# 1 Introduction

The teleological argument (i.e., the argument from design) has experienced something of a renaissance over the last half-century or so. In addition to the genetic and biochemical evidence that points to the existence of an Intelligent Designer of the cosmos, the primary fuel for this renaissance has been discoveries from and advances in fields like cosmology and theoretical physics, to name but a few. What scientists have come to discover is that the physics necessary to permit the existence of life—of any kind—depends upon a balance so unfathomably precise that it literally defies human comprehension; this is known as the fine-tuning of the universe. Here is how Stephen Hawking and Leonard Mlodinow put it:

Most of the fundamental constants in our theories appear fine-tuned in the sense that if they were altered by only modest amounts, the universe would be qualitatively different, and in many cases unsuitable for the development of life. . . . The emergence of the complex structures capable of supporting intelligent observers seems to be very fragile. The laws of nature form a system that is extremely fine-tuned, and very little in physical law can be altered without destroying the possibility of the development of life as we know it. Were it not for a series of startling coincidences in the precise details of physical law, it seems, humans and similar life-forms would never have come into being.

In agreement with those points is Lord Baron Professor Sir Martin Rees, Astronomer Royal, former President of the Royal Society, Professor of Cosmology and Astrophysics at the University of Cambridge, and Master of Trinity College:

These six numbers constitute a “recipe” for a universe. Moreover, the outcome is sensitive to their values: if any one of them were to be “untuned,” there would be no stars and no life. . . . If you imagine setting up a universe by adjusting six dials, then the tuning must be precise in order to yield a universe that could harbour life.

Despite the level of popularity this particular design argument has achieved, often we will still find discussions in which there are persons who are seriously misinformed as to what fine-tuning actually is. In this post, I will attempt to clear up some of those misconceptions by rigorously laying out the teleological argument on the basis of the fine-tuning. Moreover, what we will see is that there is widespread agreement on the fact of fine-tuning; the controversy does not begin until we ask the question, What is the best explanation of the fine-tuning? Frank Wilczek attests to this fact:

[L]ife appears to depend upon delicate coincidences that we have not been able to explain. The broad outlines of that situation have been apparent for many decades. When less was known, it seemed reasonable to hope that better understanding of symmetry and dynamics would clear things up. Now that hope seems much less reasonable. The happy coincidences between life’s requirements and nature’s choices of parameter values might be just a series of flukes, but one could be forgiven for beginning to suspect that something deeper is at work.

## 1.1 Key Definitions and Terms

In our discussion of the fine-tuning (hereafter, FT) we will be focusing on three primary areas in which instantiations of FT are said to exist:

1. Laws of nature
2. Physical constants
3. Initial conditions

With respect to (1), the laws of nature are principles of the physical world that describe the way in which physical entities interact. Here are a few examples:

• The universal attractive force, gravity;
• The strong nuclear force, which binds protons and neutrons together in the nucleus;
• The electromagnetic force;
• The weak nuclear force, responsible for radioactive decay.

Concerning (2), physical constants (i.e., parameters) are a set of fundamental invariant quantities observed in nature and appearing in the basic theoretical equations of physics when the laws of nature are expressed mathematically. An example of a fundamental constant is Newton’s gravitational constant $G$, which determines the strength of gravity via Newton’s law $$F = -\frac{Gm_{1}m_{2}}{r^2}.$$

Regarding (3), the initial conditions of the universe are the boundary conditions describing the initial distribution of mass-energy (measured by entropy).

Finally, I will define what is meant by the use of the word, universe: a universe is a causally-connected region of spacetime, over which the physics is effectively the same for all sub-regions contained by it.

## 1.2 What it Means to Say that a Law / Constant / Initial Condition is Fine-Tuned

We now turn to the most important (and often most misunderstood) points of clarification regarding FT. To claim that the universe is fine-tuned is to say the following:

FT: In the set of all possible physics (i.e., the different combinations of laws, constants, and initial quantities), the subset that permit the existence of life is vanishingly small.

FT is not about what the parameters and laws are in a particular universe; indeed, if chosen randomly, no one combination is in and of itself any more improbable than any other. But no matter which combination one randomly chooses, it is astronomically more probable that it will be one that is not in the subset that permits the existence of life. Once one grasps this fact, he will be well on his way to gaining a thorough understanding of the argument.

FT is not the claim that the universe is optimal for the existence of life or that it has the maximum amount of life per unit volume or baryon; it says nothing of the sort. Therefore, pointing to features of the universe that are not hospitable or conducive to life is in no way a refutation of the fact of FT. As John Leslie explains:

The issue here is not the rarity or otherwise of living beings in our universe. It is instead whether living beings could evolve in a universe just slightly different in its basic characteristics. The main evidence for multiple universes or for God is the seeming fact that tiny changes would have made our universe permanently lifeless. How curious to argue that the frozen desert of the Antarctic, the emptiness of interstellar space, and the inferno inside the stars are strong evidence against design! As if the only acceptable sign of a universe’s being God-created would be that it was crammed with living beings from end to end and from start to finish! As if God could only create a single universe so that he would need to ensure that it was well packed!

## 1.3 Structure of the Argument

This version of the teleological argument utilizes a standard principle of Confirmation theory—the likelihood principle1This principle can be derived from Bayes’s odds theorem $$Pr(A|B) = \frac{\Pr(B|A)\Pr(A)}{\Pr(B|A)\Pr(A)+\Pr(B|\neg A)\Pr(\neg A)}$$. It can be accurately stated by what follows: Let $h_1$ and $h_2$ be two competing hypotheses. According to the Likelihood Principle, an observation $e$ counts as evidence in favor of hypothesis $h_1$ over $h_2$ if the observation is more probable under $h_1$ than $h_2$. Put symbolically, $e$ counts in favor of $h_1$ over $h_2$ if $$P(e|h_1) > P(e|h_2)$$ where $P(e|h_1)$ and $P(e|h_2)$ represent the conditional probability of $e$ on $h_1$ and $h_2$, respectively.

Let me explain just how, exactly, the likelihood principle will be utilized in light of the FT. To say that our universe is FT is to assert a relatively uncontroversial scientific claim: virtually all scientists agree—FT is a well-established fact of physics. Thus, let $e$ represent the fact of FT and let $h_1$ and $h_2$ represent the hypotheses “The best explanation of FT is Design” and “The best explanation of FT is some naturalistic processes,” respectively. I aim to show that $P(e|h_1) > P(e|h_2)$; that is to say that it is more likely that a life-permitting universe (hereafter, LPU) would exist given that an Intelligent Designer purposefully constructed it, than the likelihood that a LPU would exist given that there is only one universe and it was created by some mindless, naturalistic processes (that hypothesis—”There is only one universe and it was created by some naturalistic processes”—is hereafter denoted, NSU).

1. $LPU$ is very, very epistemically unlikely under $NSU$—that is, $P(LPU|NSU \& k) << 1$, where $k$ represents our background knowledge, and $<<$ represents much, much less than (thus making $P(LPU|NSU \& k)$ close to zero).
2. $LPU$ is not unlikely under Theism (hereafter, $T$)—that is, $\thicksim P(LPU|T \& k) << 1$.
3. Therefore, in accord with the Likelihood Principle, $LPU$ strongly supports $T$ over $NSU$.

# 2 Cases of Fine-Tuning

At this point one might be wondering, What is the evidence for FT? How do we know that a life-permitting universe is less probable than a life-prohibiting one? After all, isn’t this the only universe that we have ever observed? Who are we to say that life would be improbable in some other universe if we have never even seen another universe? Objections like these are to be expected from the uninitiated. What the objector fails to realize, however, is that even though it’s true that we have never observed any other universes, we can still be relatively confident that we have an accurate understanding of what constitutes a life-permitting universe as opposed to a life-prohibiting universe. As Andrei Linde explains:

[Th]e existence of an amazingly strong correlation between our own properties and the values of many parameters of our world, such as the masses and charges of electron and proton, the value of the gravitational constant, the amplitude of spontaneous symmetry breaking in the electroweak theory, the value of the vacuum energy, and the dimensionality of our world, is an experimental fact requiring an explanation.

The discussion below will shed some light on why this is the case as it surveys multiple individual instances of FT.

## 2.1 Fine-Tuning in the Laws of Nature

Given some other set of laws, we could still justifiably ask, If a universe were chosen at random from the set of universes with those laws, what is the probability that it would support intelligent life? If that probability is sufficiently small, then we are justified in concluding that the region of possible phase space that is life-prohibiting is much larger when compared to the total life-permitting subset. Indeed, here are some examples provided by astronomer Luke Barnes :

• If gravity were repulsive rather than attractive, then matter wouldn’t be able to compose itself in such a way as to form complex structures.
• A universe with no quantum regime at small scales will not have stable atoms—and consequently, no chemistry. It goes without saying that life in such a universe is plausibly impossible.
• If electrons were bosons, rather than fermions, then they would not obey the Pauli exclusion principle. There would be no chemistry.
• If the strong force were a long rather than short-range force, then there would be no atoms. Any structures that formed would be uniform, spherical, undifferentiated lumps, of arbitrary size and incapable of complexity.
• If, in electromagnetism, like charges attracted and opposites repelled, then there would be no atoms. As above, we would just have undifferentiated lumps of matter.

## 2.2 Fine-Tuning of the Physical Constants

To be clear, a constant (i.e., parameter) 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, $W_{r} / W_{R} << 1$. With that definition in mind, what we want to know is, Do any of the constants meet that criteria? According to Lee Smolin:

Our universe is much more complex than most universes with the same laws but different values of the parameters of those laws. In particular, it has a complex astrophysics, including galaxies and long lived stars, and a complex chemistry, including carbon chemistry. These necessary conditions for life are present in our universe as a consequence of the complexity which is made possible by the special values of the parameters.

### 2.21 Cosmological Constant $\Lambda$

The cosmological constant, $\Lambda$, is a term used in Einstein’s equation of General Relativity. When it takes a positive value, it acts as a repulsive force—causing space to expand—and, when negative, acts as an attractive force—causing space to contract. Quantum Field Theory predicts contributions to the vacuum energy of the universe that are as much as $\thicksim 10^{120}$ times greater than the observed total value. Without FT, this value is expected to be at least $10^{53}$ to $10^{120}$ times larger than the maximum life-permitting value. The smallness of the cosmological constant compared to its theoretically expected value is widely regarded as the single greatest problem confronting current physics and cosmology. Indeed, it’s been called,

arguably the most severe theoretical problem in high-energy physics today, as measured by both the difference between observations and theoretical predictions, and by the lack of convincing theoretical ideas which address it.

Nobel-winning physicist Steven Weinberg says this about the fine-tuned nature of the cosmological constant:

There may be a cosmological constant in the field equations whose value just cancels the effects of the vacuum mass density produced by quantum fluctuations. But to avoid conflict with astronomical observation, this cancellation would have to be accurate to at least 120 decimal places. Why in the world should the cosmological constant be so precisely fine-tuned?

Stanford’s Leonard Susskind—the father of String Theory—enforces the theme:

But for reasons that have been completely incomprehensible, the cosmological constant has been fine-tuned to an astonishing degree. This, more than any other “lucky” accident, leads some people to conclude that the universe must be the result of a design.

### 2.22 Gravitational Force

Gravity is the weakest of the four fundamental forces; it is weaker by a factor of $10^{40}$ than the strongest of the fundamental forces—the strong nuclear force. The fine-tuning of gravity can be seen when we quantify its strength relative to the density of mass-energy in the early universe and other factors determining the expansion rate of the Big Bang—such as the values of the Hubble and cosmological constants. Without changing the parameters of these other constants, if the strength of gravity were different—whether stronger or weaker—by one part in $10^{60}$ of its current value, then the universe would have either exploded too quickly for stars to form, or collapsed back on itself too quickly for life to evolve . This is because the density of matter—$\rho$—at the Plank time—$10^{-43}$—must have been tuned to one part in $10^{60}$ of the critical density. The critical density—$\rho_{crit}$—, being inversely proportional to the strength of gravity, can be shown to be equivalent to the FT of the strength of gravity.

## 2.3 Fine-Tuning of the Initial Conditions

Last, but certainly not least, the final type of fine-tuning that will be mentioned is that of the initial conditions of the universe. We consider these conditions to be FT due to the fact that the initial distribution of mass-energy must fall within an infinitesimally narrow range for life to occur. For the sake of space, I shall only mention what is no doubt the most outstanding aspect of the initial condition of our universe: its low entropy. According to the eminent Roger Penrose, one of the world’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” . If $x = 10^{123}$, the volume of phase space would be about $1/10^{x}$ of the entire volume! It is difficult to convey to the layperson just how absurdly small this number is. One could point out that it is scores smaller than the ratio of the volume of a proton—$10^{−45} m^{3}$—to the entire volume of the visible universe—$\thicksim 10^{84} m^{3}$. It follows that if one were playing “cosmic darts,” this would be like hitting a single, specific proton if the entire visible universe were the dartboard!

The ratio to which we are referring is not the ratio of the particles’ / fields’ being in the exact microstate that they were in, to all other possible states. Rather, it is the ratio of the state specified by the requirement that the entropy be low enough for the occurrence of life, to all other possible states. Numerous microstates meet this requirement; but compared to the number of all possible microstates, as Penrose has shown, this ratio is infinitesimal.

# 3. Explaining the Fine-Tuning

Imagine that I were to make you the following proposal. Suppose there is a $30 × 30 × 10$ room with nothing in it except a dartboard hanging on one of the walls. Suppose further that on this dartboard there is a mark whose diameter is the exact width as the dart tip (we’ll call this the “life-permitting region” and all other spots in the room we’ll call the “life-prohibiting region). Now suppose I told you that the bet is that I will go inside the room, alone, wearing a blindfold, then I will spin around in a circle for five minutes until I am completely dizzy and have lost all sense of direction. Then, I will make my throw, and I bet you \$1,000 that I will hit that single mark in the life-permitting region. Now let’s say that you take the bet. I go in, shutting the door behind me, and five minutes later it opens, revealing that the dart is exactly wear I said it would be—in that tiny, sole mark signifying the life-permitting region. So, what do you do? Do you:

(A) Accuse me of cheating and refuse to pay.

(B) Congratulate me on my outstanding shot and pay up.

Without question, anyone in their right mind will go with (A). Why? Because of all the possible places in the room that the dart could’ve landed had I not cheated, there are overwhelmingly more places occupying the life-prohibiting region than there are places occupying the life-permitting region.

• Let $e$ represent the observation that the dart is in fact stuck in the mark representing the life-permitting region.
• Let $h_1$ represent the hypothesis, “I cheated by taking off my blindfold, walking up to the board, and intentionally inserting the dart in the life-permitting region.
• Let $h_2$ represent the hypothesis, “I threw the dart exactly like I told you that I would—without cheating.”

As I said, $e$ is an observable fact; we can clearly see that the dart is in the life-permitting region. But what we want to know is, Which hypothesis is more probable, given that the dart is in the life-permitting region? Clearly, $$P(e|h_1) > > P(e|h_2).$$ Why? Because if $h_2$ were true, it is highly unlikely that the dart should be in the life-permitting region. But if $h_1$ were true, $e$ is exactly what we should expect.

This illustration is exactly analogous to the FT:

• Let $e$ represent the fact of the FT.
• Let $h_1$ represent the hypothesis, “The FT is due to the purposeful intent of an intelligent designer.”
• Let $h_2$ represent the hypothesis, “The FT is due to some mindless, undirected, naturalistic processes.”

Remember, $e$ is an observable fact; we can clearly see that our universe is FT. But what we want to know is, Which hypothesis best explains that fact? Again, clearly, $$P(e|h_1) > > P(e|h_2).$$ Why? Because if $h_2$ were true, it is highly unlikely that there should exist a life-permitting universe. But if $h_1$ were true, a life-permitting universe is exactly what we should expect.

# References Cited

Notes   [ + ]

 1 ↥ This principle can be derived from Bayes’s odds theorem $$Pr(A|B) = \frac{\Pr(B|A)\Pr(A)}{\Pr(B|A)\Pr(A)+\Pr(B|\neg A)\Pr(\neg A)}$$
Posted in Cosmology, Natural Theology.