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In the previous post of this series, I said that Christianity can explain the two axioms of science starting from the attributes of God, whereas atheism, by starting from nothing, can explain nothing. Therefore the axioms of science counts as very strong evidence for Christianity.

Basically, the atheistic explanation is:
Step 1: There are no spirits or gods. (Atheism)
Step 2: ????
Step 3: Therefore the universe operates in a consistent, uniform manner (Axiom 1), and humans can accurately learn about how the universe operates (Axiom 2).

Whereas the Christian explanation is:
Step 1: There is a God, who is revealed in Jesus Christ. (Christianity)
Step 2: God created the universe to reflect his faithfulness, logic, wisdom, understanding, and goodness, so that we may look upon the universe and learn more about him.
Step 3: Therefore the universe operates in a consistent, uniform manner (Axiom 1), and humans can accurately learn about how the universe operates (Axiom 2).

In the rest of this post I'm going to address some common objections and counterarguments.

Now the problem for atheism comes from the fact that it lacks any explanatory power. So one may attempt to save atheism by adding on philosophical postulates on top of it which would allow it to predict the axioms of science. The easiest way to do this is to simply start with the desired conclusion, by modifying the atheistic explanation to read:

Step 1: There are no spirits or gods (Atheism). And the universe operates in a consistent, uniform manner (Axiom 1), and humans can accurately learn about how the universe operates (Axiom 2).
Step 2: See first step.
Step 3: Therefore the universe operates in a consistent, uniform manner (Axiom 1), and humans can accurately learn about how the universe operates (Axiom 2).

In fact this is precisely what metaphysical naturalism (aka scientific materialism, or scientism) does. You may think that I'm making a caricature here, but I'm not. Seriously, go read that linked Wikipedia article on metaphysical naturalism, and look at the definition. It's literally just a logical conjunction of the ideas of science and "there is nothing else".

But if we're trying to do science, and we're willing to accept this modification, why not simply abandon atheism as a postulate? It is certainly no part of science, which does not rely on it and can operate without it. Occam's razor demands that we cut atheism out. Why add on a superfluous postulate which contributes nothing?

I'm going to make this point again, because it's important: adding atheism as an axiom does absolutely nothing for science. It does not allow science to accept or reject any new hypothesis. Science functions exactly the same way as it did before. Atheism is therefore an entirely superfluous axiom, and Occam's razor demands that we cut it off from our list of axioms.

Doesn't the same apply to Christianity? Wouldn't Christianity also be a superfluous axiom if added to the axioms of science? Yes, absolutely. That's why the axioms of science are called that; because they're all that you need in order to start doing science. This is why both Christian and atheists can be scientists. It's also why the axioms of science should be treated as evidence regarding Christianity and atheism, rather than trying to add Christianity or atheism as an axiom of science.

Therefore simply attaching atheism to science as an axiom (as in scientism or metaphysical naturalism) fails. After applying Occam's razor, we're left with only the two original axioms of science, with no initial commitment to either Christianity or atheism. It is at this point that we must ask, "can these axioms themselves be explained? Can they themselves serve as evidence for a deeper truth?" That is precisely the question that we've answered in the previous post, and the evidence falls firmly on the side of Christianity.

Next, an atheist may say, "If the Christian God exists, then he can perform miracles, which are violations of the laws of nature. In that case the universe would not be consistent or uniform. Therefore Christianity predicts the violation of one of the axioms of science".

My answer is that this is a terrible definition of "miracle". My own definition, (which the atheist is obligated to use, as we are speaking about my own belief system) is that miracles are NOT defined as violations of the laws of nature, and that is NOT how God performs miracles. God almost certainly works within the laws of nature, as he created them to reflect his character and declared these laws to be good. But does this not still allow for the possibility that God could, in principle, violate the laws of nature and therefore violate the consistency and uniformity of nature? Well, even if God does violate the laws of nature, he would do so very rarely, in very subtle ways, for the reasons I just gave. Then his actions would be below the threshold of experimental verification, and therefore go undetected by scientists. Science would then operate under the assumption that "the universe operates in an almost perfectly consistent, uniform manner" as one of its axioms, which would be functionally identical to the science we have now. Basically, I'm saying that even if the earth is round, an experimentally undetectable, imperceptibly small curvature of the round earth means that you can still have a functionally flat driveway. In order to contradict me, the atheist would have to say that in order to have a functionally flat driveway, the earth must be flat.

However, it's true that any system that regularly produces violations of the laws of nature would be ruled out by considering the axioms of science. This rules out various forms of animism and paganism. It also rules out the parody versions of God, where he is viewed as a magic genie who must work against the laws of nature (when in reality God is actually the Creator who made those laws). All this only strengthens the Christian position, by eliminating rival positions.

An atheist may then say, "Your conception of the Christian God is too complex. His complexity means that you could have simply tailor-made your God by choosing his attributes so that he fits with the axioms of science. An explanation should not be more complicated than the thing it explains. In Bayesian terms, the complexity of your God reduces his prior probability down to almost zero, so that even after successfully explaining the axioms of science, the probability of God existing is still almost zero".

First, I'd like to get some minor issues out of the way: On the issue of tailor-making God, historically this simply isn't how it happened. The doctrines about God and his revelation in nature came before science was discovered, and these preexisting doctrines were found to be in agreement with the axioms of science. Consider how many different ways Christianity could have gotten this wrong: before the discovery of science, Christianity might have said that nature is so corrupted that it is dangerous to study science. It may have said that God is so far above humans that it would be useless to try to understand his creation. It may have said that (as certain heresies have said) the Devil created the universe, and therefore science should or could not be attempted. Yet Christianity avoided these errors and came to the correct doctrine which enables science, before science was discovered. The doctrines concerning God and his revelation in nature came first, then science came second. When science arrived, it validated the preexisting doctrines, thereby serving as evidence for those doctrines and for Christianity as a whole.

On the issue of Bayesian prior probabilities, it is well known that assigning objective priors are basically impossible without the having all the relevant background information for the person and the issue in question. This is why Bayesian probabilities are often interpreted as personal, subjective probabilities, and it's also why I chose to focus on the evidence (Bayesian likelihood ratio) rather than the priors. I'm simply assuming that anyone who chooses to spend their time reading my posts has a prior probability for Christianity of, say, greater than one in a million as a result of whatever background information they would personally have.

On the issue of low-probability priors for complex explanations: this is not an issue, if the evidence is strong enough. Nobody in the ancient era would have believed that everyday materials you touch and feel were made of specific combinations of atoms, which themselves are quantum mechanical arrangements of electrons and nuclei. They would have had a very small prior probability for that specific position, because they would have thought it too complex. But we are now advanced enough in our sciences that there is ample evidence for that position, so we accept it as being true. We have already seen that the axioms of science counts as very strong evidence for Christianity. By the time that we're done with this series, we will see that there is ample evidence for Christianity, enough to overcome its supposedly low prior probability. Of course, we cannot make firm statements about this without getting quantitative, and there is nothing to be done for the person whose prior probability for God is zero.

But most importantly, there is something that trumps all the issues mentioned above: the idea of divine simplicity. The Christian God is not complex. He is simple, without parts, with no "free parameters" to adjust, and with no contingency upon any other thing. As Thomas Aquinas explains, God is infinitely simple, therefore he appears infinitely complex to finite minds.

If that last sentence from Aquinas seems like just fancy words, consider that this kind of divine simplicity is exactly the same kind that's remarkably paralleled in math and science. Consider a fractal: it is infinitely complex to someone who regards it as a set of pixels on a plane, but simple to those who know the formula and the procedure for generating it. Consider also the laws of physics: as I said before, they are complicated to the uninitiated, but elegant and simple once you get past the infinite number of infinities upon which they are mathematically built. This is exactly what you'd expect if mathematics and physics were made by God as a reflection of his own infinite simplicity, serving as yet additional evidence for God and his simplicity.

To further see how God is simple, consider my own fundamental postulate, which is just one line. Consider also the answer to question four of the Westminster Shorter Catechism, which merely reads, "God is a Spirit, infinite, eternal, and unchangeable, in his being, wisdom, power, holiness, justice, goodness, and truth". Yes, it's true that English sentence lengths don't translate directly to simplicity, but at the core of these descriptions of God is a simple idea which nevertheless accounts for all that God does.

There is more I have to say about God's infinite simplicity, which I hope to get to eventually in a future post.

Lastly, one may ask "Why the Christian God, as opposed to the God of some other religion?" This is a good point, and one that I will admittedly not address fully in this series on science as evidence. Science is limited; there are things that it cannot tell us upon considering it as evidence. This series can only narrow down the possibility for God to be one who has the following characteristics: he is transcendent (beyond science and nature, so as to be able to control them), infinitely simple (which means he's a monotheistic God), and a caring creator (who made the universe to reveal himself to us). This is still very significant - by considering science, we'll have pretty much eliminated atheism, and narrowed down our possibilities among the many gods to essentially the Abrahamic God.

That, then, is the limits of science considered as evidence. Again, that is exactly what you'd expect if Christianity is true - science is valuable, but limited in what it can tell us about the universe and about God. It got us this far, but we'll need a different kind of evidence to go further. In order to know what God is really like, in order to distinguish between the Abrahamic religions, we must go to the kind of evidence that can make that distinction. We must go to Christ himself, who can tell us beyond what a creature can tell about a creator, and hear what God has to say for himself: for Christ is God himself incarnate as a human being.

In the next post of this series, I will continue the series and consider the trends in science as evidence between atheism and Christianity.