Craig, Seidensticker, and the Argument for God`s Existence From Mathematics

This post is republished from a former blog of mine back in 2015. I decided to publish it here out of laziness.

William Lane Craig brings out new argument for the existence of God, and Bob Seidensticker of the blog Cross Examined: “Clear Thinking” about Christianity comes out with a rebuttal here and here. I should begin by stating that the argument is not all that new, contrary to Seidensticker’s claim, Craig published it back in 2013 (which you can read here), first applying it in a debate with Alex Rosenberg; but this claim is nit-picky.

The first claim made is “This Argument from Math is just a variant of the Transcendental Argument”, which is not the case. The Transcendental Argument tries to prove the existence of God through the ontology of abstract concepts (mainly the laws of logic) by divine conceptualism (the view absract entities are thoughts in the mind of God) as the only conceivable option. The Argument from Mathematics is related to epistemology and not ontology. Namely, theism answers how the human mind can comprehend the universe through math better than naturalism. In that sense, it is closer to the design argument for God’s existence in explaining a feature of the world.

The next claim he makes is this argument only appears to succeed because it is confusing. The problem is that confusion is person relative. I could be very confused about equations that mathematicians make, but does not mean they are wrong. It might be that I’m accidentally overcomplicating the problem.

Lastly, it is called a deist argument. I, agree that design and design-like arguments are notoriously bad at getting us to the properties of God. However, it can still be used as a proof against naturalism, which isn’t a bad, since it places minds as more foundation to the material world. The next objections however prove to be more formidable,

Reality is what it is, and the math adapts as necessary. If one formulation of a law does a poor or incomplete job of explaining the physics (say, when Newton’s law of gravity didn’t work perfectly in environments with extreme gravity), the math can be changed(in this example, by adding corrections to account for General Relativity).

However, we should ask why any mathematical formula works at all. Why reality should fit itself to how humans think. I suppose Seidensticker could claim that we evolved these capabilities by environmental conditioning, but we could just respond with the same line of reasoning,

Reality is what it is, and our physiology adapts as necessary for those conditions. If a mathematical adaptation does a poor or incomplete job of breeding environmental benefits (say, when we can’t produce environmentally comprehending math), the dominate adaptations can be changed (in this example, by adapting traits that are better for bartering cultures, requiring little math).

Evolution cannot account for our use and understanding of high level math that can explain the universe because it does not need entail we ought to have these capabilities. Rather, even on evolutionary grounds, it is still a happy coincidence.

Wigner said that Newton’s law of gravity “has proved accurate beyond all reasonable expectations.” But what are these reasonable expectations? That the universe is mathematically describable is surprising only if we expect it to be otherwise (I’ve discussed a related topic here). Should we expect the same laws of nature but different fundamental constants? Different constants in different parts of the universe? Different laws? Or maybe a structure so chaotic that no equation would be accurate for more than an instant? Why are any of these possibilities more expected than what we actually have? What’s unreasonable about how math works in our world? Once we study hundreds of other universes, we’ll get a sense of what they look like to compare with our own, but without this data, we have nothing to go on, and we have no grounds on which to formulate “reasonable expectations.”

How about human beings with a very different evolutionary history, like stated above? Or, we could expect a universe with no life giving constants exists to form animals with mathematical thought. Why ought we expect the fictions we write to be as pragmatically helpful? We have other fictions that pale in telling us anything about the universe.

Furthermore, considering there are other adaptations that exist and are effective, without them requiring either a pre-existing fiction coincidentally working, or abstract and non-causal facts interacting with us, how does math arise as a discourse? On a Naturalist world-view, why ought I expect such questions to be answered?

Math gives neat, simple answers where it does, and it doesn’t where it doesn’t. Our awe at math’s effectiveness may be due to confirmation bias, in which we count the hits and ignore the misses. We marvel at the places where math provides a neat solution and ignore those where it doesn’t. And consider whether God or reality calls the shots. Take just one primitive truth in our reality, 2 + 2 = 4. Could God have made it anything different? If so, I await the evidence. If not, what role is left for God if reality defines the fundamentals from which the rest of math follows?

God is not the truth maker of 2+2=4, rather the question asks why are math formulas effective in granting us knowledge of the world. 2+2=4 (if a fiction that is) is as right as saying “Spider-man lives in New York” While both are true in the discussion of the fiction, only one will ever have practical significance in creating scientific theories in the first place.Does math fail, sure when we do not have an applicable theory whose explanatory power breaks, but there are more models with more power.

He doesn’t care that the consequences of his explanation are either untestable (such as the existence of heaven) or have been tested and failed (such as answered prayer). He doesn’t care that his claim isn’t even falsifiable.

Neither are the laws of logic, they are true because of the impossibility to the contrary. There is more than one way to come to a knowledge based conclusion other than science.

He doesn’t care that “God did it” raises more questions than it answers — questions about who or what God is, his motivations, how and why he created the universe, and so on.

Well, it’s not like we can formulate a discipline of philosophy of religion to either show such a being as incoherent, or explicable…oh wait, we have that.

He doesn’t care that whenever science has found an explanation, it’s always natural.

Science has accepted zero supernatural explanations.

What about the move from Aristotelian causality to occasionalism in the 17th century? To quote Menno Hulswit,

The history of the development of this outlook is extraordinarily complex, and was influenced by a web of both theological and scientific beliefs. However, the idea that causation involves determinism does not have a scientific origin, but a theological one. In spite of differences in detail, the arguments for determinism in the writings of Descartes, Hobbes, Spinoza and Leibniz, are very similar. In no case did the conclusion that all things are determined receive its justification from a concern with empirical fact. The idea was that all things are causally determined because, and only because determinism is entailed in the idea of God’s omnipotence and omniscience. If God knows everything and can do everything, whatever is must be. For the same reason, it is misleading to say that any finite agent is a genuine cause, that is to say, an active initiator of a change. Only God can be the cause of anything [1]

Here, physics depended on God in their early causal models. It was short lasting, but still an example.

He doesn’t care that, when you look around at God’s project with its natural disasters, parasites, childhood illnesses, and so on, it looks more like an experiment of the kid who burned ants with a magnifying glass, unaccountably given omnipotence, than the design of an all-loving deity.

Clearly, no theist has ever put up a defense against the problem of evil.

He doesn’t provide evidence that his god even exists.

This is the evidence.

No, Craig says, his answer has great explanatory power, “unless you’re closed to theism.”

Did you see that clever role reversal coming? If there’s a problem with embracing Craig’s position, it must be that the atheist is simply closed-minded! Or, possibly you have rational reasons to provide to being closed to theism, such as the problems of evil that Craig admits require an answer.

We see cracks begin to form, however, when he admits that his isn’t an empirical explanation but rather a metaphysical one. But then what good is it? I mean, besides advancing Craig’s pet theory?

Explaining the preconditions for empirical observation I would say.

I will end by pointing out that Seidensticker’s right. He’s clearly a terrible critic of the argument, but he is right. Mathematical knowledge is defensible from the atheist position. If I was an atheist, I would say that math is effective because the universe is coherent (obeys the law of non-contradiction) and so are the scientific models that we epistemologically attach ourselves to. They match up, but are still in a process of either falsification or augmentation to better fit the data and the feats we preform.

So, why bother writing such a long response to an underwhelming argument? The reason is that Saint Augustine was unfairly quoted and showing Seidensticker to be inept at refuting Craig was a cathartic way of pointing this out.

Unfortunately, the only “popular” quote we read from Augustine on mathematics is significantly skewed. Morris Kline (1908–1992), mathematics historian attempted to smear Augustine and the Christian faith he represented. Here is what Kline said

Augustine said (in living color): The good Christian should beware the mathematician and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of hell.”

Looking up the source (De Genesi ad Litteram, II, xvii. 37) reveals that whoever translated the Latin into English simply did not have an adequate command of Latin. In the paragraph before this misquote, Augustine says (reliably translated from Latin into English),

“What therefore is more vain, than that the mathematicus should guess from those constellations, from the very same horoscope, from the very same moon, to say that one of [those twins] is loved by the mother, and the other not loved?”

Note carefully the connection to astrology and Augustine’s condemnation of this epistemological foundation. Here are Augustine’s words in the next paragraph

(translated accurately in context): “For this reason, the good Christian should beware not only numerologists, but all those who make impious divinations, above all when they tell truth. Otherwise, they may deceive the soul, and ensnare her in a pact of friendship with demons.

Clearly, Augustine was speaking of woo merchants, not mathematicians. A group I am sure many atheists also do not like.

[1] — http://see.library.utoronto.ca/SEED/Vol4-3/Hulswit.htm