2.5.2, where I consider the “God
of the Gaps” objection, I argue that such a requirement begs the question
against theism.
Finally,
one way of avoiding the fine-tuning of the cosmological constant is to claim
that one day the current framework of modern physics will be superseded in such
a way as to avoid the fine-tuning problem.
For example, one could claim that Einstein's theory of general
relativity will be superseded by a future theory that retains the verified
predictions of general relativity but does not predict that vacuum energy will
cause space to expand.
Or one
could claim that this prediction is an artifact of general relativity that is
not to be taken realistically, in analogy to how most physicists reject waves
that travel backward in time, even though such waves are one mathematically
legitimate solution to the equations of electromagnetism. Such moves, however,
will involve giving up inflationary cosmology or radically reformulating it
(since it depends on this prediction of general relativity), and they would
present difficulties for explaining the compelling evidence that the expansion
of the universe is accelerating. Further, such moves clearly will not work for
the fine-tuning of other constants, since many of them depend on facts so basic
that they certainly will not be superseded.
For example, the fine-tuning of the strength of gravity, as discussed in
section 2.3.2, only depends on the fact that bodies with masses typical of
planets and stars attract each other with a force approximately given by
Newton’s law, and that if
the gravitational pull of a planet is too large, most organisms would be
crushed. Thus, as a general strategy,
this way circumventing the fine-tuning of the cosmological constant is of
limited value.
Two other types
of fine-tuning should be mentioned. One is that of the initial conditions of
the universe, which refers to the fact that the initial distribution of
mass-energy – as measured by entropy – must fall within an exceedingly narrow
range for life to occur. Some aspects of
these initial conditions are expressed by various cosmic parameters, such as
the mass density of the early universe, the strength of the explosion of the
big bang, the strength of the density perturbations that led to star formation,
the ratio of radiation density to the density of normal matter, and the like.
Various arguments have been made that each of these must be fine-tuned for life
to occur. (For example, see Rees, 2000; Davies 2002, chapter 4). Instead of
focusing on these individual cases of fine-tuning, I shall focus on what is
arguably the most outstanding special initial condition of our universe: its low
entropy. According to Roger Penrose,
one of Britain’s
leading theoretical physicists, “In order to produce a universe resembling the
one in which we live, the Creator would have to aim for an absurdly tiny volume
of the phase space of possible universes” (Penrose, 1989, p. 343). How tiny is
this volume? According to Penrose, if we
let x =10123, the volume of phase space would be about 1/10x
of the entire volume (1989, p. 343).
This is vastly smaller than the ratio of the volume of a proton—which is
about 10-45 cubic meters – to the entire volume of the physical
universe, which is approximately 1084 cubic meters. Thus, this
precision is much, much greater than the precision that would be required to
hit an individual proton if the entire visible universe were a dart board! Others have calculated the volume to be zero
(Kiessling, 2001).
Now phase space
is the space that physicists use to measure the various possible configurations
of mass-energy of a system. For a system of particles in classical mechanics,
this phase space consists of a space whose coordinates are the positions and
momenta (i.e., mass times velocity) of the particles, or any other so-called
“conjugate” pair of position and momenta variables within the Hamiltonian
formulation of mechanics. Consistency
requires that any probability measure over this phase space remain invariant
regardless of which conjugate positions and momenta are chosen; further,
consistency requires that the measure of a volume V(t
0) of phase
space at time t
0 be the same as the measure that this volume evolves
into at time t, V(t), given that the laws of physics are time-reversal
invariant – that is, that they hold in the reverse time direction. One measure that meets this condition is the standard
“equiprobability measure” in which the regions of phase space are assigned a
probability corresponding to their volume given by their position and momenta
(or conjugate position and momenta) coordinates. Moreover, if an additional
assumption is made – that the system is ergodic – it is the only measure that
meets this condition.
This measure is called the
standard measure of statistical
mechanics, and forms the foundation for all the predictions of classical
statistical mechanics. A related probability measure – an equiprobability
distribution over the eigenstates of any quantum mechanical observable – forms
the basis of quantum statistical mechanics.
Statistical
mechanics could be thought of as the third main branch of physics, besides the
theory of relativity and quantum theory, and has been enormously
successful. Under the orthodox view
presented in physics texts and widely accepted among philosophers of physics,
it is claimed to explain the laws of thermodynamics, such as the second law,
which holds that the entropy of a system will increase (or remain the same)
with overwhelming probability.
Applying this
measure to the initial state of the universe, we could then say that under the
standard measure, the particular state is enormously improbable, a probability
equal to the minute portion of phase space it occupies. Indeed, in discussions of the matter, it is
typically assumed that this state is enormously improbable. The probability here is not the probability
of the particles’ (or fields’) being in the exact state that they are in; that
is always zero. Rather, it is the state required for having the enormously low
entropy required for the production of stars and ultimately life. An infinite number of microstates meet this condition,
but they all must be in that tiny region of phase space that Penrose mentions.
Finally, it is important to note that the standard measure of statistical
mechanics must imply a corresponding epistemic probability measure. The reason is that statistical mechanics is
supposed to tell us what to expect a system's behavior to be. For
instance, the calculation that an increase in entropy for a physical system in
the next five minutes is enormously improbable leads us to be almost certain
that it will not occur – that is, it generates a very low epistemic probability
for its occurrence. Thus, applying the standard measure to the initial
condition of our universe implies that it has an enormously low unconditional
epistemic probability of occurring.
Many points
could be disputed in the above argument and I cannot adequately enter into the
debate here. Rather, I shall just summarize three of the major ways to avoid
assigning an extremely low epistemic probability to the initial state of the
universe. First, as suggested by David Albert (2000, pp. 150-162), one could
attempt to ground the standard probability measure of statistical mechanics in
postulated indeterministic quantum processes that have just the right
probability distribution to yield this measure.
As Albert recognizes (2000, p. 160-161), such a procedure would still
require the postulation of an enormously special, low-entropy macroscopic state
at the beginning of the universe but would not require that one postulate a
probability measure over the states of its phase space. Second, one could
simply restrict all statements of probability in statistical mechanics to
statements of conditional probability, where the statement being conditioned on
is that that the universe started out in this special macrostate of exceedingly
low entropy. Then one could treat the
measure over phase space as applying only to those scattered points in phase
space consistent with this initial assumption.
Doing this would recover all the predictions of statistical mechanics,
though it might seem an arbitrary restriction imposed to avoid treating the
initial state as improbable. Third, one
could point out, as John Earman (2006) has, that no one has been able to
develop an even near-adequate measure for the degrees of freedom of the
gravitational field, which is thought to play an essential role in the low
entropy of the initial state of the universe.
In light of
these responses, how should we view the purported improbability of the initial
state? First, we can point out that the improbability assigned by the standard
measure is the same as the one that we should assign using the method outlined
in sections 3.3.2 -3.3.3, in which we argue that scientific confirmation
requires that we place an epistemic equiprobability measure over the natural
variables in a theory. In statistical mechanics these natural variables turn
out to be the position and momenta, or other conjugate variables, used to
construct phase space. Thus, it demonstrates a certain consistency in the
method we proposed for arriving at epistemic probabilities. Second, all these
responses admit that the initial state is in some sense enormously special in
some way, while denying the degree of “specialness” can be quantified or
explained. This leaves us with a strong
qualitative, though non-quantifiable, form of fine-tuning.
As mentioned when we discussed the
fine-tuning of the cosmological constant, in the last fifteen years Victor
Stenger has emerged as one of the leading critics of the evidence for
fine-tuning. In the next two subsections
we shall look at two of his objections.
One major way in which Stenger has attempted to cast skepticism on
fine-tuning arguments is by constructing a computer program that shows that
random selections of the constants of physics generally produce viable,
life-permitting stars. He calls his
computer program “Monkey God.” Based on
his program, Stenger concludes that
No
basis exists for assuming that a random universe would not have some kind of
life. Calculations of the properties of universes having different physical
constants than ours indicate that long-lived stars are not unusual, and thus
most universes should have time for complex systems of some type to evolve
(2000, p. ___ Reference).
where
α is the dimensionless electromagnetic interaction strength, αG is
the dimensionless gravitational binding energy, mp is the mass of
the proton, me is the mass of the electron, ħ is Plank’s constant
divided by 2π, and c is the speed of light.
Using
this equation and a program that randomly selects values for the relevant
parameters in the above equation, Stenger concludes that long-lived stars are
not unusual among these randomly selected universes and takes this to count as
evidence against claims of fine-tuning. The first criticism of his approach is
that he does not address the question of whether these universes would have
other life-inhibiting features relative to ours. For example, if one decreases
the strength of the strong nuclear force by more than 50% (while keeping the
electromagnetic force constant), carbon becomes unstable, and with a slightly
greater decrease, no atoms with atomic number greater than hydrogen can exist
(Barrow and Tipler, 1986, pp.
326‑7). This would make it
virtually impossible for complex life forms to evolve. That Stenger ignores these other
life-inhibiting features is clear from his equation for the lifetime of a star
(which is unaffected by changes in the strong nuclear force, since none of the
parameters he uses depends on this strength), and is also obvious from what he
says elsewhere regarding his “Monkey God” calculations:
I find that long-lived
stars, which could make life more likely, will occur over a wide range of these parameters (Stenger 1995, 2000). For example, if we
take the electron and proton masses to be equal to their values in our universe, an
electromagnetic force any stronger than its value in our universe will give a
stellar lifetime of more than 680 million years. The strength of the strong
interaction does not enter into this calculation (2004, pp. 179-180).
Obviously,
if we increased the electromagnetic force by very much while keeping the strong
interaction the same, the nuclei of atoms other than hydrogen would break apart
due to the increased electromagnetic repulsion of the protons in the
nuclei. In this case, there could be no
nuclear fusion in stars and hence no stars.
Second,
the equation he uses is based on a simple star model of stellar evolution. The equation does not take into account the
complexities of a stellar evolution, such as whether the energy transport from
the center of the star to the surface is by convection or radiative diffusion. More importantly, it assumes that the star is
made mostly of hydrogen, which would not be the case if the strong force were
increased beyond a small amount (See Collins, 2003, p. 192 and references
therein); further, it does not take into account the effects on star stability
of quantum degeneracy, which require much more sophisticated codes to take into
account. No simple equation could incorporate these sorts of complexities. As I have shown elsewhere (Collins, 2003, pp.
192-193), using a simple star model,
one can increase the strength of gravity a million or a billion fold, and still
obtain stable, long-lived stars with around the same surface temperature as our
sun. When one takes into account quantum
degeneracy effects, however, one can only increase the strength of gravity by
around a thousand-fold before significantly decreasing the life-time of stars
(Collins, 2003, pp. 193-194). Of course,
if one also changed one of the other constants, one could increase the strength
of gravity by more than 3000-fold and still obtain a stable, long-lived star,
since it would change when electron degeneracy kicks in. In sum, life-prohibiting effects related to
stellar life-times and stability only come to light when one begins to consider
the complexity of the physics involved in stellar evolution, something Stenger
has not done.
Another
common objection to the fine-tuning argument is that it is a variation of the
“God of the Gaps” argument, and so it should be rejected. Victor Stenger raises this objection with
regard to the fine-tuning of the
cosmological
constant. According to Stenger,
While quintessence may not turn out to
provide the correct explanation for the cosmological constant problem,
it demonstrates, if nothing else, that science is always hard at work trying to
solve its puzzles within a materialistic framework. The assertion that God can
be seen by virtue of his acts of cosmological fine-tuning, like intelligent
design and earlier versions of the argument from design, is nothing more than
another variation on the disreputable God-of-the gaps argument. These rely on
the faint hope that scientists will never be able to find a natural explanation
for one or more of the puzzles that currently have them scratching their heads
and therefore will have to insert God as the explanation. As long as science
can provide plausible scenarios for a fully material universe, even if those
scenarios cannot be currently tested they are sufficient to refute the God of
the gaps (2004, p. 182).
Elsewhere, Stenger claims that one
would be justified in invoking God only if “the phenomenon in question is not
only currently scientifically inexplicable but can be shown to forever defy
natural description” (2007, pp. 13-14). As he recognizes, this requirement of
proof is exceptionally strong. Although
he qualifies his assertion regarding God as a scientific hypothesis, the
question that arises is the level of proof that we need regarding the
non-existence of a plausible scientific explanation before we are justified in
invoking God as an explanation of the fine-tuning, regardless of whether it is
considered a scientific or a metaphysical explanation.
To
answer this latter question, we must consider the reasons for thinking that a
“God of the gaps” sort of explanation is in principle something to be
avoided. The reasons partly depend on
whether one is a theist or an atheist; and if one is a theist, it will depend
on how one understands the nature of divine action. Many theists will claim that ultimately we
should avoid a God of the gaps explanation because it is bad theology. According to these theists, God would be
greater if God created a material order that could function on its own without
God’s needing to intervene and fill various gaps. If these theists are correct,
then for theological reasons one should strenuously avoid appealing to divine
intervention in the natural order to explain phenomena that science has not yet
explained and instead trust that God has created a material world with its own
integrity. Such theological reasons, however, will not apply to the structure of
the cosmos itself – its basic laws, its
initial conditions, and the values of its constants –
since these do not require any intervention in the natural order. Other
theists, such as intelligent design theorists, will be even more lenient
concerning those cases in which it is appropriate to invoke God as an
explanation.
Of
course, atheists who are fully committed to a naturalistic account of the
cosmos will always claim that it is illegitimate to appeal to God, since God
does not exist. In order for the God of
the gaps objection to avoid begging the question against the theist, however,
it has to be framed in such a way as to carry force even on theistic
assumptions. Such an argument does carry
force, at least on the assumption of many theists, when God or some other
transcendent designer is invoked to explain, for instance, seemingly
irreducibly complex biological systems, since in such cases it implies that
nature lacks sufficient integrity to produce the systems on its own. Stenger
and others have not shown that it carries any non-question begging force for
the case of the structure of the universe as a whole.
One
might object to this response by claiming that the history of science provides
independent grounds for rejecting any appeal to God to fill in the apparent
gaps left by science. The failure of such appeals, however, can be explained as
well by the theist as the naturalist: e.g., many theists would claim that Newton's famous
invocation of God to keep the planetary orbits stable implies a less-than
satisfactory picture of a constantly intervening God. The key question is how
one inductively extrapolates from these historical incidences, and that all
depends on one's background assumptions –
i.e., whether one is an atheist or a theist, and what kind of theist one
is. In themselves, these incidences can
tell us nothing about whether we can be justified in appealing to God for
explaining the fine-tuning.
But
what about the scientific strictures of methodological naturalism? These would
be relevant only if the appeal to God were considered as a scientific explanation, something that I am not assuming. Rather, God should be considered a philosophical
or metaphysical explanation of LPU. So where does this leave us with regard to
the burden of proof? The advocate of the fine-tuning argument will only need to
argue that it is unlikely that all the cases can be given a natural explanation
that removes their epistemic improbability without transferring that
improbability up one level. And as
argued in sections 6.3.1 and 7.2, even
if the fine-tuning of the constants of physics can be explained in terms of
some set of deeper physical laws, as hypothesized by the so-called “theory of
everything” or by an inflationary multiverse, this would simply transfer the
improbability up one level to these deeper laws.
There are many other cases of fine-tuning
that I have not discussed, such as those extensively discussed by biochemist Michael Denton
(1988). These latter consist of various higher-level features of the natural
world, such as the many unique properties of carbon, oxygen, water, and the
electromagnetic spectrum, that appear optimally adjusted for the existence of
complex biochemical systems (1988, Chaps 3-6, pp. 19-140). Of course, these
higher-level features of the universe are ultimately grounded in the laws,
constants, and initial conditions of the universe. Nonetheless, they provide
additional evidence that the fundamental structure of the universe is
fine-tuned for life.
As
illustrated by the case of Victor Stenger discussed above (section 2.5), it
should be pointed out that some physicists and scientists have been skeptical
of some of the prominent cases of fine-tuning in the literature. As I have shown in detail elsewhere, in some
cases this skepticism is warranted, but in other cases the physical arguments
offered for fine-tuning are solid (See Collins, 2003). Nonetheless, even if there are no cases of
fine-tuning that are sufficiently established to be beyond doubt, the argument
would still have significant force. As philosopher John Leslie has pointed out,
“clues heaped upon clues can constitute weighty evidence despite doubts about
each element in the pile” (1988, p. 300). This is especially true given that
the clues in this case fall into a variety of distinct types – there are not only three distinct types of
fine-tuning, but there are many distinct cases under each type. The only plausible response that a skeptic
could give to the multitude of different cases of fine-tuning is to find one or
two overarching reasons that would undercut all the cases of fine-tuning in a
single stroke. Given the diversity of
the cases of fine-tuning, it is very unlikely that this will happen. In any case, in section 7.2, I will address
one such attempt, an attempt I call the “More Fundamental Law” objection,
according to which there might be some fundamental law (or principle) that entails
all the cases of fine-tuning.
According
to atheist Keith Parsons,
If
atheism is correct, if the universe and its laws are all that is or ever has
been, how can it be said that the universe, with all of its 'finely tuned'
features, is in any relevant sense probable or improbable? Ex Hypothesi there are no antecedent conditions that could
determine such a probability. Hence, if
the universe is the ultimate brute fact, it is neither likely nor unlikely,
probable nor improbable; it simply is.
Further, even if the universe were
somehow improbable, it is hard to see on the hypothesis of atheism how we could
ever know this. If we were in the
position to witness the birth of many worlds--some designed, some
undesigned--then we might be in a position to say of any particular world that
it had such-and-such a probability of existing undesigned. But we simply are not in such a position. We have absolutely no empirical basis for
assigning probabilities to ultimate facts (1990, p. 182).
Though commonly raised, Parson's objection
is deeply mistaken. It fails to
recognize a common, non-statistical kind of probability that some philosophers
have called
epistemic probability and
others have called
inductive probability
(e.g., Swinburne, 2001, p. 62).
As Ian Hacking notes in his excellent study
of the history of probability theory, the idea of probability was Janus-faced
from its emergence in seventeenth-century
Europe,
with one side being the notion of statistical probability and the other side
being the notion of epistemic probability:
On
the one side it [the conception of probability] is statistical, concerning
itself with stochastic laws or chance processes. On the other side it is epistemological,
dedicated to assessing reasonable degrees of belief in propositions quite
devoid of statistical background (Hacking, 1975, p. 12).
So, for instance, when people say that the
thesis of common ancestry is probably true given the fossil and genetic
evidence we currently have, they are clearly not talking about statistical
probability since this thesis is about a unique event in Earth’s history. The same holds for any claim about the
probable truth (or "empirical adequacy") of a scientific theory. In his treatise, A Treatise on Probability (1920), John Maynard Keynes further
developed this conception, and there have been several recent attempts to
provide a more precise account of this sort of probability (e.g., Swinburne,
2001, chapters 3 and 4; Plantinga, 1993, chapter 9).
In conjunction with the likelihood
principle, this sort of probability is extensively used in scientific
confirmation. Consider, for example, the
arguments typically offered in favor of the thesis of common ancestry, continental
drift theory, and the atomic hypothesis.
The thesis of common ancestry is commonly supported by claiming that a
variety of features of the world--such as the structure of the tree of
life--would not be improbable if this thesis is true, but would be very
improbable under other contending, non-evolutionary hypotheses, such as special
creation. Consider, for instance, the following quotation from evolutionary
biologist and geneticist Edward Dodson, in which he summarizes the case for
evolution, understood as the thesis of common ancestry:
All [pieces of
evidence] concur in suggesting
evolution with varying degrees of cogency, but most can be explained on other
bases, albeit with some damage to the law of parsimony. The strongest evidence
for evolution is the concurrence of so many independent
probabilities. That such different disciplines as biochemistry and
comparative anatomy, genetics and biogeography should all point toward the same
conclusion is very difficult to attribute to coincidence (1984, p. 68, italics
mine).
Similar
lines of reasoning are given for accepting continental drift theory. For
example, the similarity between the animal and plant life on Africa and South
America millions of years ago was considered to provide significant support for
continental drift theory. Why? Because
it was judged very unlikely that this similarity would exist if continental
drift theory were false, but not if it were true.
Finally,
consider the use of epistemic probability in the confirmation of atomic theory.
According to Wesley Salmon (1984, pp. 219-220), what finally convinced
virtually all physical scientists by 1912 of the atomic hypothesis was the
agreement of at least thirteen independent determinations of Avogadro’s number
based on the assumption that atomic theory was correct. For example, one method of determining
Avogadro’s number is through observations of Brownian motion, that is, the
random motion of very small particles suspended in a liquid, a motion that was
postulated to be caused by the unequal, random impact of the molecules in the
liquid. From this motion and the kinetic
theory of heat, one can calculate what the mass of each molecule must be in
order to account for the observed motion, and then using that value one can
obtain Avogadro’s number.
The
scientists reasoned that if atomic theory
were false, then such an agreement between thirteen different determinations of
Avogadro’s number would be exceedingly epistemically improbable – in
Salmon’s words, an “utterly astonishing coincidence” (1984, p.
220). Indeed, if scientists had not
judged the agreement to be exceedingly improbable if atomic theory were false,
it is difficult to see why they would take it to count as strong evidence in
its favor. On the other hand, the
scientists reasoned, if atomic theory were true, such an agreement would be
expected. Thus, by implicitly using the likelihood principle, they reasoned that
these independent determinations of Avogadro’s number strongly confirmed atomic
theory.
It
should be noted that one could not avoid this sort of reasoning simply by
rejecting scientific realism, since even though anti-realists reject the truth
or approximate truth of certain types of well-confirmed hypotheses, they still
accept them as being reliable bases for future explanations and predictions –
that is, in Bas van Fraassen's terminology (1980), they accept them as being
"empirically adequate."
Consequently, instead of interpreting the confirming evidence as evidence
for a hypothesis’ truth, they accept it as evidence for the hypothesis’
empirical adequacy. This means that
insofar as realists need to appeal to epistemic probabilities to support the
approximate truth of a theory, antirealists will need to appeal to those same
probabilities in support of a theory's empirical adequacy – e.g., antirealists
would need to claim that it is highly improbable for the determinations of
Avogadro's number to agree if atomic theory were not empirically adequate.
Since some of the probabilities in
the aforementioned examples involve singular, nonrepeatable states of affairs,
they are not based on statistical probabilities, nor arguably other non-epistemic
probabilities. This is especially evident for the probabilities involved in the
confirmation of atomic theory since some of them involve claims about
probabilities conditioned on the underlying structure and laws of the universe
being different – e.g. atoms not existing. Hence, they are not based on actual
physical propensities, relative frequencies, or theoretical models of the
universe’s operation. They therefore cannot be grounded in theoretical,
statistical, or physical probabilities. Similar things can be said about many
other related types of confirmation in science, such as the confirmation of
quantum electrodynamics (QED) by its extraordinarily precise prediction of the
gyromagnetic moment of the electron, which we shall discuss later in this
chapter. Such cases, I contend, establish the widespread use of purely
epistemic probabilities
in scientific confirmation that are neither
grounded in other types of probability nor in experience – e.g., the
probabilities invoked in the confirmation of atomic theory clearly are not
grounded in experience, since nothing like such an agreement had ever occurred
before. We shall return to this in Sections 3.3.2 and 3.3.3 when I discuss the
Principle of Indifference.
The probabilities
in the above examples do not seem to be statistical probabilities; nor can they
in any obvious way be justified by appealing to statistical probabilities. This is especially evident in the case for
the epistemic probability involved in the confirmation of atomic theory since
it involves claims about likelihoods if the underlying structure and laws of
the universe were different – e.g., if atoms did not exist. Hence, these claims cannot be grounded in
theoretical, statistical, or physical probabilities. Similar things can be said about many other
similar types of confirmation in science, such as the confirmation of quantum
electrodynamics by its extraordinarily precise prediction of the gyromagnetic
moment of the electron, which we shall discuss below. Such cases, I contend, establish the
widespread use of purely epistemic probabilities in scientific confirmation that
are neither grounded in statistical probabilities nor experience – e.g., the
probabilities invoked in atomic theory clearly are not grounded in experience,
since nothing like such an agreement had ever occurred before. We shall return
to this in sections 3.3.2 and 3.3.3 when I discuss the principle of
indifference.
Having established the need for epistemic
probability, we now turn to developing an account of it. Accounts of epistemic
probability range from the so-called subjective theory to the logical theory.
According to the subjective theory, epistemic probability amounts to nothing
more than our purely subjective degree of belief in a claim with the only
restriction on the rationality of our degrees of belief is that they obey the
probability calculus and conform to our own personal inductive standards. In contrast, according to the logical theory,
epistemic probability refers to some human-mind independent relation analogous
to that of logical entailment. Despite its popularity, I shall say nothing more
here about subjective theory, other than that it seems to lead to an extreme
form of epistemic relativism. The reason
is that it does not distinguish between rational and irrational inductive
criteria. Consequently, given the right inductive criteria almost any set of
beliefs can be made to cohere with the probability calculus – e.g., the belief
that the sun and stars revolve around the earth can be made to cohere with all
the current evidence we have to the contrary. (For a further critique, see Swinburne
(2001, p. 73f) and Plantinga (1993, p. 143f).)
On the other hand, at least two major problems
confront the purely logical theory of epistemic probability. First, it is doubtful that we need to
hypothesize a metaphysics of human-mind independent relations of logical
probability between propositions to ground the rationality OF all of our
statements involving epistemic probability. As Keynes pointed out (1921, pp. 4,
32), all we need is the existence of relations of rational support or expectation
that are independent of merely personal or cultural beliefs and standards.
Consequently, allowing for the relations of epistemic probability to be
dependent on the contingent construction of human cognitive faculties fits much
better with my overall approach of trying to stay as close as possible to the
principles of reasoning that are part of everyday and scientific practice. (See
section 1.1.)
Second, purely logical probability would
guide the expectations only of logically omniscient agents – that is, agents
that could see all logical relations between propositions, including the
relations of logical probability. Humans, however, are limited to a partial
grasp of such relations, which is reflected in the relevant usage of epistemic
probability in science. For example, as
Swinburne acknowledges, based on the current mathematical evidence, Goldbach’s
conjecture (that every even number greater than two is the sum of two prime
numbers) is probably true, but not certainly true. That is, the current evidence – such as that
Goldbach’s conjecture has been shown to be true for the first trillion numbers
and was claimed to be proven by some otherwise truthful mathematician –
supports this conjecture, but not enough to justify our being certain that it
is true. Since it is a mathematical
claim, however, Goldbach’s conjecture is either necessarily true, or it is
necessarily false, and thus its logical probability is either one or zero. The epistemic probability being invoked here,
therefore, is not purely logical probability, but something less than that.
Even if one does not agree that this sort of epistemic probability arises in
mathematics, nonetheless it is clear that when judging the evidential support
for a scientific theory, we are not aware of all the relevant logical relations
between the evidence and the theory. Keynes, who made the degree of
logical/epistemological probability of one proposition on another relative to
human powers, recognized this issue.
According to him,
If
we do not take this view of probability, if we do not limit it in this way and
make it, to this extent, relative to human powers, we are altogether adrift in
the unknown; for we cannot ever know what degree of probability would be
justified by the perception of logical relations which we are, and must always
be, incapable of comprehending (1921, p. 33).
Following Swinburne, one could still
attempt to take logical probability as the primary kind of epistemic (or what
he calls inductive) probability, and
then attempt to accommodate human limitations.
The problem with this approach is that in order to use logical
probability to make statements about the rational degree of credence one ought
to place in a theory, or the amount by which we should take a body of evidence
to increase our confidence in a theory, one would need some account of how to
translate degrees of logical probability to rational degrees of credence for
beings subject to our limitations.
Consequently, one would still need an account of another more
human-centered type of epistemic probability that is relative to human
cognitive powers to grasp these human perceptions of logical probability; in
itself, logical probability only stipulates what the rational degrees of belief
of a logically omniscient agent ought to be, not that of a mere human
being. As far as I know, Swinburne
does not provide any account that links the two together.
I call the conception of epistemic
probability that is grounded in our perceptions of logical relations between
propositions, episto-logical
probability. In contrast to the episto-logical account of epistemic
probability, Alvin Plantinga (1993, Chap. 9, pp. 159-175) has developed an
account in which the relations of probability are grounded in the contingent
construction of our cognitive faculties, which in many cases need not involve
perceptions of logical relations. In his
account, for instance, we think that the future will resemble the past since
those aspects of properly functioning human cognitive faculties that are aimed
at truth normally incline us to believe that the future will resemble the
past. Similarly, we accept simpler
theories over complex ones for the same reason. Because of their stress on the
contingent construction of our cognitive faculties, I call views like Plantinga’s,
noetic conceptions of epistemic
probability.
The account of epistemic probability that
I favor is one in which epistemic probabilities are grounded in some
combination of both the contingent construction of our cognitive faculties and
the perceived logical relations among propositions. For the purposes of this
essay, I will leave it as an open question which of these conceptions of
epistemic probability – the logical, the episto-logical, the noetic, or some
combination thereof – is ultimately correct. A word, however, needs to be said
about a problem with Plantinga’s account of epistemic probability that is
relevant for our purposes. Plantinga
defines the conditional epistemic probability of a proposition A on a
proposition B as follows:
Plantinga’s
Definition of Conditional Epistemic Probability: P(A|B) = iff
is the smallest interval which contains all the intervals which
represent the degree to which a rational human being S (for whom the conditions
necessary for warrant hold) could believe A if she believed B, had no undercutting defeater for A, had no
other source of warrant either for A or for -A, was aware that she believed B,
and considered the evidential bearing of B on A (1993, p. 169, italics
mine).
Plantinga's
account of conditional epistemic probability is a counterfactual account that
defines epistemic probability in terms of the degree of warrant a rational
human being would have in A if she believed B, and had no other sources of
warrant for A or -A. The italicized
portion, which we shall call Plantinga’s condition
of epistemic probability (or CEP for short), primarily does the job of
excluding contributions to our warrant which arise from our epistemic
circumstances and other information besides B that is part of our background
information k.
We cannot go into a detailed analysis of
this account of conditional epistemic probability here. However, we shall consider one major
objection that is relevant to the way in which we shall be using epistemic
probability. As Bas van Fraassen has
pointed out, Plantinga's account does not account for those cases in which B
could not be the sole source of warrant for A, an objection that Plantinga
attempts to address (1993, p. 168-169).
This problem arises in the case of the fine-tuning argument, since we
claim that the epistemic probability of LPU is very small under NSU. Our own existence in a body, however,
provides a source of warrant for the claim that we live in such a universe, and
it is a source that we cannot eliminate without severely altering our cognitive
faculties (or epistemic conditions) in a way that would undermine our
rationality.
More recently, Richard Otte has given new
teeth to the objection to Plantinga's account raised by van Fraassen. Among other examples, Otte asks us to
consider the following variation of one of Plantinga's examples:
P
(people are sometimes appeared to redly | I am appeared to redly)
According to Otte,
Intuitively this probability is 1; if I am appeared
to redly, it must be
the case that people are sometimes appeared to redly.
But Plantinga
claims that it is not possible for a rational
person’s sole source
of warrant for people are sometimes appeared to
redly to be I am
appeared to redly. Thus this probability is
undefined according to
CEP, even though it obviously has a value of 1. This
example shows
that CEP does not account for our intuitive notion of
conditional
epistemic probability (2006, p. 87).
Otte
locates the problem with Plantinga’s account in his use of counterfactuals, claiming
that spelling out conditional epistemic probability in terms of counterfactuals
is the wrong approach. Some sort of
counterfactual element, however, is essential to any account of conditional
epistemic probability if we are to connect degrees of conditional epistemic
probability with rational degrees of belief, which we need to do if judgments
of conditional probability are to serve as guides to life. This requirement, however, does not imply
that we must provide a purely counterfactual analysis of conditional epistemic
probability; all it demands is that counterfactuals will play some role in
connecting conditional epistemic probability with rational degrees of belief.
Although I cannot develop this idea in
detail here, I propose that conditional epistemic probability should be
conceived as a relation between propositions that is in part determined by the
contingent nature of our cognitive faculties. Through introspection, we have
partial access to this relation. We
typically determine the epistemic probability, P(A|B), of proposition A on
proposition B – that is, the degree of
rational inclination B should give us for A – by artificially creating in our
own minds Plantinga’s conditions for CEP – i.e., by “bracketing out” all other
sources of warrant for A or –A, and any undercutting defeaters for A. Thus, for
instance, suppose I see it raining outside but want to access the conditional
epistemic probability of “it will rain today” (proposition A) on proposition B,
where B is the conjunction of the claim that “www.weather.com has predicted a
25% chance of rain” and other background information, such as that
www.weather.com is reliable weather predictor. In assessing this conditional
probability, I block out all other sources of warrant for its raining today
(such as seeing dark clouds on the horizon) except for proposition B, and
arrive at the correct conditional probability, P(A|B) = 0.25. The fact that,
for the cases when CEP applies, I come to know these counterfactual degrees of
warrant by means of this "bracketing procedure" strongly suggests
that epistemic probability should not be identified with counterfactual degrees
of belief. Rather, is should be
considered a relation of support or warrant existing between propositions that
comes in degrees and which I can know by introspection via the above bracketing
procedure. This relation in turn gives
rise to the corresponding counterfactual degrees of warrant when CEP is
met.
The fact that conditional epistemic
probability should be considered such a relation existing between propositions
that we determine by the above "bracketing procedure" is supported by
other examples. Consider, for instance,
the conditional epistemic probability, P(A|B & k´), of the claim that
“human beings exist today” (claim A) based on the claim that the asteroid that
supposedly killed the dinosaurs missed planet earth (claim B) and certain
relevant scientific theories (k') regarding the conditions necessary for the
evolution of hominids. In that case, I
might judge it would be very unlikely that the dinosaurs would have become
extinct, and hence very unlikely that humans would exist: that is, I would
judge P(A|B & k´) << 1. The
procedure I would go through is that of bracketing out all other sources of
warrant for A except the relevant scientific theories, k', and the claim B, and
then access the degree to which all that information warranted or supported
A. For instance, I would bracket out all
those everyday pieces of information that imply the existence of human beings. Since CEP cannot be met in this case, the
existence of a conditional epistemic probability in this case shows that
identifying epistemic probability with counterfactual degrees of warrant (or
belief or credence) cannot be right.
Part of the purpose of this section is to
provide a theoretical underpinning for both the existence of conditional
epistemic probability and the fact that P(A|B & k´) exists for those cases
in which the proposition B & k´ cannot be the sole source of warrant for A.
Such an assumption is crucial to the likelihood (and probabilistic tension)
formulation of the fine-tuning argument, since LPU will be improbable only on
background information k´ in which the information that embodied, conscious
observers exist is subtracted out of our background information k. (See
sections 4.3 - 4.4). Since all rational people believe that they are embodied,
it is impossible for k´ & NSU to be the sole source of warrant for LPU.
Hence Plantinga’s CEP cannot be met for P(LPU|k´ & NSU). Despite these theoretical underpinnings, some
still might question whether there can exist relations of epistemic probability
in those cases in which the antecedent (B & k´) cannot be the sole source
of warrant for the consequent (A).
To further support the existence of
epistemic probabilities in these cases, consider the sorts of cases, such as
those mentioned above, in which scientific confirmation appears to depend on
claims that some state of affairs S – such as the agreement of the various
methods of determining Avogadro’s number – is expected under a certain
hypothesis h, but very epistemically improbable under the negation of that
hypothesis, ~h. Suppose we discovered
for one of these cases that S was also necessary for our own existence. It
seems clear that such a discovery would not itself undermine the confirmation
argument in favor of the approximate truth (or empirical adequacy) of the
theory. If it did, then we could
undermine the support based on the likelihood principle for many theories of
physics simply by discovering that the state of affairs S predicted by the
theory – e.g., the degree of bending of light around the sun predicted by
general relativity – was necessary for embodied conscious life. This seems clearly wrong. Thus, there must be
a probability for P(S|~h & k´) in these cases, where k´ is some
appropriately chosen background information that does not implicitly or
explicitly include the fact that humans exist. (If k' included that humans
exist, then P(S|~h & k') = 1, destroying any likelihood confirmation; See
sections 4.3 for more discussion on choosing k´ in cases like this.)
As a specific example, consider quantum
electrodynamics’ (QED) precise prediction of the deviation from 2 of the
gyromagnetic moment of the electron to nine significant digits, as discussed in
section 3.3.3. In terms of the
likelihood principle, the reason this prediction has been thought to
significantly confirm QED is that such a precise, correct prediction seems very
epistemically unlikely if QED is
not approximately true (or
at
least
empirically adequate), but it is epistemically likely if QED is
true.
Suppose
we discovered that this precise magnitude of deviation was necessary for the
evolution of life in our universe. It seems clear that this would not undermine
the confirmation that this precise prediction gives to QED.
Finally, since no rational person could
doubt LPU, it will often be useful to use the following conceptual or
imaginative device to intuitively grasp this relation of conditional epistemic probability
between LPU conditioned on NSU & k´ and T&k´.
The device is to imagine a unembodied
alien observer with cognitive faculties structurally similar to our own in the
relevant ways, and then ask the degree of credence that such a being would have
in LPU given that she/he believes in NSU & k´ or T & k´. This device of the unembodied alien observer
should remove any lingering doubts about the existence of a conditional
epistemic probability on background information k' that we could not have –
e.g., that does not implicitly or explicitly include the existence of embodied
conscious beings. Given that such an
alien is possible, it could have k' as its background information and thus
would not have the above problem of there existing an epistemic probability for
LPU on k'; hence, the existence of LPU could significantly confirm T over NSU
for that being. It seems clear that if
we met such a being and if we discovered that LPU confirmed T over NSU for that
being, then it should do so for us too.
I believe the various arguments I have
offered above establish both the crucial role of epistemic probabilities in
scientific confirmation and their existence between some propositions A and B
& k´ in those cases in which B & k´ could never be the sole source of
warrant (or justification) for A. Our
next question is how to determine P(A|B & k´).
Now that we know what we mean by
epistemic probability, it is time to consider how it is justified. In science, many times epistemic probability
is determined by an appeal to intuition, such as many of the epistemic
probabilities considered in the last section –
e.g., those arising in conjunction with the thesis of common ancestry,
continental drift theory, and atomic theory. These probabilities clearly were not
justified by an appeal to statistical improbability – e.g., we have no
statistics regarding the relative frequency of life on a planet having those
features cited in favor of evolution either under the evolutionary hypothesis
or under some non-evolutionary hypothesis.
Indeed, these judgments of epistemic probability were never rigorously
justified in any way. Rather, after (we
hope) doing their best job of looking at the evidence, scientists and laypersons
made judgments of what kind of world we should expect under each hypothesis,
and then they simply trusted these judgments.
This sort of trust in our judgments of epistemic probability is a
pervasive and indispensable feature of our intellectual life. It is these sorts
of intuitive judgments, I contend, that ultimately ground the claim that, given
the evidence for the first type of fine-tuning we discussed in section 2.2 –
that of the laws of nature -- it is very
epistemically unlikely that such a universe would exist under NSU & k'.
Of course,
the more widely shared these judgments are by those who are relevantly
informed, the more seriously we take them. In this regard, it should be noted
that the judgment that the existence of a fine-tuned universe is surprising
under naturalism is widely shared by intelligent, informed individuals, as some
of the scientists and philosophers cited above illustrate. Of course, the
skeptic might object that scientific theories are testable, whereas the
theistic explanation is not. But why
should testability matter with regard to the acceptability of our judgments of
epistemic probability? After all, testability is about being able to find
evidence for or against a theory in the future, not about the present
likelihood of the theory or the likelihood of some body of data’s being the
case if the theory is false or not empirically adequate. Thus, I contend, the merely intuitive
judgments of epistemic probability in the case of fine-tuning are on as solid
ground as many of those accepted in science that cannot be rigorously
justified. It is dishonest, therefore, to accept one sort of inference without
rigorous justification but reject the other merely because it purportedly lacks
such justification. At any rate, we
shall present such justification for judgments of epistemic probability in the
case of the fine-tuning of the constants of physics, regarding which I shall
argue that we can go beyond a mere appeal to intuition. Instead, we can provide
a solid, principled justification based on what I shall call the restricted
principle of indifference, which we shall discuss in the next two subsections.
According
to the restricted principle of indifference, when we have
no reason to prefer any one value of a variable p over another in some range R,
we should assign equal epistemic probabilities to equal ranges of p that are in
R, given that p constitutes a “natural variable.” A variable is
"natural" if it occurs within the simplest formulation of the relevant area of physics. When there is a range of viable natural
variables, then one can only legitimately speak of the range of possible
probabilities, with the range being determined by probabilities spanned by the
lower and upper bound of the probabilities determined by the various choices of
natural variables.
Since the constants of physics used in the fine-tuning
argument typically occur within the simplest formulation of the relevant
physics, the constants themselves are natural variables. Thus, the restricted principle of
indifference entails that we should assign epistemic probability in proportion
to the width of the range of the constant we are considering. We
shall use this fact in section 5.1 to derive the claim that P(Lpc|NSU & k')
<< 1, where Lpc is the claim that the value for some fine-tuned constant
C falls within the life-permitting range.
To see why
the restriction to a natural variable is needed, consider the case in which we
are told that a factory produces cubes between 0 and 10 meters in length, but
in which we are given no information about what lengths it produces. Using our principle above, we shall now
calculate the epistemic probability of the cube being between 9 and 10 meters
in length. Such a cube could be
characterized by either its length, L, or its volume V. If we characterize it by its length, then
since the range [9,10] is one tenth of the possible range of lengths of the
cube, the probability would be 1/10. If,
however, we characterize it by its volume, the ratio of the range of volumes
is: [1000 – 93]/1000 = [1000 – 729]/1000 = 0.271, which yields
almost three times the probability for the characterization using length. Thus,
the probability we obtain depends on what mathematically equivalent variable we
use to characterize the situation.
In the
case of the constants of physics, one can always find some mathematically
equivalent way of writing the laws of physics in which Wr/WR
is any arbitrarily selected value between zero and one. For example, one could
write Newton's
law of gravity as F = U100m1m2/r2,
where U is the corresponding gravitational constant such that U100 =
G. If the comparison range for the standard gravitational constant G were 0 to
10100G0, and the life-permitting range were 0 to 109
G0, that would translate to a comparison range for U of 0 to
10U0 and a life-permitting range of 0 to 1.2U0, since 10U0
= 10100G0 and 1.2U0
= 109G0. (Here G0 is the present value of G
and U0 would be the corresponding present value of U.) Thus, using G
as the gravitational constant, the ratio, Wr/WR, would be
109G0/10100G0 = 1/1091,
and using U as the “gravitational constant,” it would be 1.2U0/10U0,
or 0.12, a dramatic difference! Of
course, F = U100m1m2/r2 is
not nearly as simple as F = G m1m2/r2, and
thus the restricted principle of indifference would only apply when using G as
one's variable, not U.
Examples
such as that of the cube above have come to be known as the Bertrand Paradoxes
(e.g., see Weatherford, 1982, p. 56).
Historically, this has been thought of as the fatal blow to the general
applicability of the principle of indifference, except in those cases in which
a natural variable can be determined by, for instance, symmetry considerations
such as in statistical mechanics. In the
next section below, however, we shall see that for purposes of theory
confirmation, scientists often take those variables that occur in the simplest
formulation of a theory as the natural variables. Thus, when there is a
simplest formulation, or non-trivial class of such formulations, of the laws of
physics, the restricted principle of indifference circumvents the Bertrand
paradoxes.
Several
powerful general reasons can be offered in defense of the principle of
indifference if it is restricted in the ways explained above. First, it has an extraordinarily wide range
of applicability. As Roy Weatherford notes in his book, Philosophical Foundations of Probability Theory, "an
astonishing number of extremely complex problems in probability theory have
been solved, and usefully so, by calculations based entirely on the assumption
of equiprobable alternatives [that is, the principle of
indifference]"(1982, p. 35).
Second, in certain everyday cases the principle of indifference seems
the only justification we have for assigning probability. To illustrate, suppose that in the last ten
minutes a factory produced the first 20-sided die ever produced (which would be
a regular Icosahedron). Further suppose that every side of the
die is (macroscopically) perfectly symmetrical with every other side, except
for each side having different numbers printed on it. (The die we are imagining is like a fair
six-sided die except that it has twenty sides instead of six.) Now, we all immediately know that upon being
rolled the probability of the die coming up on any given side is one in
twenty. Yet, we do not know this
directly from experience with twenty-sided dice, since by hypothesis no one has
yet rolled such dice to determine the relative frequency with which they come
up on each side. Rather, it seems our
only justification for assigning this probability is the principle of
indifference: that is, given that every side of the die is macroscopically
symmetrical with every other side, we have no reason to believe that it will land
on one side versus any other. Accordingly, we assign all outcomes an equal
probability of one in twenty.
In
the next section, I shall first offer a powerful reason for epistemically
privileging those variables that occur in the simplest overall formulation of
the relevant domain of physics. I shall
then show how this reason offers a further, strong support for the restricted
principle of indifference based on scientific practice.
Typically in scientific practice, precise
and correct novel predictions are taken to significantly confirm a theory, with
the degree of confirmation increasing with the precision of the
prediction. We shall argue below,
however, that the notion of the "precision" of a prediction makes sense
only if one privileges certain variables – the ones that
I shall call the natural variables. These are the variables that occur in the
simplest overall expression of the laws of physics. Thus, epistemically
privileging the natural variables as required by the restricted principle of
indifference corresponds to the epistemic practice in certain areas of
scientific confirmation; if scientists did not privilege certain variables,
they could not claim that highly precise predictions confirm a theory significantly
more than imprecise predictions.
We begin our argument by considering only
cases in which the predictions of a theory are accurate to within experimental
error. In such cases, the known
predictive precision will be equal to the experimental
precision of the measured quantity. Our fundamental premise will then be
that everything else being equal, the confirmation that a prediction offers a
theory increases with the known precision
of a prediction.
The experimental precision of a
measurement of a quantity is dependent on the experimental error. In standard
scientific notation, the experimental value of a quantity is often expressed as
V ± e, where e indicates that one’s measuring apparatus cannot distinguish
between values that differ by more than e.
More precisely, to say that the experimentally determined value is V ± e
indicates that we have a certain set degree of confidence – usually chosen to be 95% – that the
actual value is within the interval [V + e, V -e]. So, for example, one might measure the
weight of a person as 145.3 lb ± 0.1: that is, the experiment gives us a 95%
confidence that the person’s weight is within the interval [145.4 lb, 145.2
lb].
In the weight measurement example above,
the measurement is said to be accurate to within four significant digits: e.g.,
one’s measuring apparatus cannot determine whether the person weighs 145.4 lb
or 145.2 lb, and thus only three digits (that is, 145) can be relied on to give
one the value of the weight. Because
sometimes zeroes can be “placeholder” digits that determine the order of
magnitude of a quantity, these digits are not considered significant. For
example, the zeroes in 0.000841 are placeholder digits. To eliminate counting placeholder digits as
significant, one can simply express the measured value in terms of scientific
notation, and then count the number of digits that are within the margin of
error. Thus, a measurement of 0.000841 ± 0.000002 meters for the length of a
piece of steel expressed in scientific notation becomes 8.41 ± 0.02 x 10-4
meters, which yields an accuracy of two significant digits. This measure of precision will not work for
those cases in which the measured value is zero, nor should it even be applied
to those cases in which the measured value is less than the error.
A more precise way of thinking about this kind
of precision is in terms of the ratio of the width, Wr, of the
confidence interval [V + e, V - e] to the value of V, with the restriction that
V > e. Under this notion of
precision, to say that the experimental value has a precision of δ means that
Abs[Wr/V] < δ, where Abs denotes the absolute value of the
quantity in brackets, and Wr denotes the width of the range [V + e, V - e] –
that is, 2e. There is a rough
correspondence between precision expressed in terms of this ratio and
significant digits: a precision of n significant digits roughly corresponds to
a ratio of one in 10n. Thus
the in our weight example, Wr = 2e = 0.2, and hence Wr/V
= 0.2/145 ~ 1/1000.
A
more careful analysis would reveal that scientists only consider significant
digit (SD) precision as a guide to what I call WR precision, which
is the ratio of the width, Wr, of the experimentally
determined/predicted range for a variable to what is estimated to be the width
of the expected range, WR, for the variable given the background
information. The actual value, V, is
then taken as a guide to the width of the theoretically possible range, and
hence Wr/WR ~ Abs[e/V], where ~ means approximately. We
shall return to this issue below when we discuss quantum electrodynamics, but
for the purposes of this paper, we are concerned only with showing that
determining the degree of precision of a prediction –
whether SD or WR precision –
depends on privileging the natural variable(s) as defined above.
Finally,
one might wonder why we cannot define precision simply as the amount that, with
a set degree of probability, the actual value could differ from the
experimental value. We could, but it
would be a useless notion when it came to the question of experimental
confirmation. For example, how could we compare the confirmatory value of a
predictive precision of one kilogram with that of one micron? Or, is it really plausible to say that, for
instance, a predictive precision of twenty significant digits of the mass of
the universe has less confirmatory significance than a prediction of one
significant digit of the mass of a hydrogen atom because the former is less
accurate in terms of number of kilograms by which the actual value could differ
from the predicted value?
We
shall now argue that if either the degree of SD precision or the degree of WR
precision is epistemically relevant, it follows that one must privilege
variables that are closely tied with the natural variables. We shall start by
showing that SD experimental precision depends on the variable one uses to
represent the quantity being measured; consequently, in order to speak of
precision in a non-relative sense, one must specify the variable one is using
to express the physical situation. To illustrate, consider the case of a cube
discussed in the last section. The
volume of a cube is equal to the third power of the length of its side: V = L3. Suppose we determine the length of the cube
is 10 microns, to within a precision of one micron. That is, Abs[e/V] <
1/10, or one part in 10. Roughly, this
means that the length of the cube could be anywhere from 9 to 11 microns. In terms of volume, however, the cube can
vary between 93 = 729 cubic microns and 113 = 1331 cubic
microns. This means that the
experimental precision is (1331-1000)/1000 ~ 1/3, or one part in three, if we
take volume as our variable.
Now
consider a theory that predicts that the length of the side of the above cube
is 10 microns. This is equivalent to the
theory predicting the volume of the cube to be 1000 microns. In this case, the predicted value agrees with
the experimental value to within experimental precision. If we ask what the known precision of the
prediction is, however, we do not get a definite answer. If we consider the theory as predicting the
length of the cube, we get one value for the known precision, whereas if we
consider the theory as predicting the volume, we get another value for the
precision. (Remember, since we are
assuming that the theory predicts the correct value to within experimental
error, the known predictive precision is equal to the experimental precision.)
The moral here is that the known precision of a prediction depends on the
mathematical variable – for example, L3
or L in the above example – under which one is
considering the prediction. Put differently, one can speak of precision of an experimentally correct prediction only
relative to the variable one uses to represent the predicted result. In analogy to Bertrand’s cube paradox for the
principle of indifference, in the case of the above cube it seems that we have
no a priori way of choosing between
expressing the precision in terms of volume or in terms of length, since both
seem equally natural. At best, all we
can say is that the predicted precision is somewhere between that determined by
using length to represent the experimental data and that determined by using
volume to represent the experimental data.
For
an illustration from actual physics, consider the case of quantum
electrodynamics' astoundingly accurate prediction of the correction of the
gyromagnetic ratio – called the g-factor – of the electron due to its self-interaction. QED predicted that, because of the
self-interaction of the electron, the g-factor (gyromagnetic moment) of the
electron differs from 2 by a small amount: g/2 = 1.001 159 652 38 ± 0.000 000
000 26. Very accurate experimental
measurements yielded: g/2 = 1.001 159 652 ± 0.000 000 000 20. The precision of
the above prediction of g/2 is one part in a billion.
Now
determining the experimental value for g/2 is equivalent to determining the
experimental value of some arbitrarily defined function U(g/2) of g/2, say
U(g/2) = (g/2)100. Moreover,
if QED predicted the value of g/2 to within experimental error, then it follows
that it also predicted the correct value of U to within experimental
error. The precision by which U is
known, however, is one in ten million instead of one in a billion, as in the
case of g/2. Thus, in analogy to the case of probability, even to speak of the
precision of QED’s prediction, we must already assume a certain natural
variable. It seems that the only
non-arbitrary choices are the natural variables defined above, which is what
scientists actually use.
From
examples like the one above, it is also clear that WR precision also
depends on the choice of the natural variable, as we explained for the case of
fine-tuning. So it seems that in order to speak of the predictive SD or WR
precision for those cases in which a theory predicts the correct experimental
value for some quantity, one must assume a natural variable for determining the
known predictive precision. One could,
of course, deny that there exists any non-relative predictive precision, and
instead claim that all we can say is that a prediction has a certain precision
relative to the variable we use to express the prediction. Such a claim, however, would amount to a
denial that highly accurate predictions, such as those of QED, have any special
epistemic merit over predictions of much less precision. This, however, is contrary to the practice of
most scientists. In the case of QED, for
instance, scientists did take the astounding, known precision of QED's
prediction of the g-factor of the electron, along with its astoundingly
accurate predictions of other quantities, such as the Lamb shift, as strong
evidence in favor of the theory.
Further, denying the special merit of very accurate predictions seems
highly implausible in and of itself.
Such a denial would amount to saying, for example, that the fact that a
theory correctly predicts a quantity to an SD precision of, say, twenty
significant digits does not in general count significantly more in favor of the
theory than if it had correctly predicted another quantity with a precision of
two significant digits. This seems
highly implausible.
Of
course, strictly speaking, to make these sorts of comparisons of relative
degrees of confirmation, one need not privilege one particular variable for
expressing the experimental result and calculating its precision, since one
need not be committed to a specific degree of precision. Nonetheless, one must put some significant
restrictions on the functions of a given variable on which one bases one's
calculation of precision, for otherwise one cannot make any significant
comparisons. For example, in some cases, there might be several different
equally simple ways of writing the laws of physics, giving rise to several
different candidates for natural variables.
In that case, one would simply say that the degree of precision fell
into a certain range covering the different choices of natural variables.
Finally,
consider a likelihood principle reconstruction of the confirmation that QED
received from its correct, precise prediction of the correction to the g-factor
of the electron. Let QED represent the
claim that QED is approximately true or at least empirically adequate; let ~QED
represent the negation of this claim; finally, let e represent the fact that
the correction to the g-factor of the electron falls within the experimentally
determined range. Now, P(e|QED & k') = 1, since QED entails that it will
fall into the experimentally determined range. (Since e was old evidence at the
time of QED's prediction, k' is our background minus this old evidence). The value of P(e|~QED & k') will depend
on the comparison range one chooses – that is,
the range of values for the correction to the g-factor given ~QED and k'. There is no precise way of determining this
range, but given that without any correction, the g-factor is 2, it is
reasonable to suppose that most physicists would have expected it to be no
larger than 2. Suppose that it were
reasonable to expect the correction to be no greater than ± 0.01, with no
preference for any value between 0 and ± 0.01.
This would yield a width, WR, for the comparison range of
0.02. If we let Wr be the
range of the experimentally determined value of correction, and we used the
restricted principle of indifference, we would arrive at P(e|~QED & k')
= Wr/WR ~10-7,
yielding a large likelihood confirmation of QED over ~QED.
The
crucial thing to note here is that any claim of support for QED over ~QED based
on the likelihood principle will involve the use of something similar to the
restricted principle of indifference, with the epistemically privileged natural
variables being those which occur in the simplest formulation of the area of
physics in question. The same can be said for the likelihood reconstruction of
other cases of confirmation based on precise predictions. Such likelihood
reconstructions, if plausible, strongly support the epistemic role of the
restricted version of the principle of indifference in scientific practice.
To complete
the philosophical groundwork for our argument, we shall need to provide some
way of determining k'. Determining k'
will automatically determine the “possible universes” to which we are comparing
the life-permitting ones – that is, what we
called the “comparison range.” We shall
focus on the constants of physics, but everything we say applies to the laws
and initial conditions of the universe with minor modifications. First,
however, we need to get clear on what it means to vary a constant of physics.
Intuitively there is a distinction between
laws and constants, and physicists usually suppose such a distinction. In
current physics, most laws can be thought of as mathematical descriptions of
the relations between certain physical quantities. Each of these descriptions
has a mathematical form, along with a set of numbers that are determined by
experiment. So, for example, Newton’s
law of gravity (F = Gm1m2/r2) has a
mathematical form, along with a number (G) determined by experiment. We can then think of a world in which the
relation of force to mass and distance has the same mathematical form (the form
of being proportional to the product of the masses divided by the distance
between them squared), but in which G is different. We could then say that such
worlds have the same law of gravity, but a different value for G. So when we
conceive of worlds in which a constant of physics is different but in which the
laws are the same, we are conceiving of worlds in which the mathematical form
of the laws remains the same, but in which the experimentally determined
numbers are different. It should be noted that the distinction between laws and
constants need not be a metaphysical distinction, but only a conceptual
distinction.
Now these constants of physics are
relative to our current physical models, since these constants only occur
within a model. Thus, any probabilities
we calculate will only be relative to a certain model. Ian Hacking (1987,
119-227) and Bas van Fraassen (1980, pp. 178-195), among others, have
emphasized this model-relativism with regard to the relative frequency
interpretation of probabilities. Under this interpretation, probabilities are
understood as the limit of the ratio of the favorable outcomes to the total
number of outcomes as the number of trials goes to infinity. Since for most, if
not all, cases these infinite long-run frequencies do not exist in the real
world, they ultimately must make reference to frequencies in idealized models,
as Van Fraassen worked out in detail (1980, pp. 190-193). Similarly, I shall assume, epistemic
probabilities exist only relative to our models of the world and our other
background information.
At least in the case of epistemic
probabilities, this should come as no surprise since it has to do with rational
degrees of belief, which, of course, are relative to human cognition. If one denies the model dependence of epistemic
probabilities, then it is hard to see how any statements of epistemic
probabilities will ever be justified.
One reason is that they are almost always grounded in conceptualizing
alternative possibilities under some measure, as illustrated in section 3.1 by
the sort of epistemic probabilities used to justify the thesis of common
ancestry, continental drift theory, or the atomic hypothesis. But such
conceptualizations typically involve reference to some model of how those
possibilities are spread out, no matter how vague. In fact, this was illustrated by use of
natural variables in science discussed in section 3.3.3.
The relevant models for the fine-tuning
hypothesis are just the models given to us by our best theories in physics,
just as if we calculated relative frequencies we should do so using the best
models that we had in the relevant domain. At present, the best model we have
is the Standard Model of particle physics. Sometimes, however, we can calculate
the life-permitting range only for a constant that is less than fundamental, either
because we do not have a fundamental theory or because of limitations on our
ability to calculate. In that case, the most sensible thing to do is to go with
the best model for which we can do calculations, as long as we consider only
variations in the constant that fall within the limits of applicability of the
model established by the deeper theory—e.g.,
we could sensibly consider the consequences of varying mass using the model of
Newton’s theory of gravity as long as the variation were within the range of
validity of Newtonian mechanics dictated by Einstein’s theory of general
relativity.
Because we are considering only one reference class of possible
law structures (that given by variations of the constants within our best
theories and/or the ones we can perform calculations for), it is unclear how
much weight to attach to the values of epistemic probabilities one obtains
using this reference class. Hence, one
cannot simply map the epistemic probabilities obtained in this way onto the
degrees of belief we should have at the end of the day. What we can do, however, is say that given
that we choose our reference class in the way suggested, and assuming our other
principles (such as the restricted principle of indifference in section 3.3.2),
we obtain a certain epistemic probability, or range of probabilities. Then, as a second order concern, we must
assess the confidence we have in the various components that went into the
calculation, such as the representative nature of the reference class. Given
that there is no completely objective procedure for addressing this secondary
concern, I suggest that the probability calculations should be thought of as
simply providing supporting confirmation, based on a plausible, non-arbitrary
procedure, of the common intuitive sense that given the fine-tuning evidence,
LPU is very epistemically improbable under NSU. This evidence will be
strengthened by the fact that there are many different fine-tuned constants of
physics, and many different kinds of fine-tuning, so that the fine-tuning
argument does not depend on one choice of a reference class. In light of this,
we must keep in mind that our goal is to provide some exact degree by which the
fine-tuning evidence supports theism over NSU.
Rather, it is to show that the intuitive sense that LPU supports theism
over NSU is not based on some mistake in thinking or perception, or on some
merely subjective interpretation of the data, but rather can be grounded in a
justified, non-arbitrary procedure.
In premises (1) and (2) of our main
argument, the probability of LPU is conditioned on background information k¢. As we mentioned in section 1.3, we cannot
simply take k¢
to be our entire background information k, since k includes the fact that we
exist and hence entails LPU. To determine what to include in k¢,
therefore, we must confront what is called the “problem of old evidence.” The
much-discussed problem is that if we include known evidence e in our background
information k, then even if an hypothesis h entails e, it cannot confirm h
under the likelihood principle, or any Bayesian or quasi-Bayesian methodology,
since P(e|k & h) = P(e|k & ~h).
But this seems incorrect: general relativity’s prediction of the correct
degree of the precession of the perihelion of Mercury (which was a major
anomaly under Newton’s
theory of gravity) has been taken to confirm general relativity even though it
was known for over fifty years prior to the development of general relativity
and thus entailed by k.
An attractive solution to this problem is
to subtract our knowledge of old evidence e from the background information k
and then relativize confirmation to this new body of information k¢ = k
- {e}. As Colin Howson explains, “when
you ask yourself how much support e gives [hypothesis] h, you are plausibly
asking how much knowledge of e would
increase the credibility of h,” but this is “the same thing as asking how much
e boosts h relative to what else we know” (1991, p. 548). This “what else” is
just our background knowledge k minus e. As appealing as this method seems, it
faces a major problem: there is no unambiguous way of subtracting e from k.
Consider the case of the fine-tuning of the strength of gravity. The fact, Lpg,
that the strength of gravity falls into the life-permitting range entails the
existence of stable, long-lived stars.
On the other hand, given our knowledge of the laws of physics, the
initial conditions of the universe, and the value of the other constants, the
existence of stable, long-lived stars entails Lpg. Thus, if we were to obtain k¢ by
subtracting Lpg from our total background information k without also
subtracting our knowledge of the existence of long-lived stable stars from k,
then P(Lpg|k¢)
= 1.
To solve such problems, Howson says that
we should regard k as “in effect, an independent axiomatization of background
information and k-{e} as the simple
set-theoretic subtraction of e from k” (1991, p. 549). That is, Howson proposes
that we axiomatize our background information k by a set of sentences {A} in such a way that e is logically independent of
the other sentences in {A}. Then k¢
would simply consist of the set of sentences {A}
-e. One serious problem with this method
is that there are different ways of axiomatizing our background information.
Thus, as Howson recognizes, the degree to which e confirms h becomes relative
to our axiomatization scheme (1991, p. 550).
Howson argues that in practice this is not as serious a problem as one
might expect, since in many cases our background information k is already
represented to us in a partially axiomatized way in which e is logically
isolated from other components of k. As
he notes, “the sorts of cases which are brought up in the literature tend to be
those in which the evidence, like the statements describing the magnitude of
the observed annual advance of Mercury’s perihelion, is a logically isolated
component of the background information.” (1991, p. 549). In such cases, when
we ask ourselves how much e boosts the credibility of h with respect to what
else we know, this “what else we know” is well-defined by how we represent our
background knowledge. Of course, in those cases in which there are alternative
ways of axiomatizing k that are consistent with the way our background
knowledge is represented to us, there will be corresponding ambiguities in the
degree to which e confirms h. I agree with Howson that this is not necessarily
a problem unless one thinks that the degree of confirmation e provides h must
be independent of the way we represent our background knowledge. Like Howson, I see no reason to make this
assumption: confirmation is an epistemic notion and thus is relative to our
epistemic situation, which will include the way we represent our background
information.
In the case of fine-tuning, our knowledge
of the universe is already presented to us in a partially axiomatized way. Assuming a deterministic universe, the laws
and constants of physics, along with the initial conditions of the universe,
supposedly determine everything else about the universe. Thus the set of
propositions expressing these laws, constants, and initial conditions
constitutes an axiomatization of our knowledge. Further, in scientific
contexts, this represents the
natural
axiomatization. Indeed, I would argue, the fact that this is the natural
axiomatization of our knowledge is part of our background knowledge, at least
for scientific realists who want scientific theories to “cut reality at its
seams.”
Furthermore, we have a particularly powerful
reason for adopting this axiomatization when considering a constant of physics.
The very meaning of a constant of physics is only defined in terms of a
particular framework of physics. Saying that the strong force constant has a
certain value, for instance, would be meaningless in Aristotelian physics.
Accordingly, the very idea of subtracting out the value of such a constant only
has meaning relative to our knowledge of the current set of laws and constants,
and hence this constitutes the appropriate axiomatization of our relevant
background information k with respect to which we should perform our
subtraction.
Using Howson’s method, therefore, we have
a straightforward way of determining k - {e}
for the case of the constants of physics: we let k be axiomatized by the set of
propositions expressing the initial conditions of the universe and the laws and
fundamental constants of physics within our currently most fundamental theory
which we can do calculations. Since the constants of physics can be
considered as given by a list of numbers in a table, we simply subtract the
proposition expressing the value of C from that table to obtain k¢. Thus, k¢ can be thought of as including the initial conditions of the universe,
the laws of physics, and the values of all the other constants except C.
It should be noted that although Howson’s
method was developed in the context of subjective Bayesian conception of
probability, his argument for this method does not depend on this
conception. All it depends on is the
claim that “when you ask yourself how much support e gives [hypothesis] h, you
are plausibly asking how much knowledge of e would increase the credibility of h,” and that this is “the same thing
as asking how much e boosts h relative to what else we know” (1991, p.
548). Anyone who subscribes to a
probabilistic confirmation account of evidence according to which e counts as
evidence for h if and only if knowledge of e increases our degree of confidence
in h should at least be sympathetic to the underlying premises of his
argument.
Finally, it is worth considering how the
old evidence problem plays out in the method of probabilistic tension. As mentioned above, the major problem with
Howson's method is that the background information k' depends on the
subtraction procedure one uses. If we
cast the fine-tuning argument in terms of probabilistic tension, as elaborated
in section 1.4, this problem can be avoided; we do not need to privilege any
particular subtraction procedure.
According to that method, both NSU and theism should be elaborated in
such a way that each of them entails LPU.
Thus, LPU does not directly confirm one of these hypotheses over the
other. Nonetheless, the fine-tuning
evidence creates severe probabilistic tension for one of the hypotheses but not
for the other. Thus, it gives us a
significant reason to prefer theism over NSU: if with respect to some domain,
one hypothesis h1 has much more probabilistic tension than another,
h2, then the probabilistic tension gives us strong reason to prefer
h1 over h2, everything else being equal.
To determine the
degree of probabilistic tension generated for NSU by the fine-tuning evidence,
we need to probe NSU for hidden probabilistic tension related to the fine-tuning evidence. Now, when considering only
a single constant C, the fine-tuning evidence only generates probabilistic
tension because of the data Lpc. To bring this probabilistic tension out, we
first write NSU&k as NSU&k'&Lpc, where k = Lpc &k', and k' = k-{Lpc}, where no
particular subtraction procedure is used.
To fully bring this probabilistic tension to light, therefore, one must
consider all k¢
such that k = k¢ & Lpc, and then take
the true probabilistic tension for NSU as given by the lower bound of P(Lpc|NSU
& k¢),
for all possible k¢,
and likewise for theism. Using the lower bound guarantees that the information
that a constant fell into the life-permitting range is not implicitly left in
the k' one uses to assess probabilistic tension, as we saw in our example above
for the fine-tuning of gravity where the existence of long lived, stable stars
was left in k¢.
This is a determinate procedure that does not depend on any choice of
subtraction procedure and demonstrates the power of the idea of probabilistic
tension. (As an alternative to Howson’s method, one might also use this
approach to determine k¢ for the likelihood principle method above, though we
will not pursue this further here.)
4.4. Determining k¢: The Epistemically Illuminated Region
Next, for any given fine-tuned constant C,
we must determine the comparison range of values for C. My proposal is that the
primary comparison range is the set of values for which we can make
determinations of whether the values are life-permitting or not. I will call
this range the “epistemically illuminated” (EI) range.
Thus,
given that the EI range is taken as our comparison range, we will say that a
constant C is fine-tuned if the width, W
r, of the range of
life-permitting values for the constant is very small compared to the width, W
R,
of the EI range.
To motivate the claim that the comparison
range, WR, should be taken as the EI range, we shall consider a more
mundane case of a very large dartboard with only some small, finite region
around the bull’s eye that is illuminated, with the bulk of the dartboard in
darkness. In this case, we know neither
how far the dartboard extends nor whether there are other bull’s eyes on it. If we saw a dart hit the bull’s eye in the
illuminated (IL) region, and the bull’s eye was very, very small compared to
the IL region, we would take that as evidence that the dart was aimed, even
though we cannot say anything about the density of bull’s eyes on other regions
of the board.
One way of providing a likelihood
reconstruction of the confirmation of the aiming hypothesis is to include the
fact that the dart fell into the IL region as part of the information being
conditioned on: that is, include it into the background information k¢. We could then use the likelihood principle to
argue as follows: given that we know that the dart has fallen into the IL
region, it is very unlikely for it to have hit the bull’s eye by chance but not
unlikely if it was aimed; hence, its falling in the bull’s eye confirms the
aiming hypothesis over the chance hypothesis.
Similarly, for the case of fine-tuning, we should include the fact that
the value of a constant is within the EI region as part of our background
information k¢.
Is including in k¢ the fact that C falls
into the EI range an adequate procedure?
The case of the dartboard, I believe, shows that it is not only a
natural procedure to adopt, but also arguably the only way of providing a
likelihood principle reconstruction of the inference in this sort of mundane
case. First, it is clearly the ratio of
the area taken up by the bull’s eye to the illuminated region around the bull’s
eye that leads us to conclude that it was aimed. Second, one must restrict the comparison range to
the illuminated range (that is, include IL in k') since one does not know how
many bull’s eyes are in the un-illuminated portion of the dartboard. Thus, if one expanded the comparison range
outside the illuminated range, one could make no estimate as to the ratio of
the area of the bull’s eye regions to the non-bull’s eye regions and thus could
not provide a likelihood reconstruction.
Yet it seems intuitively clear that the dart’s hitting the bull’s eye in
this case does confirm the aimed hypothesis over the chance hypothesis.
Another way of seeing why the comparison
range should be equal to the EI range is in terms of the rational degrees of
credence in Lpc of the fictional unembodied alien observer introduced at the
end of section 3.2. In accordance with the method of dealing with old evidence,
we imagine our alien observer holding background information k' in which the
knowledge of the value of C is subtracted out.
Then we imagine that our alien observer learns that C falls into the EI
range. Call this new information Q. Even
assuming that it makes sense to speak of C as possibly having any value between
minus infinity and infinity, the alien observer would not know whether the sum
of the widths of all the life-permitting regions outside of the EI region are
finite or infinite. Hence it would not know the value of P(Q|T & k'), since
to say anything about the chance of God's creating C in the EI region, it would
have to know if there are other life-permitting regions besides the ones in EI.
Hence P(Q|T & k')/P(Q|NSU & k') could be zero, greater than zero, or
simply indeterminate. This means that knowledge of Q neither confirms nor
disconfirms theism relative to NSU.
Suppose our alien observer learns the
additional information, Lpc, that C falls into the life-permitting region of
EI. Since our observer knows Q,
assessing whether this additional information confirms T with respect to NSU
will depend on the ratio P(Lpc|k' & Q & T)/P(Lpc|k' & Q & NSU). Now, since k' & Q & NSU entails that
C falls into the EI region, it would leave our alien observer indifferent as to
whether it falls into the life-permitting region. Assuming the validity of the
restricted principle of indifference (see section 3.3.2 above), P(Lpc|k' &
Q & NSU) = Wr/WR, where WR is equal to
width of the EI region. Thus, including
the information Q that C falls into the EI region in our background information
k' is equivalent to choosing our comparison range as the EI range.
At this point, one might question the
legitimacy of including Q in our background information k': that is, k' à
k' & Q. Besides appealing to
examples such as the above dartboard case, in general when comparing
hypotheses, we can place into the background information any evidence that we
have good reason to believe neither confirms nor disconfirms the hypothesis in
question. In some cases this is obvious:
for example, when assessing the ratio of the probabilities of the defendant's
fingerprints’ matching those on the gun under the guilt and innocence hypothesis,
respectively, the fact that Jupiter has over sixty moons would be irrelevant
information. Thus, jurors would be free to include it as part of their
background information.
Another way of thinking about this issue
is to note that k' determines the reference class of possible law structures to
be used for purposes of estimating the epistemic probability of Lpc under NSU:
the probability of Lpc given k' & NSU is the relative proportion of law
structures that are life-permitting in the class of all law structures that are
consistent with k' & NSU. (The measure over this reference class is then
given by the restricted principle of indifference.) Thinking in terms of reference classes, the
justification for restricting our reference class to the EI region is similar
to that used in science: when testing a hypothesis, we always restrict our
reference classes to those for which we can make the observations and
calculations of the frequencies or proportions of interest – what in statistics is called the sample
class. This is legitimate as long as we
have no reason to think that such a restriction produces a relevantly biased
reference class. Tests of the long-term efficacy of certain vitamins, for
instance, are often restricted to a reference class of randomly selected
doctors and nurses in certain participating hospitals, since these are the only
individuals that one can reliably trace for extended periods of time. The assumption of such tests is that we have
no reason to think that the doctors and nurses are relevantly different than
those who are neither doctors nor nurses and thus that the reference class is
not biased. As discussed in section
4.2, the justification for varying a constant instead of varying the
mathematical form of a law in the fine-tuning argument is that, in the reference
class of law structures picked out by varying a constant, we can make some
estimate of the proportion of life-permitting law structures. This is something we probably could not do if
our reference class involved variations of mathematical form. The same sort of
justification underlies restricting the class to the EI range.
It is also important to keep things in
perspective by noting that there are really two separate issues here. First is the issue of the existence of a
meaningful probability for P(Lpc|Q & k
¢ & NSU). That question
reduces to whether there is an epistemic probability measure over the EI
region; this will uncontroversially be the case if the EI region is finite and
the restricted principle of indifference is true and applies. The second question is whether Q & k
¢ is
the appropriate background information.
If one allowed for prior probabilities and the full use of Bayes’s
theorem, then any choice is appropriate as long as one also has meaningful
prior probabilities for P(NSU|Q&k
¢), P(T|Q&k
¢),
and P(Lpc|Q & k
¢ & T).
Since I have attempted to avoid the use of
prior probabilities, it became important to have some procedure of determining
the appropriate background information k
¢. So this issue arises
only for the likelihood version of the argument that avoids prior
probabilities. It does not arise for other versions, including the secondary
method of probabilistic tension since, as we saw above, that does not depend on
the particular choice of appropriate background information.
Including Q in k' provides a likelihood
principle reconstruction of John Leslie’s “fly on the wall” analogy, which he
offers in response to the claim that there could be other unknown values for
the constants of physics, or unknown laws, that allow for life:
If
a tiny group of flies is surrounded by a largish fly-free wall area then
whether a bullet hits a fly in the group will be very sensitive to the
direction in which the firer's rifle points, even if other very different areas
of the wall are thick with flies. So it
is sufficient to consider a local area of
possible universes, e.g., those produced by slight changes in gravity's
strength …. It certainly needn't be claimed that Life and Intelligence could
exist only if certain force
strengths, particle masses, etc. fell within certain narrow ranges … All that
need be claimed is that a lifeless universe would have resulted from fairly minor changes in the forces etc.
with which we are familiar. (1989, pp. 138-9).
Finally,
notice how our methodology deals with a common major misunderstanding of the
fine-tuning argument based on the constants of physics. On this misunderstanding, advocates of the
fine-tuning argument are accused of implicitly assuming the laws somehow existed
temporally or logically prior to the constants, and then afterwards the values
of the constants were determined. Then one imagines that if NSU is true, the
values occur by "chance" and hence it is very, very unlikely for them
to fall into the life-permitting range.
Thus, critics of the fine-tuning argument, such as Ian Hacking (1987,
pp. 129-130) and John Earman (2006), have claimed that it begs the question
since it already presupposes the existence of a creator. According to Earman, talk of the existence of
a fine-tuned universe’s being improbable “seems to presuppose a creation
account of actuality: in the beginning
there is an ensemble of physically possible universes – all satisfying the laws
of our universe but with different values of the constants – awaiting to be anointed [
sic] with the property of actuality by
the great Actualizer...”. (2006 ). It should be clear that the way in which I
spell out the argument makes no such metaphysical assumption. We simply consider the ratio of the epistemic
probability P(Lpc|T & k')/P(Lpc|NSU &k'), where Lpc denotes the claim
that a constant fell into the life-permitting range; this does not presuppose a
creation account of the laws any more than likelihood reconstructions of
scientific theories when old evidence e is involved, in which the same procedure
is involved.
In this section, we shall
consider how to estimate the EI region for the force strengths and some other
constants. In doing this, we first note
that, as argued in section 4.2, we must make our estimates of epistemic
probability relative to the best calculation-permitting models we have, as long
as those models are reasonable approximations of the best overall models we
currently have. Consider the case of the strong nuclear force. We know that this model has only limited
applicability since the strong nuclear force is ultimately the byproduct (or
residue) of the "color force" between the quarks of which neutrons
and protons are composed. Further, the
physical model, quantum chromodynamics, describing the color force, is thought
to have only limited range of applicability to relatively low energies. Thus,
the EI region will be finite, since we can only do calculations for those
values of the strong nuclear force or color force that result in the theory’s
staying within a relatively low energy regime.
This
limitation of energy regime does not apply just to the theory of strong
interactions, but to all of the fundamental quantum theories of nature. In the
past, we have found that physical theories are limited in their range of
applicability – --for example, Newtonian
mechanics was limited to medium size objects moving at slow speeds relative to
the speed of light. For fast-moving
objects, we require special relativity; for massive objects, general
relativity; for very small objects, quantum theory. When the Newtonian limits are violated, these
theories predict completely unexpected and seemingly bizarre effects, such as
time dilation in special relativity or tunneling in quantum mechanics.
There
are good reasons to believe that current physics is limited in its domain of
applicability. The most discussed of
these limits is energy scale. The
current orthodoxy in high-energy physics and cosmology is that our current
physics is either only a low-energy approximation to the true physics that
applies at all energies or only the low-energy end of a hierarchy of physics,
with each member of the hierarchy operating at its own range of energies.
The
energy at which any particular current theory can no longer to be considered
approximately accurate is called the
cutoff
energy, though (despite its name) we should typically expect a continuous
decrease in applicability, not simply a sudden change from applicability to
non-applicability. In contemporary terminology, our current physical theories
are to be considered
effective field
theories. The limitation of our
current physics directly affects thought experiments involving changing the
force strengths. Although in everyday
life we conceive of forces anthropomorphically as pushes or pulls, in current
physics forces are conceived of as interactions involving exchanges of quanta of
energy and momentum.
The strength of a particular force,
therefore, can be thought of as proportional to rate of exchange of
energy-momentum, expressed quantum mechanically in terms of probability
cross-sections. Drastically increasing
the force strengths, therefore, would drastically increase the energy-momentum
being exchanged in any given interaction.
Put another way, increasing the strength of a force will involve
increasing the energy at which the relevant physics takes place. So, for instance, if one were to increase the
strength of electromagnetism, the binding energy of electrons in the atom would
increase; similarly, an increase in the strength of the strong nuclear force
would correspond to an increase in the binding energy in the nucleus.
The
limits of the applicability our current physical theories to below a certain
energy scales, therefore, translates to a limit on our ability to determine the
effects of drastically increasing a value of a given force strength – for example, our physics does not tell us what
would happen if we increased the strong nuclear force by a factor of 10
1000. If we naively applied current physics to that
situation, we should conclude that no complex life would be possible because
atomic nuclei would be crushed. If a new physics applies, however, entirely new
and almost inconceivable effects could occur that make complex life possible,
much as quantum effects make the existence of stable atomic orbits possible
whereas such orbits were inconceivable under classical mechanics. Further, we
have no guarantee that the concept of a force strength itself remains
applicable from within the perspective of the new physics at such energy
scales, just as the concept of a particle’s having a definite position and
momentum, or being infinitely divisible, lost applicability in quantum
mechanics; or the notion of absolute time lost validity in special relativity;
or gravitational “force” (versus curvature of space‑time) in general
relativity.
Thus, by inductive reasoning from the past,
we should expect not only entirely unforeseen phenomena at energies far
exceeding the cutoff, but we even should expect the loss of the applicability
of many of our ordinary concepts, such as that of force strength.
The
so-called Plank scale is often assumed to be the cutoff for the applicability
of the strong, weak, and electromagnetic forces. This is the scale at which unknown quantum
gravity effects are suspected to take place thus invalidating certain
foundational assumptions on which current quantum field theories are based,
such a continuous space-time. (For example, see Sahni and Starobinsky, 1999, p. 44; Peacock, p.
275.) The Plank scale occurs at the
energy of 1019 GeV (billion electron volts), which is roughly 1021
higher than the binding energies of protons and neutrons in a nucleus. This
means that we could expect a new physics to begin to come into play if the
strength of the strong force were increased by more than a factor of ~1021.
Another commonly considered cutoff is the GUT (Grand Unified Theory) scale,
which occurs around 1015 GeV. (Peacock, 1999, pp. 249, 267.). The
GUT scale is the scale at which physicists expect the strong, weak, and
electromagnetic forces to be united.
From the perspective of GUT, these forces are seen as a result of
symmetry-breaking of the united force that is unbroken above 1015
GeV, where a new physics would then come into play. Effective field theory approaches to gravity
also involve general relativity’s being a low-energy approximation to the true
theory. One common proposed cutoff is
the Plank scale, though this is not the only one (see, for example, Burgess,
2004, p. 6).
Where
these cutoffs lie and what is the fundamental justification for them are
controversial issues. The point of the
above discussion is that the limits of our current theories are most likely
finite but very large, since we know that our physics does work for an
enormously wide range of energies. Accordingly, if the life-permitting range
for a constant is very small in comparison, then Wr/WR
<< 1, and then there will be fine-tuning.
Rigorously determining Wr/WR is beyond the scope
of this paper. Almost all other purportedly fine-tuned constants also involve
energy considerations: for example, because of Einstein's E = mc2,
the rest masses of the fundamental particles (which are fundamental constants)
are typically given in terms of their rest energies –
e.g., the mass of the proton is 938
MeV (million electron volts). Further, the cosmological constant is now thought
of as corresponding to the energy density of empty space. Thus, the considerations of energy cutoff
mentioned above will play a fundamental role in defining the EI region, and
hence WR, for many constants of physics.
Finally,
let us suppose that the comparison range is infinite, either because of some
new theory that applies at all energy scales or because the reasoning in the
last two subsections is incorrect.
Timothy McGrew, Lydia McGrew, and Eric Vestrup (2001) and independently,
Mark Colyvan, Jay Garfield, and Graham Priest (2005) have argued that if the
comparison range is infinite, no meaningful probability can be assigned to a
constant’s landing in the life-permitting region. (They also mistakenly assume
that the only non-arbitrary comparison range for the constants of nature
consists of all possible values (-∞ to ∞).)
These authors first assert that (i) the total probability of a
constant’s being somewhere in the infinite range of possible values has to be 1
(since it must have some value), and (ii) if we assume an equiprobability
distribution over the possible values – which
they claim is the only non-arbitrary choice –
the probability of its being in any finite region must be zero or
undefined. Finally, (iii) they consider
any arbitrary way of dividing up the entire range into a countably infinite set
of finite, non-overlapping regions, and assert that the total probability of
its being in the entire region must the sum of the probabilities of its being
in each member of the set. For example, the probability of its being in the
entire region is the sum of the probability of its landing between 0 and 1, of
its being between 1 and 2, of its being between 2 and 3, ad infinitum, plus the sum of the probability of its being between
0 and -1, between -1 and -2, ad infinitum. But since no matter how many times one adds
zero together, one gets zero, this sum turns out to be zero. Hence, if we assume that the probability is
zero, we get a contradiction since the probability of the constant having a
value somewhere in the region is 1.
Therefore, it must be undefined.
The
problem with this argument is the assumption that the total epistemic
probability is the sum of the individual probabilities of each finite disjoint
region. In cases where the number of
alternatives is finite, this is true: the sum of the probabilities of a die
landing on each of its sides is equal to the probability of the die landing on
some side. This is a fundamental principle of the probability calculus called finite additivity. When finite additivity
is extended to a countably infinite number of alternatives, it is called countable additivity, which is the
principle that McGrew and Vestrup implicitly invoke.
This latter principle, however, has been
very controversial for almost every type of probability, with many purported
counterexamples to it. Consider, for
example, the following situation. Suppose that what you firmly believe to be an
angel of "God" tells you that the universe is infinite in extent and
that there are a countably infinite number of other planets with civilizations
on each planet. Finally, the "angel" tells you that within a billion
miles of one and only one of those planets is a golden ball one mile in
diameter and that it has delivered the same identical message to one person on
each of those planets. Finally, you decide on the following arbitrary numbering
system to identify the planets: the planet that is closest to Earth you label
1, the planet that is next farther out you label 2, and so forth. Since within current big bang cosmology an
infinite universe would have no center, there is nothing special about Earth's
location that could figure into one's probability calculation. Accordingly, it
seems obvious that, given that you fully believe the angel, your confidence that
the golden ball is within a billion miles of earth should be zero, and zero for
every planet k. Yet this probability distribution violates countable
additivity. One cannot argue that the
scenario I proposed is in any way self-contradictory, unless one wants to argue
that an infinite universe is self-contradictory. This, however, ends up involving substantive
metaphysical claims and is arguably irrelevant since the issue is the degree to
which the propositions delivered by the angel justifies, or warrants, the
belief that the ball is not within a billion miles of our planet, not whether
these propositions ultimately could be true.
The McGrews (2005) have responded to these
sorts of arguments by claiming that when the only non-arbitrary distribution of
degrees of belief violates the axiom of countable additivity, the most rational
alternative is to remain agnostic. They
point out that one need not assign epistemic probabilities to all propositions.
I do not believe this is an adequate response, since I think in some cases it
would be irrational to remain agnostic in such circumstances. For example, it would be irrational for a
billionaire who received such a message to spend millions, or even hundreds, of
dollars in search of the golden planet, even if it were entirely rational for
him to believe what the angel told him; it would even be irrational for him to
hope to discover the planet. This is
radically different than cases where people are legitimately agnostic, such as
perhaps about the existence of extraterrestrials or the existence of God; it
seems rationally permitted at least to hope for and seek evidence for the
existence of extraterrestrials or God.
The implausibility of being agnostic in
the "golden planet case" is further brought out when one considers
that if the billionaire were told that the universe was finite with exactly 1010,000
planets with civilizations, clearly he should be near certain that the
golden planet is not near earth. But, clearly, if the billionaire is told that
there are even more planets –infinitely many – the billionaire should be at
least as confident that the planet is not near Earth; and certainly it should
not become more rational for him to search for it than in the 1010,000
planets case.
So the McGrews and others are wrong in
claiming that there would be no epistemic probability if the range is
infinite. However, they are correct in
claiming that this would turn the fine-tuning argument into what the McGrews
and Vestrup (2001) have called the course-tuning
argument (CTA). As they correctly
point out, if the comparison range is infinite, then no matter how large the
life-permitting range is, as long as it is finite the ratio Wr/WR
will be zero. This means that the narrowness of the range becomes irrelevant to
our assessment of degree of fine-tuning.
The McGrews and Vestrup, reiterating a point made by Paul Davies (1992,
pp. 204-205), claim that it is obvious that the CTA is not a good argument,
since the CTA would have the same force no matter how "un-fine-tuned"
a constant is, as long as the life-permitting range is finite. Thus, they argue, this would render the
appeal to physics, and the narrowness of the life-permitting range, completely
superfluous.
In response, an appeal to physics would
still be necessary: we still should have to have good physical reasons to think
the life-permitting range to be finite, which itself would involve having a
model that we had good reasons to believe was accurate for all values of the
parameter in question. This would
involve a substantial appeal to physics.
Of course, if it turned out that the comparison range were infinite, the
restrictiveness of the life-permitting range would no longer play a role, and
thus the popular presentation of the argument would have to be modified. Nonetheless, the formal presentation of the
argument, based on the claim that Wr/WR << 1 and
the restricted principle of indifference, would remain. As is, I suggest that
the reason we are impressed with the smallness is that we actually do have some
vague finite comparison range to which we are comparing the life-permitting
range, namely the EI range.
Finally, rejecting the CTA for the reasons
the McGrews and Vestrup give is counterintuitive. Assume that the fine-tuning
argument would have probative force if the comparison range were finite. Although they might not agree with this
assumption, making it will allow us to consider whether having an infinite
instead of finite comparison range is relevant to the cogency of the
fine-tuning argument. Now imagine
increasing the width of this comparison range while keeping it finite. Clearly, the more W
R increases,
the stronger the fine-tuning argument gets.
Indeed, if we accept the restricted principle of indifference (section
3.32), as W
R approaches infinity, P(Lpc|NSU & k') will converge
to zero, and thus P(Lpc|NSU &k') = 0 in the limit as W
R
approaches infinity. Accordingly, if we deny that CTA has probative force
because W
R is purportedly
infinite, we must draw the counterintuitive consequence that although the
fine-tuning argument gets stronger and stronger as W
R grows,
magically when W
R becomes actually infinite, the fine-tuning
argument loses all probative force.
The
justification of premise (1) will depend on which fine-tuned feature of the
universe is being considered. For the fine-tuning of the laws of nature,
premise (1) would be justified by an appeal to widely shared intuitions, as
explained in section 3.3.1. For the
fine-tuning of the initial conditions of the universe, we have two
choices. First, we could appeal to the
standard measure of statistical mechanics (as is typically done). Second, if we have qualms about the
applicability of the standard measure discussed in section 2.4, we could appeal
to the compelling reasons given in that section for thinking that the universe
started in an extraordinarily special state; hence, in some real sense it is
still epistemically enormously improbable, even if we cannot provide a rigorous
mathematical grounding for that probability.
Finally,
for the fine-tuning of the constants of physics, we shall appeal to the
restricted principle of indifference (section 3.3.2). This is the case we shall elaborate in
detail. We shall begin by justifying premise (1) for the case of individual
constants that are fine-tuned and then consider the case in which the constants
are combined. The argument has two
steps:
(i) Let C be a constant that is
fine-tuned, with C occurring in the simplest current formulation of the laws of
physics. Then, by the definition of
fine-tuning, Wr/WR << 1, where Wr is the
width of the life-permitting range of C, and WR is the width of the
comparison range.
(ii) Since NSU and k¢ give
us no reason to think that the constant will be in one part of the EI range
instead of any other of equal width, and k¢ contains the information
that it is somewhere in the EI range, it follows from the restricted principle
of indifference that P(Lpc|NSU & k¢) = Wr/WR,
which implies that P(Lpc|NSU & k¢) << 1.
Some
have faulted the fine-tuning arguments for only varying one constant at a time,
while keeping the values of the rest fixed. For example, Victor Stenger claims
that "One of the many major flaws with most studies of the anthropic
coincidences is that the investigators vary a single parameter while assuming
all the others remain fixed!" (2007, p. 148).
This
issue can be easily addressed for a case in which the life-permitting range of
one constant, C1, does not significantly depend on the value that
another constant, C2, takes within its comparison range, R2. In that case, the joint probability of both C1 and C2
falling into their life-permitting ranges is simply the product of the two
probabilities. To see why, note that by the method explicated in sections
4.3-4.4, the appropriate background information k'12 for relevant
conditional probability of Lpc1 on NSU is k'12= k - Lpc1
& Q1 - Lpc2
& Q2 = k'1 & k'2. Here, -Lpc1
and the -Lpc2 represent the subtraction of the information that C1
and C2 have life-permitting values, respectively; Q1 and
Q2 represent, respectively, the knowledge that they each fell into
their respective EI regions (which is added back in, as explained in section
4.4 above); and k'1 = k - Lpc1 & Q1 and k'2
= k - Lpc2 & Q2 represent the appropriate background
information for C1 and C2, respectively, when they are
considered separately.
By
the definition of conditional probability, P(Lpc
1 &Lpc
2|NSU
& k'
12) = P(Lpc
1|NSU
& k'
12 & Lpc
2) x P(Lpc
2|NSU & k'
12). Now, Q
2 & Lpc
2 =
Lpc
2, since the claim that C
2 fell into its (known)
life-permitting region entails that it fell into its EI region: that is, Lpc
2
à
Q
2. Hence, k'
12 & Lpc
2 = k - Lpc
1
& Q
1 - Lpc
2 & Q
2 & Lpc
2
= k - Lpc
1 & Q
1 - Lpc
2 & (Q
2
& Lpc
2) = k - Lpc
1 & Q
1 - Lpc
2
& Lpc
2 = k - Lpc
1 & Q
1 = k'
1.
It follows, therefore, that P(Lpc
1|NSU & k'
12 &
Lpc
2) = P(Lpc
1|NSU & k'
1), which was
merely the probability we calculated for Lpc
1 on the background
information in which we held all the other constants fixed. So, our next
question is, what is the value of P(Lpc
2|NSU & k'
12)? Now, k'
12 includes the values of
all the other constants besides C
1 and C
2. For C
1
and C
2 it only includes the information that they are in their
respective EI regions. Thus, if the width, W
r2, of the
life-permitting range of C
2 is not significantly dependent on the
value of C
1 in C
1's EI region, then by the restricted
principle of indifference, P(Lpc
2|NSU & k'
12) ~ W
r2/W
R2
= P(Lpc
2|NSU & k'
2 ), where W
r2 is
the width of EI region for C
2 when all other constants are held
fixed.
This
means that P(Lpc
1 &Lpc
2|NSU & k'
12) ~
P(Lpc
1|NSU & k'
1) x
P(Lpc
2|NSU & k'
2).
Thus,
we can treat the two probabilities as effectively independent.
When
will two constants be independent in this way? Those will be cases in which the
factors responsible for C1’s being life-permitting are effectively
independent of the factors responsible for C2’s being
life-permitting. For example, consider
the case of the fine-tuning of the cosmological constant (C1) and
the fine-tuning of the strength of gravity (C2) relative to the
strength of materials – that is, the first case of the fine-tuning of gravity
discussed in section 2.3.2. The
life-permitting range of gravity as it relates the strength of materials does
not depend on the value of the cosmological constant, and hence P(Lpc2|k'12
& NSU) = P(Lpc2|k'2 & NSU). This means that the joint probability of both
gravity and the cosmological constant’s falling into their life-permitting
ranges is the product of these two probabilities: Wr/WR
for gravity times Wr/WR for the cosmological
constant. This same analysis will hold
for any series of cases of fine-tuning in which the considerations for the
life-permitting range are independent of the value of the constant in its EI
range: e.g., the fine-tuning of the
strong nuclear force needed for stable nuclei and the above example of the
fine-tuning of gravity.
In order to justify premise (2), we shall
need to argue that God has some reason to bring about a life-permitting
universe.
For definiteness, we
shall first consider the case of the fine-tuning of the constants under the
assumption that theism is true and that there is only one universe. That is, we
shall attempt to justify the claim that for any constant C that is fine-tuned,
~P(Lpc|TSU & k
¢)
<< 1, where TSU is the theistic single universe hypothesis and k' is the
background information defined in sections 4.3 - 4.4. It should then be clear how this case
generalizes to cases in which the constants are combined, and for the two other
types of fine-tuning discussed in section 2. Finally, we shall indicate how
this argument generalizes for a theistic multiverse hypothesis.
To determine P(Lpc|TSU & k¢),
let us invoke our imaginative device (section 3.2) of a unembodied, alien
observer with cognitive faculties relevantly similar to our own and who
believes TSU and k¢. This observer would designate our universe as
“the universe that is actual” – which we shall abbreviate as U – and would know
that U has the laws that our universe has and the values of all the other
constants, except it would know that constant C only had a value in the EI
region. Now if this unembodied being
could perceive no reason for God to create the universe with C in the
life-permitting region instead of any other region, then P(Lpc|TSU & k¢) = Wr/WR
<< 1. So the claim that ~P(Lpc|TSU & k’) << 1 hinges on this
unembodied being's (and hence our) perceiving some reason why God would create
a life-permitting universe over other possibilities.
As Richard Swinburne has argued (2004, pp. pp. 99-106), since God is
perfectly good, omniscient, omnipotent, and perfectly free, the only motivation
God has for bringing about one state of affairs instead of another is its
relative (probable) contribution to the overall moral and aesthetic value of
reality.
Simple forms of life, such as bacteria, do
not seem in and of themselves to contribute to the overall moral value of
reality, though it is possible that they might contribute to its overall
aesthetic value. On the other hand, embodied moral agents seem to allow for the
realization of unique types of value. Hence it is this form of life that is
most relevant for arguing that ~ P(Lpc|k' & T) << 1, and thus the
most relevant for the fine-tuning argument.
Now let EMA represent the claim that the
universe contains embodied moral agents, and let Wh represent whatever else God
must do over and above creating the universe with the right laws, constants,
and initial conditions to ensure that it contains such agents, such as God’s
intervening in the unfolding of the universe.
Now P(EMA|TSU & k¢) = P(Lpc & Wh|TSU & k¢) = P(Wh|Lpc & k¢
& TSU) x P(Lpc|TSU & k¢), given that
these probabilities have well-defined values or ranges of value. Since P(Wh|Lpc & k¢
& TSU) ≤ 1, it follows that P(Lpc|TSU & k¢) > P(EMA|TSU & k¢),
once again assuming that these probabilities have well-defined values or ranges
of value. Thus, if we can establish that
~P(EMA|TSU & k¢)
<< 1, we shall have established that ~P(Lpc|TSU & k¢)
<< 1 (which will automatically be true if the probabilities are not
well-defined). In order for ~P(EMA|TSU
& k¢)
<< 1, it must be plausible to
suppose that on balance, God has more reason to make U in such a way that EMA
is true than to make it in such a way that EMA is false. We must be very careful about what is
required here. Since we are dealing with
epistemic probabilities, which are relative to human cognitive faculties and
limitations, to establish that ~P(EMA|TSU & k¢) << 1 does not
require that we show that God actually has more reason, only that it is
plausible to suppose that God does.
This will require first that we perceive,
however dimly, that it is plausible to think that the existence of embodied
creatures like us – that is, finite, vulnerable, embodied moral agents –has a
(probable) overall positive value, thus giving God a reason to create a world
in which such beings could come about.
One cannot merely argue for the value of personal agents in
general. The reason is that God's
fine-tuning universe U to make EMA true will result in various forms of moral
and natural evil, unless God constantly intervenes to prevent it, which clearly
does not happen in our world.
Thus, in order for God to have a reason to adjust C so that U contains our type
of embodied moral agents, there must be certain compensatory goods that could
not be realized, or at least optimally realized, without our type of
embodiment. This brings us directly to the problem of evil.
If we have an adequate theodicy, then we could
plausibly argue that our unembodied alien observer would have positive grounds
for thinking that God had more reason to create the universe so that EMA is
true, since it would have good reason to think that the existence of such
beings would add to the overall value of reality. In that case, we could argue that P(Lpc|TSU
& k') > 0.5.
On the
other hand, if we have no adequate theodicy, but only a good defense – that is,
a good argument showing that we lack sufficient reasons to think that a world
such as ours would result in more evil than good – then our unembodied being
would both lack sufficient reason to expect that God would make U so that EMA
would be true and lack sufficient reason to expect God to create U so that EMA
would be false. Hence, there would be no conditional epistemic probability of
EMA on TSU &k' and therefore no conditional epistemic probability for
P(Lpc|TSU & k'). It would still
follow, however, that Lpc is not epistemically improbable under theism: that
is, ~P(LPU|T &k') << 1. This
would still mean that NSU suffers from a severe probabilistic tension relative
to the fine-tuning evidence for the constants of physics from which TSU does
not suffer. Hence the fine-tuning evidence would still give us good reason to
believe in single-universe theism over NSU.
Thus, unless the atheist can show that it
is highly improbable that God would create a world which contained as much evil
as ours, it will still be the case that, given the evidence of the fine-tuning
of the constants, the
conjunction of
the existence of evil and a life-permitting universe strongly confirms theism.
This means that when the strongest evidence that atheists typically offer for
their position (
i.e., the existence
of evil) is combined with the evidence of the fine-tuning of the constants,
single-universe theism is still strongly confirmed over NSU. That is, if we let Ev denote the existence of
the kinds and degrees of evil we find in the world, then Lpc & Ev together
give us good reason to believe in TSU over NSU.
What
about the case of the theistic multiverse hypothesis (TMU) -- that is, the
hypothesis that God exists and created many universes. In that case, there are
two possibilities for the evidence we might claim is relevant. One possibility is the evidence, Lpc*, where
Lpc* = "the value of the constant C of this
universe falls into the life-permitting range," where "this
universe" refers to our universe by some means other than "the one
and only actual universe": e.g., by means of some sort of indexical, such
as "the universe that contains this
electron," where the unembodied being has some way of referring to "this electron" other
than by definite description that uses only purely qualitative properties. Now, some might worry here that given the
existence of multiple universes, God would have no reason to make this universe
life-permitting, and thus that P(Lpc*|TMU & k') << 1. For example, Roger White claims that,
"It is only the assumption that there are no other options that we should
expect the designer to fine-tune this
universe for life." (2000, p. 243).
I disagree. Given that the
existence of our type of embodied moral agents is a (probable) overall good, it
would contribute to the overall value of reality even if there were such beings
in other universes. Thus, God would still have a reason for fine-tuning this
universe, and hence ~P(Lpc|TMU & k') << 1.
Even
if White is correct, however, our unembodied alien would still have the same
reason as offered above for thinking that God would create some life-permitting universe. Thus, ~P(LPU*|TMU & k') <<
1, where LPU* is the claim that "some life-permitting universe
exists." Nonetheless, since for
every constant C, NSU & k' & LPU* entails Lpc & NSU & k',
P(LPU*|NSU & k') = P(Lpc|NSU & k') << 1. Thus, by the restricted version of the
likelihood principle, LPU* confirms TMU over NSU. If White is right, therefore, the relevant
confirmatory evidence for TMU versus NSU would become "some
life-permitting universe exists" instead of "this universe has
life-permitting values for its constants."
The
multiverse hypothesis is the hypothesis that there exist many regions of
space-time – that is, “universes” – with different initial conditions,
constants of physics, and even laws of nature. It is commonly considered the
major alternative to the competing hypotheses of divine creation of the
universe and NSU. Just as in a lottery in which all the tickets are sold, one
is bound to be the winning number, so given a varied enough set of universes
with regard to some life-permitting feature F, it is no longer surprising that
there exists a universe somewhere that has F. Multiverse hypotheses differ both
in the features that vary from universe to universe – e.g., the initial conditions, the constants of physics, etc. – and what physical process, if
any, produced them.
The multiverse objection can be interpreted
as either claiming that the multiverse provides an alternative explanation of
the fine-tuning of the cosmos, or that it simply eliminates the epistemic
improbability of the fine-tuning. We shall focus primarily on the latter
objection, since such an objection would undermine any argument based on the
likelihood principle that the fine-tuning provides evidence for theism over a
naturalistic version of the multiverse hypothesis. Put precisely, this version of the multiverse
objection is that ~P(LPU|NMU & k¢) << 1, where k¢ is some
appropriately chosen background information and NMU is the relevant
naturalistic multiverse hypothesis. Thus, it is claimed, LPU does not provide
evidence via the likelihood principle
for theism over an appropriately chosen multiverse hypothesis.
To address this objection, we
first need to get clear on exactly how multiverse hypotheses are supposed to
explain, or take away the seeming improbability of, the fine-tuning. To begin, we need to distinguish between
three facts with regard to the fine-tuning that are candidates for explanation:
(1) what I call the observer-relative
life-permitting (LP) fact that we, or I, observe a life-permitting universe
instead of a non-life-permitting universe; (2) what I call the indexical LP fact that this universe is life-permitting – or has some life-permitting feature F, where
"this" is an indexical that picks out the universe we inhabit; and
(3) what I call the existential LP
fact that a life-permitting universe exists. The so-called weak anthropic
principle, which states that the universe we inhabit must have a
life-permitting structure, appears to be enough to make the observer-relative
LP fact unsurprising. With regard to the
indexical LP fact, some philosophers claim that we cannot make a purely
indexical reference to our universe
but can only refer to our universe via
an implicit description. Thus, for
instance, one could claim that "this universe" is reducible to "the universe we inhabit," where
the "we" is in turn reducible to some other description such as
"conscious observers with characteristics X," where X refers to some
set of purely qualitative properties. If
this analysis is correct, then the claim that "this universe is
life-permitting" would be a tautology, and hence have an epistemic
probability of one. Even if one
rejected this analysis, one could still claim that the life-permitting
character of our universe is a defining, or at least an essential, feature of
it, so the indexical LP fact is a necessary truth and thus not surprising.
Consequently, it is questionable whether this indexical fact is in any way improbable.
In any case, it is clear that the multiverse hypothesis does not itself explain
or render probable this indexical LP, since whether or not other universes
exist is irrelevant to the features our
universe might have.
So the only place where the multiverse
hypothesis could help in explaining the fine-tuning or undercutting its
improbability is by explaining or undercutting the apparent improbability of
the very existence of a life-permitting universe – that is, the existential LP fact expressed
by (3). A hypothesis postulating a sufficiently varied multiverse will entail
that a life-permitting universe exists; hence, purportedly it will not only
explain why some such universe exists but undercut any claim that the existence
of such a universe is improbable. It
is here, and only here, that the multiverse could do any work in undercutting
the fine-tuning argument for theism. The
so-called observer-selection effect, often considered an essential part of the
multiverse explanation, does not itself contribute at all; this effect only
explains the observer-relative LP fact given by (1) and is already taken into
account by the weak anthropic principle.
Now it is important to
distinguish between two categories of multiverse hypotheses: the unrestricted
version (which I shall label UMU) and various types of restricted
versions. The unrestricted version is
the hypothesis that all possible worlds exist, a version most famously
advocated by philosopher David Lewis as an account of modal claims. According
to Lewis, every possible world actually exists (as a region of
space-time) parallel to our own. Thus, for instance, there exists a reality
parallel to our own in which objects can travel faster than the speed of
light. Dream up a possible scenario, and
it exists in some parallel reality, according to Lewis. These worlds, however, are completely
isolated from ours, and there are no spatio-temporal or causal relations
between the worlds – e.g., things in
one world do not happen before, at the same time, or after things in our world.
Further, they do not overlap in any way, except for the possibility of sharing
immanent universals. (1986, p. 2).
Lewis
advocates his hypothesis as an account of modal statements – that is,
statements that make claims about possibility and impossibility: e.g., "it is possible that Al Gore
won the U.S.
presidential election in 2004," and "it is impossible for an object
to be a perfect cube and a perfect sphere at the same time." Thus Lewis
calls his view modal realism, with the term “realism” indicating that every
possible world exists in as real a way as our own. This term, however, is a misnomer since it implies that other accounts
of modal claims are anti-realist, which they are not. The other major advocate of a similar view is
MIT astrophysicist Max Tegmark (1998, 2003).
According to Tegmark, “everything that exists mathematically exists
physically” (1998, p. 1), by which he means that every self-consistent
mathematical structure is in one-to-one correspondence with some physical
reality (1998, pp. 1-3). Unlike Lewis,
Tegmark’s primary argument for his view is to explain LPU. Further, it is unclear whether Tegmark is
claiming that every possible universe exists, or only that every possible
universe that can be described purely mathematically; in the latter case it
would not be a completely unrestricted multiverse hypothesis.
In contrast to Lewis’s and
perhaps Tegmark’s hypothesis, restricted multiverse hypotheses postulate some
restriction on the possible universes (or worlds) that actually exist. The most
widely discussed versions are those that claim that a multitude of varied
universes are generated by some physical process (what I will call a
“multiverse generator”). We shall
discuss these in section 6.3. The
important point here is that such a restriction will run the danger of
re-instantiating the problem of fine-tuning at the level of the restrictions
placed on the set of existing universes.
In section 6.3 I shall argue in detail that this is what happens in the
case of the most widely discussed multiverse-generator hypothesis, the
inflationary-superstring hypothesis.
Unlike the restricted versions
of the multiverse hypothesis, the unrestricted version does not run any danger
of re-instantiating the problem of fine-tuning.
As I shall argue in the next subsection, however, it faces the following
devastating dilemma as an alternative to a theistic explanation of the
fine-tuning:
it either undercuts almost all scientific reasoning and
ordinary claims of improbability, or it completely fails to undercut the
fine-tuning argument for theism.
To
begin our argument, consider a particular event for which we would normally
demand an explanation, say, that of Jane’s rolling a six-sided die 100 times in
a row and its coming up on six each time.
Call the type of sequence “coming up 100 times on six” type Tx. Further,
let “D” denote the particular die that Jane rolled and DTx the state of affairs
of D’s falling under type Tx for the particular sequence of die rolls: that is,
DTx is the state of affairs of D’s coming up 100 times in a row on that
particular set of die rolls. Normally
we should not accept that DTx simply happened by chance; we should look for an
explanation. The reason is that DTx is both
very improbable, having A one in 6100 chance of occurring, and
in some way “special.” The quality of
being “special” is necessary for our seeking an explanation, since all 100
sequences of rolls are equally improbable, but they are not all in need of an
explanation. In general, what makes an improbable occurrence special, and thus
a coincidence in need of explanation, is difficult to explicate
precisely. John Leslie, for example, has
proposed that this specialness consists of our being able to glimpse a simple,
unified explanation of the occurrence (Leslie, 1988, p. 302). In whatever way one explicates being
“special,” however, certainly a six-sided die coming up 100 times in a row on
six qualifies.
Now,
for any possible state of affairs S – such as DTx above – , the unrestricted
multiverse hypothesis (UMU) entails that this state of affairs S is
actual. Thus, with regard to
explanation, for all possible states of affairs S, advocates of UMU must claim
that the fact that UMU entails S either (i.a) undercuts all need for
explanation, or (i.b) it does not. Further, with regard to some state of
affairs S (such as DTx) that we normally and uncontroversially regard as
improbable, they must claim that the fact that UMU entails S either (ii.a)
undercuts the improbability of S (since it entails S), or (ii.b) it does not.
Both (i.a) and (ii.a) would constitute a
reductio of UMU, since it would
undercut both all justifications in science based on explanatory merits of an
hypothesis and ordinary claims of probability, such as in our die example
above. If advocates of UMU adopt (i.b)
and (ii.b), however, then the mere fact that UMU entails LPU undercuts neither the
need to explain LPU nor its apparent improbability.
Part
of what gives rise to the temptation to think that UMU can explain, or render
unsurprising, LPU (without doing the same for every other occurrence) is the
existence of other "many-trials" scenarios that appear to be
analogous but which are really crucially disanalogous. The way in which they are disanalogous is
that they only entail the occurrence of a very limited number of states of
affairs that we find highly surprising, without entailing the existence of all
such states of affairs. The limited
scope of such hypotheses allows one to affirm what I will call the
entailment principle. This is the principle that if h&k
¢ is
known to entail S, or known to render the statistical probability of S near 1,
then the conditional epistemic probability of S on h&k
¢ is
near 1: that is, P(S|h & k
¢) ~ 1.
Advocates of these more limited
multiple-trial hypotheses can then use the entailment principle to render
epistemically probable the actuality of some state of affairs whose actuality
would otherwise be considered highly improbable, without at the same time
rendering the actuality of other states of affairs probable that we normally
consider improbable. Consider, for example, what could be called the
multiple-die-roll (MDR) hypothesis, according to which an enormous number of
dice are being rolled at every moment throughout the galaxy, in fact so many
that the statistical probability that some sequence of 100 die rolls will come
up all sixes is almost one. By the
entailment principle, it follows that it is highly epistemically probable under
MDR that
some sequence of die rolls
will come up all sixes. The conjunction
of MDR and the entailment principle, however, does not change the probability
of other states of affairs whose improbability is critical for everyday inferences,
such as some particular sequence of die rolls coming up all sixes as in DTx
above.
Now
advocates of UMU could exploit the entailment principle in order to retain the
claim that for some states of affairs S, the actuality of S is still
epistemically improbable under UMU. As
we saw above, if S is a possible state of affairs, then UMU entails that S is
actual. If we can know that S is possible without knowing that S is actual,
then the claim that S is possible would be part of our background information k
¢ and hence P(S|UMU & k') = 1. Suppose that for some cases, however, we
cannot know whether S is possible apart from S’s actually occurring. In those cases, the entailment principle
could be true and yet for some S, P(S|UMU & k') < 1, even though UMU
entails S. In the case of the die D in
our example above, the particular die D exists only as part of the world W it
occupies, and thus the only possible sequence of rolls of that particular die
are those that it has in W.
Consequently, unless we know the sequences of rolls of D that have actually
occurred in W, we cannot know whether it is
possible
for D to fall in sequence type Ty (
e.g.,
100 fours in a row) without knowing whether D has
actually fallen in type Ty.
This means that even though the UMU might entail that D lands in type
Ty, we could not deduce this from UMU, and, hence, the conditional epistemic
probability of D's falling in Ty could be less than 1. The epistemic
probability of P(DTy|k' & UMU) would then be given by the degree to which
k' & UMU of itself rationally justifies the proposition, DTy, that die D
came up in sequence type Ty. Call this the
non-deducibility loophole,
since it arises from the fact that even though the UMU entails the actuality of
all actual states of affairs S, we cannot always
derive S’s actuality from the UMU.
Now the nondeducibility
loophole will work only if we can refer to D in W in a way that is not
equivalent or reducible to providing some qualitative description that uniquely
picks it out from among all dice that exist across worlds, since such a
qualitative description would have to include everything about D that
distinguishes it from its counterparts in other worlds, including DTx, or ~DTx.
Put differently, it will work only if we can make statements about the die that
essentially involve the use of indexicals – that is, involve the use of
indexicals, such as “this die,” in a way that cannot be translated in terms of
statements that only use qualitative descriptions such as “the die with
properties P,” where the properties P are purely qualitative properties.
If we allow such essentially
indexical propositions about particular objects in the universe, such as the
die, then it seems we can also make such essentially indexical statements about
the universe we inhabit: we could simply specify that universe U (or “this
universe”) refers to the universe that contains some particular object – e.g., some particular electron– that we
are referring to in an essentially indexical manner. This will allow us to
adopt the same loophole to the entailment principle as adopted by advocates of
UMU. Put differently, what I called the indexical LP fact – that is, the
fact that universe U is life-permitting – could no longer be simply dismissed as needing no explanation (or
lacking improbability) because it is purportedly a defining or essential
feature of this universe that it is life-permitting. The reason is that even
though it would be an essential feature of this universe, we could not deduce
it from UMU without already knowing that it is possible for universe U to be
life-permitting, just as we could not deduce DTx from UMU without knowing that
DTx is possible.
Finally, to exploit the
non-deducibility loophole for the indexical LP fact, we simply apply our
standard procedure for subtracting out old evidence – such as that the universe
has life-permitting values for its constants – to obtain background information k'.
Now, although k' and UMU entail that universe U is life-permitting, a
being with cognitive faculties relevantly similar to our own could not deduce
that simply by knowing k' and the UMU:
e.g.,
if our unembodied being introduced at the end of section 3.2 were given the
information k' and UMU, it would not know whether U was life-permitting or
not. Consequently, by the same argument
used for the case of the naturalistic-single universe hypothesis, P(Universe U
is life-permitting |UMU & k') << 1 and P(Lpc|UMU & k') <<
1.
Of course, one might argue against this
subtraction procedure, but this sort of argument is a direct challenge to my
version of the fine-tuning argument itself, not a challenge arising from UMU.
(See section 4.3 for a defense of the subtraction procedure).
A general lesson to be gained
from the above analysis is that any multiverse hypothesis that purportedly undercuts
the fine-tuning argument by entailing LPU will have to be restricted in the
right way: specifically, it will have to be such that it does not entail states
of affairs S that we normally take to be improbable. Consider, for example, a
multiverse hypotheses M that attempts to explain the special initial conditions
of our universe by hypothesizing that it is part of a vast array of universes
all of which have the same laws L but in which every possible initial condition
is realized. The standard inflationary-superstring
scenario discussed in the next section contains such a multiverse as a
subset. So do standard multiverse
theories based on the existence of an infinite universe with widely varying
initial conditions. Assuming that universes lack haecceities – which in this
case implies that they are distinguished only by their initial conditions – and
assuming the laws are deterministic, then M will entail the existence of our
universe along with all of its properties.
For example, M will entail DTx. Hence, the mere fact that M entails the
existence of our universe and its life-permitting structure cannot be taken as
undercutting the claim that it is improbable without at the same time
undercutting claims such as that DTx is improbable. Of course, an advocate of M could always use
the non-deducibility loophole discussed above to save the improbability of the
actuality of these states of affairs, but that will open the door to the
advocate of the fine-tuning argument’s using the same loophole.
If this analysis is correct, it will spell
trouble for those who claim that the multiverses discussed in contemporary
cosmology – such as the inflationary multiverse – can undercut the
improbability of the extraordinarily special initial conditions of our universe
by claiming that every possible initial condition is realized in some universe
or another.
As mentioned in section 6.1 above, by far
the most commonly advocated version of the restricted multiverse hypothesis is
the “multiverse-generator” version that claims that our universe was generated
by some physical process that produces an enormous number of universes with
different initial conditions, values for the constants of nature, and even
lower-level laws. Many scenarios have
been proposed – such as the oscillating big bang model and Lee Smolin’s claim
that many universes are generated via black holes (Smolin, 1997). Among these,
the one based on inflationary cosmology conjoined with superstring theory is by
far the most widely discussed and advocated, since this is the only one that
goes beyond mere speculation. According to inflationary
cosmology, our universe started from an exceedingly small region of space that
underwent enormous expansion due to a hypothesized inflaton field which
both caused the expansion and imparted a constant, very large energy density to
space as it expanded. The expansion
caused the temperature of space to decrease, causing one or more so-called
“bubble universes” to form. As each
bubble universe is formed, the energy of the inflaton field is converted into a
burst of “normal” mass‑energy thereby giving rise to a standard big-bang
expansion of the kind we see in our universe.
In chaotic
inflation models – widely
considered the most plausible –
space expands so rapidly that it becomes a never-ending source of bubble
universes. Thus, an enormous number of
universes naturally arise from this scenario.
In order to get the parameters of physics to vary from universe to
universe, however, there must be a further physical mechanism/law to cause the
variation. Currently, many argue that this mechanism/law is given by
superstring theory or its proposed successor, M-theory, which are widely
considered the only currently feasible candidates for a truly fundamental
physical theory. It should be stressed, however, that both inflationary
cosmology and superstring-M-theory are highly speculative. For example, Michio Kaku states in his recent
textbook on superstring theory, “Not a shred of experimental evidence has been
found to confirm . . . superstrings” (1999, p. 17). The same remains true
today. The major attraction of
superstring-M-theory is its mathematical elegance and the fact that many
physicists think that it is the only game in town that offers significant hope
of providing a truly unified physical theory of gravitation with quantum
mechanics (Greene, 1999, p. 214).
One major possible theistic response to
the multiverse generator scenario, whether of the inflationary variety or some
other type, is that the laws of the multiverse generator must be just right –
fine-tuned – in order to produce
life-sustaining universes. To give an
analogy, even a mundane item like a bread machine, which only produces loaves
of bread instead of universes, must have the right structure, programs, and the
right ingredients (flour, water, yeast, and gluten) to produce decent loaves of
bread. If this is right, then invoking
some sort of multiverse generator as an explanation of the fine-tuning
re-instates the fine-tuning up one level, to the laws governing the multiverse
generator. So, at most, it could explain the fine-tuning of the constants and
initial conditions. (Even the latter will be problematic, however, as we shall
see in the next two sections.)
As a test case, consider the inflationary
type multiverse generator. In order for it to explain the fine-tuning of the
constants, it must hypothesize one or more "mechanisms" or laws that
will do the following five things: (i) cause the expansion of a small region of
space into a very large region; (ii) generate the very large amount of
mass-energy needed for that region to contain matter instead of merely empty
space; (iii) convert the mass-energy of inflated space to the sort of
mass-energy we find in our universe; and (iv) cause sufficient variations among
the constants of physics to explain their fine-tuning.
Glossing over the details, in inflationary
models, the first two conditions are met via two factors. The first factor is the postulated inflaton
field that gives the vacuum (that is, empty space), a positive energy density. The second factor is the peculiar nature of
Einstein’s equation of general relativity, which dictates that space expand at
an enormous rate in the presence of a large near-homogenous positive energy
density (see section 2.3.3). Finally,
because the inflaton field gives a constant positive energy density to empty
space, as space expands the total vacuum energy within the space in question
will increase enormously. This in turn
generates the needed energy for the formation of matter in the universe. As one text in cosmology explains, “the
vacuum acts as a reservoir of unlimited energy, which can supply as much as is
required to inflate a given region to any required size at constant energy
density” (Peacock, 1999, p. 26).
So, to achieve (i) – (ii), we effectively
have a sort of “conspiracy” between at least two different factors: the
inflaton field that gives empty space a positive energy density, and Einstein’s
equation. Without either factor, there
would neither be regions of space that inflate nor would those regions have the
mass-energy necessary for a universe to exist.
If, for example, the universe obeyed Newton’s theory of gravity instead of
Einstein’s, the vacuum energy of the inflaton field would at best simply create
a gravitational attraction causing space to contract, not to expand.
The conversion of the energy of the
inflaton field to the normal mass-energy of our universe (condition (iii)
above) is achieved by Einstein’s equivalence of mass and energy, E = mc2,
along with the assumption that there is a coupling between the inflaton field
and the matter fields. Finally, the
variation in the constants (and to some extent the laws) of nature is typically
claimed to be achieved by combining inflationary cosmology with superstring-M
theory, which purportedly allows for an enormous number (e.g., 10500) of possible combinations of values for the
constants of physics. The important point here is that the laws underlying the
inflationary scenario must be just right in order to cause these variations in
the constants of physics from one universe to another. If the underlying laws
are those given by superstring-M theory, arguably there is enough variation;
this is not the case, however, for the typical grand unified theories that have
been recently studied, which allow for only a very limited number of variations
of the parameters of physics, about a dozen or so in the case of the simplest
model (Linde, 1990, p. 33). As Joseph
Polchinski notes in his textbook on superstring theory (1998, Vol. II, pp.
372-73), there is no reason to expect a generic field to have an enormous
number of stable local minima of energy, which would be required if there is to
be a large number of variations in the constants of physics among universes in
inflationary cosmology.
In addition to the four factors listed
above, the fundamental physical laws underlying a multiverse generator --
whether of the inflationary type or some other -- must be just right in order
for it to produce life-permitting
universes, instead of merely dead universes. Specifically, these fundamental
laws must be such as to allow the conversion of the mass-energy into material
forms that allow for the sort of stable complexity needed for complex
intelligent life. For example, as
elaborated in section 2.2, without the principle of quantization, all electrons
would be sucked into the atomic nuclei, and, hence, atoms would be impossible;
without the Pauli-exclusion principle, electrons would occupy the lowest atomic
orbit, and, hence, complex and varied atoms would be impossible; without a
universally attractive force between all
masses, such as gravity, matter would not be able to form sufficiently large
material bodies (such as planets) for life to develop or for long-lived stable
energy sources such as stars to exist.
Although some of the laws of physics can
vary from universe to universe in superstring-M theory, these fundamental laws
and principles underlie superstring-M theory and therefore cannot be explained
as a multiverse selection effect. Further, since the variation among universes
would consist of variation of the masses and types of particles, and the form
of the forces between them, complex structures would almost certainly be atom‑like
and stable energy sources would almost certainly require aggregates of
matter. Thus, the above fundamental laws
seem necessary for there to be life in any
of the many universes generated in this scenario, not merely in a universe
with our specific types of particles and forces.
In
sum, even if an inflationary/superstring multiverse generator exists, it must
have just the right combination of laws and fields for the production of
life-permitting universes: if one of the components were missing or different,
such as Einstein’s equation or the Pauli-exclusion principle, it is unlikely
that any life-permitting universes could be produced. Consequently, at most this highly speculative
scenario would explain the fine-tuning of the constants of physics, but at the
cost of postulating additional fine-tuning of the laws of nature.
Inflationary cosmology runs into a major
problem in explaining the low entropy of the universe. This is a critical
problem, since unless it can do this, arguably much, if not all, of the
motivation for inflationary cosmology vanishes. Further, this problem will cast
severe doubt on the ability of an inflationary multiverse to explain the
fine-tuning. The problem is that,
applied to the universe as a whole, the second law of thermodynamics demands
that the entropy of the universe always increase. Indeed, even if one has
doubts about the applicability of the second law to the universe as a whole,
inflation invokes a thermalization process, and thermalization is known to be a
paradigmatic entropy-increasing process.
As Cambridge
University physicist
Roger Penrose states,
Indeed, it is fundamentally misconceived to
explain why the universe is special in any particular respect by
appealing to a thermalization process.
For, if the thermalization is actually doing anything (such as making
temperatures in different regions more equal than they were before), then it
represents a definite increasing of entropy.
Thus, the universe would have had to be more special before the
thermalization than after. This only
serves to increase whatever difficulty we might have had previously in trying
to come to terms with the initial extraordinarily special nature of the
universe. . . . invoking arguments from thermalization, to address this
particular problem [of the specialness of the universe], is worse than useless!
(2004, P. 756.)
Based on this sort of argument, it is now
widely accepted that the pre-inflationary patch of space-time that inflated to
form our universe must have had lower entropy than the universe right after
inflation. For example, Andreas Albrecht, a defender of inflationary cosmology,
admits that inflationary cosmology must hypothesize a special initial low
entropy state: "For inflation, the inflaton field is the out-of-equilibrium
degree of freedom that drives other subsystems.
The inflaton starts in a fairly homogeneous potential-dominated state
which is certainly not a high-entropy state for that field . . . " (2004,
p. 382). Elsewhere, he says the pre-inflation patch must have been in a
"very special state" (2004, p. 380).
So, how does inflation explain the special
initial conditions of the big bang, which is the primary aim of the
theory? According to Albrecht, it
explains the initial conditions by a two-stage process, via the “chaotic inflation”
models mentioned in section 6.3 above. First, as Albrecht explains, "One
typically imagines some sort of chaotic primordial state, where the inflaton
field is more or less randomly tossed about, until by sheer chance it winds up
in a very rare fluctuation that produces a potential-dominated state. ..”
(Albrecht, 2004, p. 384).
Potential-dominated states are those in which the potential energy of
the inflaton field is enormous compared to the rate of change of the inflaton
field with respect to time and space.
That is, in order for inflation to occur, the inflaton field must be both
spatially and temporally almost uniform relative to the total energy density of
the field (Peacock, p. 329).
Although macroscopic uniformity of matter is typically a state of very high
entropy (such as perfume spread throughout a room), it is generally accepted
that in the case of the gravitational field and the inflaton field, greater
uniformity entails lower entropy. This is said to explain why the universe
becomes more and more inhomogeneous as it expands (with matter clustering into
galaxies and stars forming), and yet at the same time its entropy
increases. Entropy increases because the
gravitational field becomes less uniform.
Since the gravitational field would play a significant role in the
space-time of the early universe, a near uniform inflaton field would
correspond to extremely low entropy.
Now a general requirement for inflation is
that the inflaton field be nearly uniform, in the potential-dominated sense defined
above, over some very small patch. Although these states will be extremely
rare, given a large enough initial inflaton field, or enough time, they are
likely eventually to occur in some small patch of space simply as a result of
thermal fluctuations. Once they occur,
inflation sets in, enormously expanding the patch. Eventually, because of the postulated nature
of the inflaton field, in one or more regions of this expanded space, the field
decays, resulting in re-heating that produces a bubble universe with ordinary
matter. So, in effect, because inflation
can only occur in highly uniform states of the inflaton field, any universe
produced from an inflated region will have initially low entropy.
Accordingly, Albrecht proposes that
inflation explains the low entropy of our universe by a two-stage process: (i)
a low entropy patch occurs as a result of a statistical fluctuation, and then
(ii) that patch inflates into our universe.
As John Barrow and Frank Tipler pointed out over twenty years ago (1986,
p. 437), however, if the right special initial conditions must be stumbled upon
by a statistical fluctuation, why not simply hypothesize a very large, or
infinite, material field that undergoes a random fluctuation that produces a
universe relevantly like ours? Why invoke the additional mechanism of
inflation?
The answer requires looking at the
standard objection to "random fluctuation models." The objection is
that universes being produced by such a fluctuation (without inflation) would
almost certainly lead to small islands of observers surrounded by chaos, not
one with a low degree of entropy throughout.
Even more ominously, a random observer most likely would be a so-called
"Boltzmann Brain." A Boltzmann Brain (BB) is a small region of
mass-energy with the same structure as our brains (including the same sort of
apparent memory and sensory experiences), but with the surrounding regions of
space and time in a chaotic, high-entropy state. Although the experiences of
such brains would be highly ordered for a brief time, they would not in any way
correspond to reality, and any sort of inductive reasoning would fail.
The BB concept was originally articulated
as part of an objection raised against the proposed anthropic-selection-effect
explanation of the low initial entropy offered by Ludwig Boltzmann, one of the
principal founders of statistical mechanics. Boltzmann attempted to explain the
relatively low entropy of the universe by claiming that it was the result a
fluctuation from the normal “chaotic,” equilibrium state, and that a
fluctuation with a high degree of order was necessary for the existence of
observers. As theoretical physicist
Paul Davies and many others have pointed out in responding to Boltzmann’s
anthropic explanation, a fluctuation “the size of the solar system would be
sufficient to ensure the existence of life on Earth, and such a fluctuation is far
more probable than one of cosmic proportions” (Davies, 1974, p. 103.)
Indeed, fluctuations of even smaller dimensions – ones in which matter
has the same organization as the brain with all its apparent memories and sense
experiences but in which the surrounding space-time was chaos – would be even
more likely. Consequently, insofar as a random fluctuation world contained
observers, any randomly selected observer would almost certainly be a BB.
To intuitively see why Davies’s statement
is correct, consider an analogy of a very large scrabble-board. If we were to shake the scrabble board at
random, we would be much more likely to get an ordered, meaningful arrangement
of letters in one small region, with the arrangement on the rest of the board
essentially chaotic, than for all the letters on the entire board to form
meaningful patterns. Or, as another
analogy, consider a hundred coins lined up in a row, which are then shaken at
random. Define a local island of order
to be any consecutive sequence of five coins which all are on the same side –
that is, either all heads or all tails.
It is much more likely for the sequence of a hundred coin tosses to
contain one or more subsequences of five consecutive heads or tails than for it
to be all heads or all tails. Indeed, it
is likely that such a sequence of coins will have at least one such island of five
consecutive heads or tails; the probability of the coins coming up all heads or
all tails, however, is around one in 1030, or one in a thousand,
billion, billion, billion.
The
same argument applies to the mass-energy configurations of our visible
universe, with the argument being grounded in probability calculations based on
the standard probability measure of statistical mechanics over phase
space. These calculations show that
among all possible configurations, it is enormously more likely (by a factor of
around 1 in 10x, where x = 10123) for local islands of
low entropy to form than the whole visible universe to be in a low-entropy
state. (For example, see Penrose, 2004, pp. 762-765.). Indeed, if we consider the set of all
configurations of mass-energy that would result in an observer – e.g., an organized structure with the
same relevant order as our brain – the subset of such configurations that are
dominated by BB observers would be far, far larger than those configurations
that are dominated by non-BB observers.
Some people attempt to draw from
these calculations the conclusion that if the random fluctuation model is
correct, we should then expect ourselves to be BBs. This assumption, however,
is difficult to justify. We can, however, derive the more limited conclusion
that under the random fluctuation model it is epistemically very likely that we
are BBs conditioned on only our purely subjective experiences: that is, P(BB|k′ & RF) ~ 1, where BB represents the hypothesis that “I am a
BB,” RF the claim that the random fluctuation model is correct, and k′ includes all of one’s own “purely subjective” experiences but
no claim that these experiences correspond to reality.
Many
have argued, however, that we have noninferential knowledge of the existence of
the external world – that is, knowledge of the external world that cannot be
deduced from k
′. If this
is right, then P(BB|k & RF) = 0, where k* = there is an external world that
generally corresponds to our subjective experiences, and k = k
′ & k* is our relevantly complete background information.
This is the reason we cannot derive the skeptical conclusion that if the random
fluctuation model is true, we should expect ourselves to be BBs. However, since
P(~BB & k*|RF & k
′)
<< 1, the elaborated RF hypothesis, k & RF = ~BB & k
′ & k* & RF, suffers from a severe probabilistic tension
that the elaborated ~RF hypothesis, k & ~RF = ~BB & k
′ & k* & ~RF, does not. (Here, ~BB is the claim that we
are not BBs, and ~RF is the denial of the RF model.) This probabilistic tension
gives us strong reasons to accept ~RF over RF, given that that we are not BBs.
Or, given that ~RF is not
ad hoc in the sense defined in section 1.3,
the restricted version of the Likelihood Principle implies that ~BB & k*
strongly confirms ~RF over RF, since P(~BB & k*|RF & k
′) << 1 and ~P(~BB & k*|~RF
& k
′) << 1.
A
major question for a chaotic inflationary multiverse model is whether it can
circumvent the BB problem that plagues the random fluctuation model. If not,
such a model will encounter the same disconfirmation as RF, thus giving us
strong reasons to reject it. According to Albrecht, the inflationary model can
avoid the BB problem, and this is its key advantage. Says Albrecht,
Inflation is best
thought of as the “dominant channel” from random chaos into a big bang-like
state.
The exponentially large volume of
the Big Bang-like regions produced via inflation appear to completely swamp any
other regions that might have fluctuated into a Big Bang-like state via some
other route. So, if you went looking
around in the universe looking for a region like the one we see, it would be
exponentially more likely to have arrived at that state via inflation, than
some other way, and is thus strongly predicted to have the whole package of
inflationary predictions (Albrecht, 2004, p. 385, italics mine).
The
idea here is that inflation takes small, low entropy regions and expands them
into enormously large regions with enough order so that they will be dominated
by non-BB observers (if they have observers).
The assumption is that the regions that undergo inflation are so small
that they are much more likely to occur than regions that generate observers by
random fluctuations; further, because of inflation, these initial small regions
become so large that they dominate over those regions that produce observers by
means of random fluctuations. Albrecht admits, however, that his argument that
inflation would be the dominant channel "rests on very heuristic
arguments" and that "the program of putting this sort of argument on
firmer foundations is in its infancy" (2004, p. 396).
Several
articles have been written in recent years arguing that inflation will generate
universes in which BBs enormously dominate among observers in the far future
(E.G., Bousso and Freivogel, 2006; Banks, 2007).
These arguments, however, present a problem
only if one adopts a block universe view, according to which future events have
the same ontological status as present and past events. Although advocates of inflation typically
assume such a view, they need not. If one adopts a metaphysical view in which
the future is not yet real, these arguments will not themselves show that
inflation leads to a present dominance of BB universes. Further, as cosmologist
Don Page has pointed out (2006), the same dominance of BBs occurs for
long-lived single universes; further, the evidence at present strongly suggests
that our universe will continue existing for an enormously long time, if not
forever, if there is no supernatural intervention. In any case, I shall next present a powerful
reason for thinking that Albrecht’s argument is flawed and that without
assuming highly special initial conditions, inflationary cosmology leads to a
dominance of BBs for
any period of
time in which observers exist.
There is a simple argument that if the BB problem exists for
the random fluctuation multiverse, then the same problem exists for the
inflationary multiverse. Define a
megaverse as some very large finite,
or even infinite, region of space-time of a universe or multiverse that has
some configuration of mass-energy in it.
[54]
The BB problem arises for a random fluctuation multiverse because, when the
standard measure
M of statistical mechanics is applied to the phase
space of an arbitrary megaverse, the measure of configurations dominated by
non-BB observers is much, much smaller than that of those configurations
dominated by BB observers. Further, if this is true for the entire megaverse,
then it will have to be true for any arbitrarily chosen spacelike hypersurface,
hp, of constant time t of the megaverse. Thus, if we let M
t(BB)
designate the measure of volume, V
t(BB), of the phase space of hp
corresponding to those configurations dominated by BB observers, and M
t(~BB)
designate the measure of the volume, V
t(~BB), of hp corresponding to
configurations dominated by non-BB observers, then M
t(~BB)/Mt(BB)
<< 1.
[55] That is,
the measure for the possible mass-energy-momentum configurations of hp that are
non-BB dominated will be much, much smaller than the measure for those
configurations that are BB dominated. Assuming that the laws of physics are
deterministic and time-reversal invariant, then the measure is time-invariant,
as explained in Section 2.4. If we consider the mass-energy-momentum
configurations of hp as evolving with time, this means that for any volume of
phase space V(t
0) of measure M
V(t0) at time t0, V(t
0)
will evolve into a volume V(t) of the same measure at time t: that is, M
V(t)
= M
V(t0).
Now, consider the initial conditions
of the megaverse defined on some spacelike hypersurface of constant time t0.
Let Vt0(BB) and Vt0(~BB) represent the volume of phase
space of that hypersurface that evolves into configurations dominated by BB
observers and by non- BB observers, respectively, for some later hypersurface
at time t. Since the statistical mechanics measure m is time-invariant, the
ratio of the measure of Vt0(~BB) to Vt0(BB), that is, Mt0(~BB)/Mt0(BB),
will remain the same. Consequently, Mt0(~BB)/Mt0(BB) = Mt(~BB)/
Mt(BB) << 1. This means that the measure of initial states
that give rise to a universe dominated by non-BB observers at some arbitrarily
chosen later time t is much, much smaller than the measure of initial states
that give rise to a universe dominated by BB observers at t. Consequently,
unless the initial state of the megaverse is in a very special low-probability
state – that corresponding to volume Vt0(~BB) – it will not give
rise to a universe dominated by non-BBs. This is true for any megaverse in
which the laws of physics are deterministic and time-reversal invariant.
Inflationary cosmology denies neither of these assumptions. Further, even
though the laws of physics are not strictly speaking time-reversal invariant –
since timereversal symmetry is broken in weak interactions, notably the decay
of neutral kaons – the argument offered by Albrecht and others that was
explicated in Section 6.3.3 does not, in any way, exploit this lack of
invariance, nor does it exploit any sort of quantum indeterminacy. Thus,
without assuming highly special initial conditions, inflationary cosmology
cannot do better with regard to the BB problem than the random fluctuation
multiverse.
To illustrate this argument,
consider the following analogy. Let a highly ordered, lowentropy
non-BB-dominated megaverse of finite volume containing observers be represented
as a black-and-white TV screen with rows and rows of O’s throughout, and let a
megaverse dominated by BBs be represented by occasional O’s with large patches
of “snow” – that is, “random” configurations of black-and-white pixels. We
shall call the former arrangement the ordered, non-BB-pixel arrangement, and
the latter the BB-pixel arrangement. For simplicity, suppose there are only a
finite number of pixels on the TV screen. In that case, the number of ordered
non-BB-pixel arrangements would be very small compared with BB-pixel
arrangements. Further, suppose the image on the TV screen is being generated by
some small magnetic patch on a videocassette recorder (VCR) tape that the VCR
head is reading. Finally, suppose that there is a one-to-one correspondence
between arrangements of magnetic particles on the patch and the possible
configurations of black and- white pixels on the screen.
Because of the one-to-one
correspondence, the ratio of possible configurations of magnetic particles on
the patch of tape that give rise to non-BB-pixel arrangements to those that
give rise to BB arrangements will be the same as the ratio of non-BB-pixel
arrangements to BB-pixel arrangements on the TV screen. Thus, if the latter
ratio is enormously small, so will the former ratio. This is analogous to what
happens in the inflationary megaverse: because the laws of physics are
deterministic and time-reversal invariant, every microstate m(t0) at time t0
evolves into one and only one microstate, m(t), at time t, and, hence, they can
be put into a one-to-one correspondence. Consequently, just as the ratios of
the number of non-BB-pixel configurations to the BB-pixel configurations is
preserved from VCR patch to TV screen, the ratio of the measure of initial
configurations that lead to non-BB-dominant universes to the measure of those
that lead to BB-dominant universes is the same as the corresponding ratio at a
later time t.
[56]
Some might try to dispute one or
more of the assumptions of this argument. The most vulnerable assumptions are
the problems of non-arbitrarily dealing with the possible infinities that might
arise when one attempts to define a measure for the entire megaverse, along
with the additional problem of making rigorous the claim that in the entire
phase space, the measure of non-BB-dominated hypersurfaces is much, much less
than that of BB-dominated hypersurfaces. These problems, however, are as much a
problem for making Albrecht’s argument rigorous. The whole point of Albrecht’s
argument is that inflation does better with regard to BBs than the random
fluctuation multiverse. In order for this claim to be true, there must be some
“correct” measure M for the possible mass-energy states of the
multiverse (or at least for arbitrarily chosen very large finite subsets of it)
such that non-BB-observer-dominated states have a much, much smaller measure
than those of BB-observer-dominated states for the random fluctuation
model.
In response, perhaps Albrecht could
appeal to some notion of a “generic” initial state that is not dependent on the
existence of a measure over phase space. Such an appeal, however, will
immediately run afoul an objection Penrose has raised. Consider an enormously
large universe that eventually collapses back on itself and assume that all the
special laws that are required by inflation hold in that universe. (We could
even have an infinite universe with a negative cosmological constant to ensure
collapse.) Suppose that this universe had many domains, some of which are
highly irregular. In fact, we can suppose that it is chock full of BBs. As
Penrose points out, the collapse of such a universe will result in “a generic space-time
singularity, as we can reasonably infer from precise mathematical theorems”
(2004, p. 756). Assuming that the laws of physics (including those of
inflation) are time-symmetric (as is typically assumed in these contexts), if
we now reverse the direction of time in our model, we shall “obtain an evolution
which starts from a general-looking singularity and then becomes whatever
irregular type of universe we may care to choose” (2004, p. 757). Since the
laws governing inflation will hold in this time-reversed situation, it follows
that one cannot guarantee that a uniform or non-BB-dominant universe will arise
from generic initial conditions. Thus, inflationary cosmology can explain such
a universe only by effectively presupposing those subsets of generic initial
conditions that will lead this type of universe. As Penrose notes, “The point
is that whether or not we actually have inflation, the physical possibility of
an inflationary period is of no use whatever in attempts to ensure that
evolution from a generic singularity will lead to a uniform (or spatially flat)
universe” (2004, p. 757).
The
above arguments do not show that inflationary cosmology is wrong or even that
scientists are unjustified in accepting it.
What they do show is that the inflationary multiverse offers no help in
eliminating either the fine-tuning of the laws of nature or the special
low-entropic initial conditions of the big bang. With regard to the special low-entropic
initial conditions, it can explain the special conditions of the big bang only
by hypothesizing some other, even more special, set of initial conditions. Although a chaotic inflationary model might
lead one to expect a universe like ours, unless highly special initial
conditions are assumed across the entire multiverse, it leads to a multiverse dominated
by BBs for all later times and thus does no better than a random fluctuation
model. It also runs into the generic problems faced by multiverse hypotheses
discussed at the end of section 6.2. If we find the existence of a BB dominated
multiverses unacceptable, it follows that an inflationary-superstring
multiverse at best eliminates only the need to explain the life-permitting
values of the constants of physics (and perhaps other non-entropic types of
special initial conditions). Because of the highly speculative extra laws and
conditions required to make an inflationary multiverse work, one could not be
blamed if one judged that such purported explanatory ability were far too
costly.
Perhaps
the most common objection that atheists raise to the argument from design is
that postulating the existence of God does not solve the problem of design, but
merely transfers it up one level to the question, “Who or what designed
God?” The eighteenth-century philosopher
David Hume hinted at this objection:
For
aught we can know a priori, matter
may contain the source or spring of order originally within itself, as well as
mind does; and there is no more difficulty conceiving that the several
elements, from an internal unknown cause, may fall into the most exquisite
arrangement, than to conceive that their ideas, in the great universal mind,
from a like unknown cause, fall into that arrangement (Hume,
1980, pp. 17 - 18).
A
host of atheist philosophers and thinkers, such as J. L. Mackie (1982, p. 144),
Graham Oppy (2006, pp. 183-184), J. J. C. Smart (1985, pp. 275-276), Richard
Dawkins (1986, p. 316), and Colin McGinn (1999, p. 86) have also repeated this
objection. For example, J. J. C. Smart
claims that:
If
we postulate God in addition to the created universe we increase the complexity
of our hypothesis. We have all the
complexity of the universe itself, and we have in addition the at least equal
complexity of God. (The designer of an
artifact must be at least as complex as the designed artifact) (1985, pp.
275-276).
As
an objection to our version of fine-tuning argument, it is flawed on several
grounds. I have addressed this objection
in detail elsewhere (Collins, 2005a).
Here I shall present a brief response. To begin, this objection would
arise only if either the theistic hypothesis were constructed solely to explain the fine-tuning, without any independent motivation for
believing it, or one considered these other motivations as data and then
justified the theistic hypothesis by claiming that it is the best explanation
of all the data. Our main argument,
however, is not that theism is the best explanation of all the data, but only
that given the fine-tuning evidence, LPU strongly confirms theism over NSU.
Further,
we have substantial reasons for not
treating the other motivations for theism like data, which we then combine with
the fine-tuning evidence to infer to the best explanation. To illustrate, let
me focus on one such motivation. Many theists have claimed that for most people
at least, belief in God is grounded in a fundamental intuition regarding the existence
of God, an intuition relevantly similar to moral intuitions or the intuitions
regarding epistemic norms. If this is
right, then, as Keith Ward and others have noted, treating the existence of God
like a scientific hypothesis that needs to be justified by some form of
inference to the best explanation is "like trying to justify moral belief
by reference to the findings of the natural sciences" (1987, p. 178). On this view, faith can be seen as itself “a
response to one who claims my loyalty by showing the true nature of my present
mode of being and the way of salvation” (p. 178). It is “a basic and
distinctive mode of human thought and activity” (Ward, p. 180). Thus, in analogy to our ethical intuitions,
faith should be considered a mode of knowing, not just a mere leap of belief
under insufficient evidence. Plantinga (2000) has provided one way of carefully
developing this view and shows it has been commonplace in the Christian
tradition – e.g., Thomas Aquinas and
John Calvin (Plantinga, 2000, chap 6).
The religious mode of knowing or justification involved in faith,
therefore, should not be treated as providing data for an inference to
the best explanation, but rather analogous to our ethical intuitions, or even
our intuitions regarding epistemic virtues – e.g., that, everything else being equal, simpler theories are more
likely to be true or empirically adequate than complex theories. Clearly, one
cannot ground our belief in these epistemic virtues in an inference to the best
explanation, since all such inferences presuppose the virtues. Finally, William
Alston (1993) and others have made similar claims with regard to our knowledge
of God based on religious experience, claiming it is relevantly analogous to
our knowledge of the material world, which they claim is not justified by
appeal to an inference to the best explanation.
If
we do not treat these other motivations for theism as part of a body of data
for which we employ the strategy of inference to the best explanation, then the
“who designed God” objection largely evaporates. The existence of God is not a hypothesis that
is being offered as the best explanation of the structure of the universe, and
hence it is not relevant whether or not God is an explanatorily better (e.g.,
simpler) terminus for ultimate explanation than the universe itself.
Nonetheless, via the restricted
version of the likelihood principle (section 1.3), the various features of the
universe can be seen as providing confirming
evidence for the existence of God.
One advantage of this way of viewing the situation is that it largely
reconciles the views of those who stress a need for faith in coming to believe
in God and those who stress reason. They
each play a complementary role.
To
illustrate the above point, consider the following analogy. Suppose that in the
year 2050 extraterrestrials visit earth, and we find that they share the same
fundamental ethical beliefs as we do –
e.g.,
that it is wrong to torture others for no compelling ethical reason. Further, suppose that we were able to show
that it is very epistemically unlikely that such an agreement would occur under
ethical antirealism – for example, because we have good reason to believe both
that unguided naturalistic evolution would not produce these beliefs and that
ethical antirealism is not compatible with viable, alternative explanations of
human beings based on design (such as theism). Finally, suppose we could show
that it is not unlikely for this agreement to occur under ethical realism.
The discovery that these aliens shared the
same ethical beliefs as we do would therefore confirm ethical realism, even
though we would not believe ethical realism because it provided the best
explanation of some set of phenomena. In
fact, I believe it would decisively tip the balance in favor of ethical
realism. I suggest that the evidence of
fine-tuning does the same for theism.
Apart
from rejecting the claim that the justification for the existence of God is
based on some sort of inference to the best explanation, however, one can also
object to the atheist’s key assumption, articulated by J. J. C. Smart in the
quotation above, that the “designer of an artifact must be at least as complex
as the artifact itself.” This assumption
is not even clearly true in the human case, since it is at least conceivable
that one could produce a computer that is more complicated than oneself, which
is a common theme of science fiction. In
the case of God, however, we have even less reason to believe it. If the theist
were hypothesizing an anthropomorphic god, with a brain and a body, then this
objection would be much stronger: one would then be tempted to ask, isn’t that
god’s brain and body as much in need of explanation as the universe
itself? Thus, this objection might seem
to have significant bite against such a conception of God. Within traditional
theism, however, God has always been claimed to lack any sort of significant
internal complexity. In fact, most of
the Western medieval tradition claimed that God was absolutely simple in every
way – God did not even have complexity with regard to God’s properties. Aquinas, for instance, claimed that all of
God’s properties (such as God's omnipotence and perfect goodness) were
absolutely identical; these were in turn identical with God’s essence and
existence. Although I do not think that
this view of God as being absolutely simple is coherent, the point here is that
the “who designed God” objection begs the question against traditional theism,
by assuming a type of God which traditional theists would all disavow. Even the heirs to traditional theism who deny
absolute divine simplicity, such as Richard Swinburne 2004), claim that God’s
overall being is extraordinarily simple.
Thus, what these atheists really need to show is that the God of all
varieties of traditional theism is logically incoherent insofar as those
versions of theism hold on to some form of divine simplicity. This, however, is a very different objection
– and a much harder task – than simply raising the “who designed God?”
objection and then claiming that one has eliminated the theistic explanation in
a single stroke.
One criticism of the fine-tuning argument
is that, as far as we know, there could be a more fundamental law that entails
both the current laws of physics and the values of the constants of physics.
Thus, given such a law, it is not improbable that the laws and constants of
physics fall within the life-permitting range. Besides being entirely
speculative, three problems confront such a hypothesis. First, although many
physicists had hoped that superstring theory would entail all the current laws
and constants of physics, that hope has almost completely faded as string
theorists have come to recognize that superstring theory (and its proposed
successor, M-theory) has many, many solutions, estimated at 10500 or
more. Consequently, the prospects of
discovering such a fundamental law are much dimmer than they once were. Second,
such a fundamental law would not explain the fine-tuning of the initial
conditions of the universe. Finally,
hypothesizing such a law merely moves the epistemic improbability of the
fine-tuning of the laws and constants up one level, to that of the postulated fundamental
law itself. Even if such a law existed, it would still be a huge coincidence
that the fundamental law implied just those laws and values of the constants of
physics that are life‑permitting, instead of some other values. As
astrophysicists Bernard Carr and Martin Rees note “even if all apparently
anthropic coincidences could be explained [in terms of some fundamental law],
it would still be remarkable that the relationships dictated by physical theory
happened also to be those propitious for life”
(1979, p. 612). It is very unlikely, therefore, that the fine‑tuning of
the universe would lose its significance even if such a law were verified.
To illustrate the last response, consider
the following analogy. Suppose that super-determinism is true: that is,
everything about the universe, including its initial conditions, is determined
by some set of laws, though we do not know the details of those laws. Now consider a flip of a coin and let Lh
and Lt denote the claims that the laws are such as to determine the
coin to come up heads and tails, respectively.
We would have equal reason to believe that Lh as that Lt.
Hence, since Lh entails that the coin will come up heads, and Lt
that the coin will come up tails, the
epistemic probability of heads remains 50%, and likewise for tails. This would be true even though each of their
physical probabilities would be one or zero.
The fact that the laws of nature determine the initial conditions,
instead of the initial conditions’ not being determined by any law, has no
influence on the epistemic probability.
This can be seen also by the fact that when Laplacian determinism was
thought to be true, everyone nonetheless gave a fair coin a 50% chance of
coming up heads.
A similar sort of response can be given to
the claim that fine-tuning is not improbable because it might be
logically necessary for the constants of
physics to have life-permitting values.
That is, according to this claim, the constants of physics must have
life-permitting values in the same way 2 + 2 must equal 4, or the interior angles
of a triangle must add up to 180 degrees in Euclidian geometry. Like the “more fundamental law” proposal
above, however, this postulate simply transfers the epistemic improbability up
one level: of all the laws and constants of physics that conceivably could have
been logically necessary, it seems highly
epistemically
improbable that it would be those that are life-permitting, at least apart from
some sort of
axiarchic principle
discussed in section 8 below.
According
to what I call the "Other Life-Permitting Laws Objection," there
could be other life-permitting sets of laws that we know nothing about. This
objection is directly answered by the way in which I have formulated the
fine-tuning argument. As I formulated it, the fine-tuning argument does not
assume that ours is the only possible set of life-permitting laws. Rather, it
only assumes that the region of life-permitting laws (or constants or initial
conditions) is very small compared to the region for which we can determine
whether the laws, constants, or initial conditions are life-permitting – that
is, what I called the epistemically illuminated (EI) region (see section
4.5). In the case of the constants of
nature, it assumed only that given our current laws of nature, the
life-permitting range for the values of the constants of physics (such as
gravity) is small compared to the surrounding
EI range for which we can determine whether or not a value is life-permitting.
As raised against the fine-tuning argument
based on the constants of physics, this objection claims that as far as we
know, other forms of non-carbon based life could exist even if the constants of
physics were different. So, it is
claimed, the fine-tuning argument ends up presupposing that all forms of
embodied, conscious life must be carbon-based (e.g., Stenger, 2004, pp. 177- 178). Besides the extreme difficulty
of conceiving of how non-carbon based material systems could achieve the sort
of self-reproducing material complexity to support embodied moral agents,
another problem with this objection is that many cases of fine-tuning do not
presuppose that all life must be carbon based. Consider, for instance, the
cosmological constant. If the cosmological constant were much larger than it
is, matter would disperse so rapidly that no planets and indeed no stars could
exist. Without stars, however, there
would be no stable energy sources for complex material systems of any sort to
evolve. So, all the fine-tuning argument presupposes in this case is that the
evolution of embodied moral agents in our universe require some stable energy
source. This is certainly a very
reasonable assumption.
According to the weak version of so-called
anthropic principle, if the laws of
nature were not fine-tuned, we should not be here to comment on the fact. Some have argued, therefore, that LPU is not
really improbable or surprising at
all under NSU, but simply follows from the fact that we exist. The response to
this objection is simply to restate the argument in terms of our existence: our
existence as embodied moral agents is extremely unlikely under NSU, but not
improbable under theism. As explained in section 4.3, this requires that we
treat LPU and our existence as “old evidence,” which we subtract from our
background information. This allows us
to obtain an appropriate background information k¢ that does not entail
LPU. The other approach was to use the
method of probabilistic tension, which avoided the issue entirely. (See sections 1.4 and 4.3 - 4.4).
The
methods used in section 4. deal with this problem of old evidence, and our
arguments in section 3.2 for the existence of conditional epistemic
probabilities for P(A|B &k') even when A implies our own existence, provide the formal underpinnings in support
of the intuitions underlying the “firing-squad” analogy offered by John Leslie
(1988, p. 304) and others in response to this objection. As Leslie points out,
if fifty sharp shooters all miss me, the response “if they had not missed me I
wouldn’t be here to consider the fact” is inadequate. Instead, I would naturally conclude that
there was some reason why they all missed, such as that they never really
intended to kill me. Why would I conclude this? Because, conditioned on
background information k′ that does not include my continued existence – such
as the background information of a third-party observer watching the execution
– my continued existence would be very improbable under the hypothesis that
they intended to kill me, but not improbable under the hypothesis that they did
not intend to kill me.
As
I developed in sections 1.3 and 1.4, the fine-tuning argument concludes that,
given the evidence of the fine-tuning of the cosmos, the existence of a
life-permitting universe (LPU) significantly confirms theism over what I called
the naturalistic single-universe hypothesis (NSU). In fact, as shown in section
5.2, a good case can be made that LPU conjoined
with the existence of evil significantly confirms theism over NSU. This does
not itself show that theism is true, or even likely to be true; or even that
one is justified in believing in theism. Despite this, I claimed that such
confirmation is highly significant – as significant as the confirmation that
would be received for moral realism if we discovered that extraterrestrials
held the same fundamental moral beliefs that we do and that such an occurrence
was very improbable under moral anti-realism (see section 7.1). This
confirmation would not itself show that moral realism is true, or even
justified. Nonetheless, when combined with other reasons we have for endorsing
moral realism (e.g., those based on
moral intuitions), arguably it tips the balance in its favor. Analogous things, I believe, could be said
for theism.
I
also considered the challenge raised by the two most widely advocated versions
of the multiverse hypothesis – what I called the unrestricted multiverse hypothesis advocated by Lewis and Tegmark,
according to which all possible universes exist, and the restricted multiverse hypothesis arising out of inflationary
cosmology. I argued that neither of
these is able adequately to explain away the fine-tuning or undercut the
fine-tuning argument.
Finally,
one might wonder whether there are other viable alternative explanations of LPU
to that offered by theism, NSU, or the multiverse hypothesis. One such possibility is various non-theistic
design hypotheses – either non-theistic supernatural beings or aliens in some
meta-universe who can create bubble universes. The postulated designer, D,
could not be a merely "generic" designer but must be hypothesized to
have some motivation to create a life-permitting universe; otherwise P(LPU|D
& k') = P(LPU|NSU & k'), as explained in section 5.2. Unless these hypotheses were advocated prior
to the fine-tuning evidence, or we had independent motivations for them, they would
not pass the non-ad-hocness test of
the restricted version of the likelihood principle (section 1.3). Furthermore, from the perspective of
probabilistic tension, these alternative design hypotheses typically would
generate a corresponding probabilistic tension between the claim that the
postulated being had a motive to create a life-permitting world instead of some
other type of world and the beings’ other attributes, something that does not
arise for classical theism (see section 5.2). Finally, for some of these
postulated beings, one could claim that even if LPU confirms their existence,
we lack sufficient independent reasons to believe in their existence, whereas
under theism we have such reasons; or one could claim that they simply transfer
the problem of design up one level (see section 7.1).
The
only one of these alternatives that I consider a serious contender is the
axiarchic hypothesis, versions of which
have been advanced in the last thirty years by John Leslie (e.g., 1989, Chap.
8) and recently by Hugh Rice (2000) and others, wherein goodness or ethical
“required-ness” has a direct power to bring about concrete reality. Whatever the merits of this hypothesis, it is
likely to entail theism. Since God is
the greatest possible being, it is supremely good that God exist (Leslie, 1989,
pp. 168-69). Therefore, it is unclear
that the axiarchic hypothesis actually conflicts with theism.
In any case, this essay has shown that we
have solid philosophical grounds for claiming that given the fine-tuning
evidence, the existence of a life-permitting universe provides significant
support for theism over its non-axiarchic contenders.
Red
highlighted text: Unsure how to
reference these. These are for the
physics/astrophysics/cosmology, etc., archive, which everyone in the physics,
astrophysics, cosmology, etc., field knows and it is widely used. I know how they are commonly referenced, but
those assume one knows the URL of the web location: e.g., the Don Page
reference below would typically be referenced as hep-th/0612137v1, even though
full URL location (for pdf format) is
http://arxiv.org/PS_cache/hep-th/pdf/0612/0612137v1.pdf [This archive is located at
http://arxiv.org . "arXiv is an
e-print service in the fields of physics, mathematics, non-linear science,
computer science, quantitative biology and statistics. The contents of arXiv
conform to Cornell
University academic
standards. arXiv is owned, operated and funded by Cornell University,
a private not-for-profit educational institution. arXiv is also partially
funded by the National Science Foundation."]
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There are many reasons why the likelihood
principle should be accepted (e.g., see Edwards 1972, Royall 1997, Forster and
Sober 2001, Sober 2002); for the purposes of this essay, I take what I call the
restricted version of the likelihood
principle (see below) as providing sufficient conditions for when evidence
e supports an hypothesis, h
1, over another h
2. For a counterexample to the likelihood
principle being a necessary condition, see Forster, 2006. For an application of
the likelihood principle to arguments for design, see Sober 2005. (I address Sober’s main criticism of the
fine-tuning argument in sections 3.2, 5.2, and 7.5 below.)
The
likelihood principle can be derived from the so-called odds form of Bayes's
theorem, which also allows one to give a precise statement of the degree to
which evidence counts in favor of one hypothesis over another. The odds form of
Bayes's theorem is: P(h1|e)/P(h2|e) = [P(h1)/P(h2)] x
[P(e|h1)/P(e|h2)]. The
likelihood principle, however, does not require the applicability or truth of
Bayes's theorem and can be given independent justification by appealing to our
normal epistemic practices.
There is
one worry about premise (3), though: theism was not advocated prior to the
evidence of a life-permitting universe, since the life-permitting character of
our universe follows from our existence, and all the motivations for theism are
intertwined with the fact that we exist.
If this is a real difficulty, one might need to use my alternative
version of the fine-tuning argument, the method of
probabilistic tension (section 1.4), for which this problem
clearly does not arise.
Choosing units in which the speed of light, c, is equal to one (as is commonly
done), it follows from Einstein's equation that ρ
vac = 8πGΛ
vac and
ρ
max = 8πGΛ
max, where G is
Newton's constant of gravity. Hence the vacuum energy and the cosmological
constant are strictly proportional to each other.
See
Collins, 2003, endnote 9, p. 196, for more analysis of this case.
Although the Higgs fields and the other fields of physics could contribute to
inflation, for various technical reasons inflationary cosmology requires a
distinct energy field that helps create a very large effective cosmological
constant in the very early universe.
There is no candidate for this field that is "deeply rooted in
well-established theories of fundamental physics" (Albrecht, 2004, p.
381).
The assumption that Λ
eff >
0 is regarded by most physicists as the best way of accounting for the
evidence, based on redshifted light from distant supernovae, that the universe
is accelerating. An effective cosmological constant is not the only way of explaining
the cosmic acceleration, however.
Olga Mena
and
José Santiago
(2006) have recently developed a modification of Einstein's theory of gravity
that explains the acceleration of the universe without appealing to an
effective cosmological constant. Their
model, however, still must assume some non-material substance in addition to
normal matter. As stated in their abstract, “the inverse-curvature gravity
models considered
cannot explain the
dynamics
of the Universe just with a baryonic matter component.” If
a successful non-
ad hoc and
non-fine-tuned modification of general relativity could be developed that would
account for the acceleration of the universe, it could serve as an alternative
to steps (2) and (3) in an attempt to avoid the fine-tuning of the cosmological
constant.
For example, physicists Christopher Kolda and David H. Lyth note that “an
alternative to a cosmological constant is quintessence, defined as a
slowly-varying scalar field potential V(φ). . . . In contrast with ordinary
inflation, quintessence seems to require extreme fine tuning of the potential
V(φ´´)." (1999, abstract). Further,
as physicist Gabriela Barenboim notes, models that combine inflation and
quintessence “require significant
ad hoc
tuning to simultaneously produce the features of inflation and quintessence”
(2006, p. 1).
A rigorous justification of the epistemic improbability of
the initial conditions of the universe is a little trickier, since it
presupposes that one can apply the standard measure of statistical mechanics to
the initial state of the universe, something John Earman and others have
questioned (see section 2.4). We cannot pursue this issue further in this
chapter, however.
A full-scale defense of the restricted principle of
indifference is beyond the scope of this chapter. See Schlesinger (1985,
chapter 5) for a lengthy defense of the standard principle of indifference.
Given
the multiplicity of possible references classes, one could simply decide not to
assign any epistemic probability to LPU.
As with skepticism in general, such a practice would also undercut any
sort of rational commitment to the approximate truth or empirical adequacy of a
theory, since the epistemic probabilities used in justifying these theories
also lack a complete fundamental justification.
Given that we are not skeptics, the best we can do is use the least
arbitrary procedure available to assign epistemic probabilities.
This is
a different approach than in one of my earlier papers on the issue (2005b),
where the range was constrained by what values are consistent with a universe’s
existing --
e.g., too high of a value
for the gravitational constant would reduce the whole universe to a singularity
and so forms a natural bound of the range. The "universe existing
constraint" is still valid (since NSU & k' presuppose the existence of
a universe), but it is typically trumped by the EI region constraint, since the
latter is more stringent.
See,
for instance, Zee (2003, pp. 437-438 ), Cao (1997, pp. 349-353), and Teller
(1988, p. 87). For example, Zee says
that he espouses “the philosophy that a quantum field theory provides an
effective description of physics up to a certain energy scale Λ, a threshold of
ignorance beyond which physics not included in the theory comes into play.” (P.
438).
Speaking of gravitational force as involving energy exchange is highly
problematic, though speaking of gravitational binding energy is not nearly as
problematic. One problem is that in general relativity, gravity is not
conceived of as a force but as curvature of space-time. Another problem is that there is no
theoretically adequate definition for the local energy of a gravitational field
or wave. (See, for instance, Wald, 1984, p. 70, note 6 and p. 286.) Finally, although physicists often speak of
gravitons as the carriers as the carrier of the gravitational force, the
quantum theory of gravity out of which gravitons arise is notoriously
non-renormalizable, meaning that infinities arise that cannot be
eliminated. Nonetheless, since
gravitational waves cause changes in the energy of material objects at a
certain rate, we can still meaningfully speak of energy scales at which a
particular gravitational “force” is operating, which is all that is needed for
this argument.
The
weak force does not involve binding energies, but is an interaction governing
the transmutation of particles from one form to another, and so this last
argument would not apply to it.
More
generally, since constants are only defined with respect to the theories of
physics in which they occur, their range of applicability, and thus the EI
range, is restricted to the range of applicability of those theories.
For an
argument showing that various inferences in contemporary cosmological
speculation use infinite ranges, and for some mathematical justification of
these, see Jeffrey Koperski, 2005.
One might challenge this conclusion by
claiming that both the restricted likelihood principle and the method of
probabilistic tension require that a positive probability exist for Lpc on
T&k'. This seems incorrect, as can
be seen by considering cases of disconfirmation in science. For example,
suppose some hypothesis h conjoined with suitable auxiliary hypotheses, A,
predict e, but e is found not to obtain. Let ~E be the claim that the
experimental results were ~e. Now, P(~E|h & k) << 1, yet P(~E|h &
k) ≠ 0 because of the small likelihood of experimental error. Further, often
P(~E|~h & k) will be unknown, since we do not know all the alternatives to
h or what they predict about e. Yet, typically we would take ~ E to disconfirm
h in this case because P(~E|h & k) << 1.
Finally, in a worst case scenario in which
an atheist offered good reason to believe that Ev is unlikely under theism, it
would still probably be the case that Lpc & Ev would disconfirm NSU over
TSU, not only because the improbability of Lpc is so great under NSU that it
would be less than P(Ev|TSU & k'),
but also because P(Lpc|NSU & k') << 1 receives a principled
justification -- via the restricted principle of indifference -- whereas the
arguments offered for P(Ev|T & k) << 1 are typically based on highly
controversial intuitions.
I would
like to thank the John Templeton Foundation for a grant to support this work,
William Lane Craig for comments on an earlier draft of this paper and final
editorial comments, David Schenk for comments on the next-to-final version,
physicists Don Page and Robert Mann for comments on an earlier version of the
section on inflationary cosmology, and many other people, such as Alvin
Plantinga, who have encouraged me in, raised objections to, and offered
comments on my work on the fine-tuning over the years.
