KindiakMath

Let’s introduce the God question using modern science. In some sense, the existence of God can be formulated as a scientific hypothesis.

The fool says in his heart, “There is no God.” They are corrupt, they do abominable deeds; there is none who does good. [Psalm‬ ‭14:1‬]

Remark 1. Since I am unashamedly Christian, I will be quoting Scripture throughout these blog posts. However, I will not use them as part of my arguments until I have established that the Scriptures are the true words of God—a central goal in these blog posts as well.

In the modern age, it is common to look at the rationality of science and mathematics and conclude that the world can be completely rationally explained away using purely physical and mathematical reasons. Therefore, it is understandable to formulate the theory “there is no God”. After all, if there were a God, we would expect the presence of more God-like activity that disrupts the workings of natural science.

How long, O LORD? Will you forget me forever? How long will you hide your face from me? [Psalm‬ ‭13:1‬]

Therefore, if the latter is more likely to be false, then so is the former. Here, of course, by “God” we mean a divinely intelligent being that has designed life here on earth to exist. This expectation is commonly referred to as the divine hiddenness problem, and itself has its own plethora of explanations.

We call the statement “there is no God” the null hypothesis—the understandable default explanation, and its competing (i.e. alternative) hypothesis “there is a God”. The fine-tuning argument‘s fundamental thesis is a hypothesis testing argument—if we assume the null hypothesis (i.e. “there is no God”), then the probability of observing a life-permitting universe would be astronomically small, and therefore, it is reasonable for us to reject the null hypothesis, thereby concluding that the alternative hypothesis holds (i.e. “there is a God”).

Axiom 1 (Hypothesis Testing). Make the following definitions:

• a default proposition known as the null hypothesis,
• a competing alternative hypothesis ,
• a failure threshold known as the level of significance,
• the -value .

The principle of hypothesis testing states this: if , then there is sufficient evidence to reject and conclude that is true.

Theorem 1. Under Axiom 1 and a threshold of , there is sufficient evidence to conclude that God exists.

Proof. To justify the probability claim, suppose the null hypothesis holds, i.e. there is no God. Then by definition, there is no divinely intelligent being that has created our world. Therefore, our world arose from pure chance, and it is not unreasonable to assume that the various fundamental constants of physics arise independently from one another.

The astrophysicist Luke Barnes, was able to supply the following list of well-established instances of finely tuned constants and quantities:

• 2 constants for the Higgs field: the vacuum expectation value (vev) and the Higgs mass,
• 12 fundamental particle masses, relative to the Higgs vev: 6 quarks () and 6 leptons (),
• 3 force coupling constants for the electromagnetic (), weak () and strong () forces,
• 4 parameters that determine the Cabibbo-Kobayashi-Maskawa matrix, which describes the mixing of quark flavours by the weak force,
• 4 parameters of the Pontecorvo-Maki-Nakagawa-Sakata matrix, which describe neutrino mixing,
• 1 effective cosmological constant (),
• 3 baryon (i.e., ordinary matter) / dark matter / neutrino mass per photon ratios,
• 1 scalar fluctuation amplitude (),
• 1 dimensionless spatial curvature ().

These constants are among the bare minimum required for a universe to support life as we know it.

Barnes estimates that the probability* that these quantities are suitable to support life, assuming the null hypothesis, is not more than . That is, (this is the probability of boarding a plane that crashes given existing rigorous airline safety standards; see below), we have sufficient evidence to reject the null hypothesis in favour of the alternative hypothesis. What is this alternative hypothesis? That there is a God.

Here’s the summary of the fine-tuning argument (also known as the teleological argument):

• Premise 1. If there is no God, then the life-permitting physical constants arose by pure probability.
• Premise 2. The probability of the physical constants being life-permitting is extraordinarily small.
• Conclusion. There is sufficient evidence to reject the null hypothesis that “there is no God” and conclude the alternative hypothesis that “there is a God”.

Remark 1. Technically, Barnes computed the likelihood, which though technical, can be thought of as a proxy for probability in this discussion. Furthermore, this likelihood is relative to the alternative hypothesis in the following sense: the likelihood that constants required for a universe to support life given the null hypothesis hypothesis is times smaller than that given the alternative hypothesis.

Remark 2. Note that Axiom 1 doesn’t mathematically prove that holds. All it says is that the probability of wrongly rejecting (thereby concluding that holds) is upper-bounded by the failure threshold . In particular, all the fine-tuning argument has established is that if God doesn’t exist, then the probability of obtaining a universe that is fine-tuned for living is extremely, extremely, extremely small. Is it *technically* possible that God doesn’t exist? Absolutely. But its probability is miniscule, and upper bounded by our failure threshold.

The LORD by wisdom founded the earth; by understanding he established the heavens; byhis knowledge the deeps broke open, and the clouds drop down the dew. [Proverbs‬ ‭3:19–20‬]

You might argue, “In this case, you’re are still concluding that God exists without proof.” That is true, even though the evidence certainly points to God. Practically speaking, however, such conclusions are not automatically rendered false. In fact, the evidence we have presented leads to the conclusion that the proposition “God does not exist” is false is extremely small and thus exceedingly rational to reject, leading do a very rational conclusion that “God exists”.

You and I make conclusions without proof all of the time in order to get on with life. For example: consider the statement “this plane will not crash”. Is it technically possible that this statement is false? Sure. However, given the rigour in air travel standards, the probability of an air crash is exceedingly small (an upper bound of ). For people who understandably are afraid of plane crashes, we can use other real-life examples to make a similar case mutatis mutandis.

Therefore, we set our failure threshold to be . Using the probabilities obtained from computing the fundamental constants, we obtain that

Therefore, with sufficient evidence, we reject the proposition “there is no God” and conclude its alternative—”there is a God”.

Once again, while this inference principle does not mathematically prove anything, we use this inference principle all the time, and in our air crash example, conclude that if we are willing to ride planes on the probabilistic conclusion that “this airplane will not crash”, we should conclude that “God exists”, at least plausibly if not actually. The ontological argument will strengthen this claim for us.

As a quick aside, the Kalam cosmological argument follows a similar thought process:

• Premise 1. Everything that begins to exist has a cause.
• Premise 2. The universe began to exist.
• Conclusion. The universe has a cause.

Furthermore, by analysing the various properties of the universe, this cause must be timeless, spaceless, immaterial, causeless, and powerful. We call this cause “God”. Premises 1 and 2 are considered true using a similar hypothesis testing procedure.

Finally, the “God” defined using the fine-tuning argument and the Kalam cosmological argument must be the same “God” as defined in the ontological argument for God, since the latter defines “God” as the maximally great being.

Remark 3. While these arguments credit God for being the chief designer and originator of the universe as we know it, they speak of nothing pertaining God’s methodology or design process. The theological basis for modern science, therefore, is not that science “replaces” God in any means, but that God uses highly specific scientific and mathematical principles to design the universe. The general pushback from atheists to theists in using “God” as the explanation is an empathizable one—many theists arrogantly use “God” as a placeholder for “I don’t know how it happened,” incurring not only the God-of-the-gaps argumentative fallacy, but more crucially denying an intellectually honest response to the atheist’s challenge.

As such, I call this explanation for God a “proof” by hypothesis testing. It doesn’t *guarantee* that God exists; only that it strengthens the case that the existence of God is at least plausible. But even if we have established the theoretical and empirical case for God, how can we narrow it down to the Christian God? This is where we need to go into the central claims of Christianity, and proceed carefully yet clearly. The central question we will aim to answer affirmatively is this: is Jesus really God?

We will return to Jesus in a moment. For now, the plausibility of the existence of God seems trivial, but coupled with the ontological argument, actually guarantees the existence of said God. This argument we will explore next.

—Joel Kindiak, 30 Sept 25, 1529H