The Best Argument for God's Existence

The Bayesian Fine-Tuning Argument

Contents

1. Introduction
2. Defining God
3. Understanding Bayesian Epistemology
4. Understanding Fine-Tuning Arguments
5. The Bayesian Fine-Tuning Argument
6. Why it Outperforms Rival Arguments
7. Addressing a Potential Criticism: The Bayesian Problem of Evil
8. Verdict 

INTRODUCTION

"You don't answer the question, you answer the questioner."—Dr. John Lennox

I think Lennox—a renowned mathematician and theologian—is right to say that the strongest argument for God's existence depends on the person; he does an excellent job of explaining why. And as a truth relativist, I already have to agree by default. So, instead of trying to find the best argument for everybody (or even for the majority of rational agents), I will just write about the strongest argument for me personally. It is the Bayesian fine-tuning argument.

Disclaimer: This is by far the longest blog I have written yet, and I apologize in advance for the length. The only reason I wrote so much is that I am intensely passionate about philosophy of religion, and the arguments for and against God's existence are the branch of philosophy of religion that I am most intensely passionate about. So, this might just be my greatest pleasure in life. For example, I have spent two years thinking for many hours a day about concepts associated with Anselm's Ontological Argument for God's existence, my favorite argument of all time. (Disclaimer inside a disclaimer: this blog does not defend Anselm's Ontological Argument for God's existence). If I wrote a blog about that, it might just be two or three times longer than this one!

DEFINING GOD

Before analyzing any argument for God's existence, one must commit to a specific definition of God. Only in that way can one clearly delineate between atheism and theism. Traditionally, God is defined as a metaphysically necessary being that is:

1. All-powerful: capable of doing anything that is logically possible to do (assuming that God cannot violate the laws of logic, and that God cannot inflict self-pathology, such as bringing about His own non-existence);
2. All-knowing: affirming all true propositions and denying all false propositions;
3. All-good: working and behaving exactly as intended—that is, having absolutely no privations.

I will work with this definition. I am not opposed to permissible tinkering—the practice of modifying the definition of God without losing a proper or intellectually stimulating concept of God in the process—but I will conform to said definition for the sake of brevity.

UNDERSTANDING BAYESIAN EPISTEMOLOGY

Before I articulate the Bayesian fine-tuning argument for God's existence, I will first articulate Bayesian epistemology and fine-tuning arguments separately.

Conditional probability is simply the probability of one event occurring given that another has already occurred. Bayesian epistemology is a philosophy for calculating this conditional probability. The word "Bayesian" inherits its name from Thomas Bayes, an intellectually heroic English statistician and Presbyterian minister. (As a brief historical aside, the majority of early empirical science comes from Protestant Christians, especially those influenced by William of Ockham's teachings. Calvinism is an Ockhamist fork of Protestantism, and Presbyterianism is a fork of Calvinism).

Bayesian epistemology is not the only philosophy for calculating conditional probability, just one of them. Something like conditional empiricism would probably be considered the major competing philosophy for calculating conditional probability. Indeed, Bayesian epistemology and conditional empiricism disagree on exactly how conditional probability should be calculated.

With Bayesian epistemology, the idea is that you calculate the probability of the consequent given the antecedent by multiplying the probability of the antecedent given the consequent by the prior probability of the consequent, and then by dividing that product by the prior probability of the antecedent. Generally, the antecedent is the evidence for a hypothesis, and the consequent is your degree of confidence that the hypothesis is true.

That is to say:

P(H|E) = (P(E|H) * P(H)) / P(E)

Where E is the antecedent (the evidence) and H is the consequent (your degree of confidence in the hypothesis).

The complete formula—Bayes' Theorem—can also be written as:

P(B|A) = (P(A|B) * P(B)) / P(A)

Bayes' Theorem has a wide range of applications, ranging from weather forecasting to medicine to cybersecurity. Most importantly for this discussion, Bayes' Theorem has profound applications in the philosophy of religion!

I expect this information to be somewhat dense for one sitting. So, read it carefully, read it multiple times, and rejoice in the fact that understanding the Bayesian fine-tuning argument would be nearly impossible without knowing these fundamentals of Bayesian epistemology.

UNDERSTANDING FINE-TUNING ARGUMENTS

Fine-tuning arguments belong to a general family of arguments for God's existence that can be described as empirical arguments. That is, they observe an effect P and purport the probable cause Q to be God. Aside from the fine-tuning argument, other empirical arguments include, but are not limited to, design arguments, cosmological arguments, and historical arguments (e.g., the Kuzari principle).

The fine-tuning argument in particular assumes that scientific phenomena—particularly facts about physics and initial conditions of the universe—are evidence of fine-tuning, and that fine-tuning is evidence of God. It claims that certain fundamental physical constants and parameters of the universe fall within a very narrow range that allows for the existence of life.

If even one parameter—something like the strength of gravity, the electromagnetic force, the weak nuclear force, the strong nuclear force, the difference between the mass of the neutron and the mass of the proton, or the rate of acceleration of the universe's expansion (also known as the cosmological constant)—were modified even just a tiny bit, then the universe as we know it would not be able to support any form of life. For example, if the rate of acceleration of the universe's expansion were a tiny bit faster, the universe would expand too rapidly for galaxies, stars, and planets to form at all. And if it were a tiny bit slower, the universe would collapse far too soon for life to have time to evolve.

Because the probability of these constants falling into this life-permitting range by chance seems vanishingly low, the argument concludes that God is the best probable cause of the universe’s physical structure.

This is a mouthful, but it will be very helpful for understanding the rest of this blog. Now, I will transition my focus to articulating the Bayesian fine-tuning argument itself.

THE BAYESIAN FINE-TUNING ARGUMENT

Do you see where I said that scientific phenomena are assumed evidence for fine-tuning, and that fine-tuning is assumed evidence for God? Well, the idea of specifically Bayesian fine-tuning is that the more scientific phenomena that we discover, the greater the probability of the existence of God.

This idea has immense power! The Bayesian fine-tuning argument is the only argument I am aware of where the case for God's existence gets stronger as science advances. This is unlike the traditional design argument, where the case for God's existence often gets weaker as biological science advances. Couple this with the estimation that we currently only understand roughly 1% of reality, with the remaining 99% misunderstood or unknown. And to top it off, our current body of science is already enough to make the case that the Bayesian fine-tuning argument for God's existence results in something like a 99.99% chance (specifically, with 144 leading 9s after the decimal point) that God exists. If our body of science completed 99% of reality instead of just 1%, that probability for God's existence would then become astronomically greater than this already-massive probability!

Let us go over how I got this number:

I took the formula P(B|A) = (P(A|B) * P(B)) / P(A)

My P(A) is the prior probability of the observed scientific phenomena existing. I assigned this number to be 0.5 * (1 - 10^-144) + 0.5 * 10^-144, meaning that the observed scientific fine-tuning is virtually impossible without God.

My P(B) is the prior probability of God existing before considering the evidence. I assigned this to be 0.5, meaning a 50/50 chance that God exists or does not exist. In other words, a state of pure agnosticism.

My P(A|B) is my estimate of how probable the scientific phenomena would be if God exists. I assigned this number to be 1 - 10^-144, meaning that the observed fine-tuning is virtually certain if God exists.

These assigned values are preferential to some extent. For example, a person who feels almost certain that God does not exist might assign P(B) to be a tiny number like 1 * 10^-100 instead of 0.5. With this in mind, I don't see the point in mathematically working out exactly how I got my numbers for P(A) or P(A|B) here. But the general idea is that I got those numbers by looking at a list of different phenomena which require an extremely narrow range for this universe to support life, and I looked at exactly how narrow those ranges are. The more phenomena we discover in the future, the more extreme the numbers become for P(A) and P(A|B).

WHY IT OUTPERFORMS RIVAL ARGUMENTS

In my view, the fine-tuning argument avoids the pitfalls that the design argument and the Kalam cosmological argument have to suffer. Unlike the design argument, which gets more obsolete as science progresses, the fine-tuning argument uniquely gets stronger as science progresses. (Even the cosmological argument doesn’t necessarily get stronger as science progresses, although it is arguably less affected than the design argument in the face of scientific advancement).

Unlike the cosmological argument, which rigidly asserts that whatever begins to exist has a cause, the fine-tuning argument is flexible; it can work with that assumption, or it can work with the assumption that whatever exists has always existed. Our modern understanding of physics reveals that the constants of nature—such as the gravitational constant, the mass of each atom, the weak and strong nuclear forces, and the cosmological constant—fall within an infinitesimally narrow range required for a life-permitting universe. For example, if the strong nuclear force were just a tiny bit stronger, then stars would never form because hydrogen would fuse too easily. If the strong nuclear force were a tiny bit weaker, then no heavy elements (e.g., iron, cobalt, or copper) would be able to form.

To reiterate, the beauty of the fine-tuning argument is that it uniquely gets stronger as science progresses. Why? Because there is a robust way to understand conditional probability—namely, Bayesian epistemology—and the fine-tuning argument is amenable to Bayesian formalization in a way that no other argument for God’s existence is shown to be.

By using Bayes’ theorem, we can compare the likelihood of the evidence (E: a life-permitting universe) under two hypotheses: 1) Naturalism (N); and 2) Theism (T). Under naturalism, the values of the life-permitting constants of the universe are condemned to be brute facts or random outcomes of physical processes. Given the vast range of theoretically possible values and the narrowness required for all constants that allow for life to occur, the probability that they would all fall into the life-permitting ranges is astronomically low. Thus, one can rationally estimate the probability of a life-permitting universe, given naturalism, is approximately 0.

Under theism, which posits God, life would have intrinsic and objective value. Namely, moral, aesthetic, and intellectual worth. If God exists, then he would have a reason to actualize a universe where life can exist. Even though he could create a universe without these specific constants (maybe a nonphysical realm), the probability that he would create a physical, life-permitting universe is close to nonnegotiable. Thus, P(E|T) >> P(E|N). That is, the probability that a life-permitting universe exists, given theism, greatly exceeds the probability that a life-permitting universe exists, given naturalism.

And the more that we advance our understanding of science, the more that probability increases! Because historically, these findings have always provided further evidence for the fine-tuning of our universe. Colloquially, many people regard new scientific findings to be damning for theism in the sense that things previously explained as God’s doing can be replaced with scientific explanations. But the fine-tuning argument turns this colloquialism completely on its head.

ADDRESSING A POTENTIAL CRITICISM: THE BAYESIAN PROBLEM OF EVIL

In maintaining that the fine-tuning argument is compelling, one challenge is to address what I would consider to be its most potent Bayesian rival: A Bayesian treatment of the evidential argument from evil. I anticipate its proponent may argue that if Bayesian reasoning raises the probability of God’s existence, then—by that same line of thinking or reasoning—Bayesian epistemology implies that the existence of gratuitous suffering dramatically lowers the probability of God’s existence.

The critic can calculate or even reason that the probability of gratuitous evil given naturalism is much higher than the probability of gratuitous evil given theism. Because if the universe is governed by blind forces, then random tragedy is expected. In contrast, if God exists, we would expect him to be powerful, knowing, and good enough to limit gratuitous evil. Worse yet—it is reasonably assumed that the more gratuitous evil we have, the higher the probability of naturalism.

To defend the Bayesian fine-tuning argument against the Bayesian problem of evidential evil, I will respond by showing that the probability of seemingly gratuitous evil given theism is not as low as the critic assumes. If it is assumed that God’s primary goal is hedonism—that is, the maximization of pleasure and the minimization of suffering—then evil is indeed a defeater of the Bayesian fine-tuning argument.

However, if God’s goal is the creation of “significant” beings—creatures capable of moral and intellectual significance, and meaningful relationships—then our reality must be structured to support this. As Alvin Plantinga argues, a world containing free creatures who voluntarily choose the good is morally significant compared with a world where all free creatures automatically choose the good. Many consider this to be an adequate explanation for gratuitous human evil, but not for gratuitous natural evil.

In order to explain gratuitous natural evil without invoking demons micromanaging natural disasters or something to that effect, I will borrow Plantinga’s principle to point out how a world of natural evils facilitates intellectual significance compared with a world without any natural dangers. If God’s goal is the creation of significant beings, then agents need intellectual significance. And we grant this by having a world that structurally allows for natural evils (e.g., natural disasters, viral pandemics, casualties from fires) to occur.

That a world is governed by regular and natural physical laws where “random” tragedy occurs, is needed for agents to be capable of learning, planning, and conquering their environment in a way that is intellectually significant. If God prevented natural evil, then the causal regularity of the world would collapse. And this kind of regularity is both evident and needed for the world to be fine-tuned.

For these reasons and no less, I find the concept of intellectual significance to be compelling for supporting a Bayesian fine-tuning argument over a Bayesian problem of evidential evil. But on top of that, the fact that the Bayesian fine-tuning argument gets stronger as science advances suggests that maybe evidential evil is actually there for us to get closer to finding and understanding God’s existence. Because evidential evil drives us to advance scientifically, and this scientific advancement shows that reality is more fine-tuned than once believed—so much so that the best probable cause is God. In this way, the fine-tuning of the life-permitting constants is not limited to survival, but entails creating rich moral and intellectual struggle that is meaningful. Hence, with all things considered, evidential natural evil is intelligible within the probability of a life-permitting universe given theism.

Verdict

I find the Bayesian fine-tuning argument for God's existence to be the most compelling, because: (1) the combination of the facts that the case for God's existence gets stronger as science gets stronger, that we currently only understand 1% of reality, and that we have enough understanding of reality for a Bayesian calculation to yield an astronomically high chance of God's existence; and (2) the fine-tuning argument is the only argument I know of that provides a minimalistic yet perfectly sufficient solution for the dreaded problem of natural evil that theologians have never been able to answer without assuming that all gratuitous natural disasters are willed by demons.