Mathematical Argument for God Debunked?

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Introduction

Stephen Woodford has a YouTube channel called Rationality Rules and he posted a video titled Craig's Mathematical Argument for the Existence of God DEBUNKED in which Woodford is himself responding to a Reasonable Faith video explaining that argument. In this article I’ll explain the argument (something like this is one of the reasons I retained my belief in God in moments of doubt) and respond to some of what Woodford said.

The mathematical argument for God’s existence

To get a better idea behind the mathematical argument for God’s existence I’m going to kind of use a computer analogy. Consider these two conceivable universes:

1. A universe akin to a hard drive that has its ones and zeros randomly set; a chaotic jumbled mess, disorderly unpredictable behavior at every moment.
2. A universe akin to a complex computer program with sophisticated mathematical algorithms directing behavior; a universe with consistent mathematical patterns ubiquitously imprinted into nature via physical laws such that it makes physics almost ludicrously successful in precisely predicting behavior (examples: relativity and quantum mechanics). The physical laws are akin to a program’s mathematical algorithms in that behavior is directed in an orderly and predictable fashion.

To get a clearer idea of what I mean by universe (2), consider this equation for the relation between mass, velocity, and kinetic energy.



Where m0 is the rest mass (roughly, the mass it has at zero velocity), c is the speed of light, and v is the velocity of the mass. Or for our purposes (well below the speed of light) it gets pretty close to this:



So for example the approximate kinetic energy values for the following mass and velocity would be the following:

K.E. (joules)	mass (kg)	velocity (m/s)
9	2	3
18	4	3
27	6	3
36	8	3

This provides a sort of mathematical elegance and robust consistency for the universe’s behavior. But we can conceive the kinetic energy relation being more like a randomized hard drive, where the kinetic energy values for various pairs of mass and velocity are assigned haphazardly with no meaningful pattern rather than fitting some neatly ordered equation:

K.E. (joules)	mass (kg)	velocity (m/s)
79	2	3
20	4	3
13	6	3
24	8	3

With the universe also yielding different kinetic energy values for the same mass/velocity pairs for different locations. We can conceive the relation being even more like a randomized hard drive in that the relation changes unpredictably from moment to moment. This is all still describable with math just like a randomized hard drive is with its randomly set ones and zeros, but this doesn’t have the same type of robustly consistent mathematical elegance as in the case where this mathematical algorithm is ubiquitously imprinted into the universe:



As you may have guessed, our universe operates like universe (2). Physics has been extraordinarily effective in predicting accurate and precise behavior thanks to the mathematical algorithms ubiquitously imprinted into nature. (The Reasonable Faith video describes this quite well at around 0:39 to 2:00, which among other things notes how scientists used math to pinpoint the location of a previously undiscovered planet, and Peter Higgs using math to predict an elementary particle which scientists found after exerting billions of dollars and millions of work-hours.) Conceivably, this scientific use of math didn’t have to be nearly as stunningly effective as we observe. So why is it?

For theists the answer is simple: the universe has this remarkable mathematical order because it was designed. For the atheist, the only viable option for this type of mathematical applicability is that it’s just a happy coincidence. But a happy coincidence of this magnitude strikes some people as...too coincidental to be very plausible.

The aforementioned Reasonable Faith video presents this mathematical argument for the existence of God (around 4:21 to 4:38):

1. If God does not exist, the applicability of mathematics is just a happy coincidence.
2. But the applicability of mathematics is not just a happy coincidence.
3. Therefore, God exists.

Woodford’s Response

As I suggested earlier, Stephen Woodford of Rationality Rules responded to the Reasonable Faith video. For sake of time I’m not going to discuss everything Woodford says, instead focusing mostly on the argument from the universe’s mathematical order, but I would like to respond to couple somewhat off topic things.

Regarding providing an alternative explanation for the effectiveness of mathematics Woodford’s video (around 8:23 to 11:04) shows clips of scholars some of which include the following:

Sabine Hossenfelder: I don’t think it’s all that unreasonable that mathematics is effective in the natural sciences, because what is mathematics about? It is a way to describe patterns, to describe regularities, and that’s exactly what we do in the natural sciences.

Steven Weinberg: I don’t think mathematics can ever be regarded as an explanation in itself of anything, and this has not always been—well, understand, perhaps it’s even still controversial—physical theories aren’t the way they are because of principles of mathematics. Principles of mathematics are the language in which we state our physical principles, and they are the way—the intellectual tools we use for calculating the consequences of those principles, but nothing is the way it is because of some mathematical principles.

George Lakoff: It’s [mathematics] not in the world The world is as it is. Let’s take a very simple case. Take a spiral nebula. The logarithmic spiral is not in the nebula, it’s in your understanding of the nebula. The marvelous thing about mathematics is that we can create mathematics with our brains that fiat phenomena in the world remarkably. It is not a miracle that that’s the case because we have the capacity to see and understand the world, to categorize it in terms of what our brains do, and then we can create a mathematics out of that in a systematic way using what our brains allow us.

None of that really answers the question at hand. For example, yes we describe regularities in the natural sciences, but conceivably these precise mathematical regularities didn’t have to exist, and their existence is exactly what is to be explained in the first place. This is no more an explanation for the consistent mathematical patterns in the universe than saying that the reason opium causes sleepiness is because of its dormitive powers, where “dormitive powers” just means it has the power to cause sleepiness. In philosophy this type of pseudo-explanation is called a “dormitive principle” where one reiterates the thing to be explained in different words, which potentially gives the illusion of an explanation where none existed. The rest of the clips, while they may say true or plausible stuff, also don’t answer why the universe has the remarkable mathematical structure it has, because again, the universe conceivably didn’t have to be this way (think back to the kinetic energy example, where the values for kinetic energy for given a mass/velocity pair could conceivably have varied from location to location or from one moment to the next).

Woodford said he has an explanation, but what is it? At around 11:50 to 12:02 in response to why the universe has such a stunningly elegant mathematical structure:

At the risk of sounding like a broken record, it’s because the laws of the universe are robustly consistent.

We kind of have a dormitive principle here. The Reasonable Faith video referenced Eugene Wigner’s paper The Unreasonable Effectiveness of Mathematics in the Natural Sciences which had this:

It is, as Schrodinger has remarked, a miracle that in spite of the baffling complexity of the world, certain regularities in the events could be discovered. One such regularity, discovered by Galileo, is that two rocks, dropped at the same time from the same height, reach the ground at the same time. The laws of nature are concerned with such regularities.

Yes, the laws of the universe are robustly consistent, so much so that we actually have mathematical algorithms ubiquitously imprinted into the universe in which physics is almost ludicrously successful in making accurate and precise predictions, but that is exactly what is to be explained. Reiterating the thing to be explained in different words is a non-answer; it’s the equivalent of, “Because I said so.”

Conclusion

Ultimately the only viable alternative to design for why the universe behaves more a hard drive imprinted with algorithms, rather than a randomized hard drive with ones and zeros assigned haphazardly, is that it’s just a happy coincidence. A proposed explanation that is actually just a dormitive principle is a non-answer, stalls progress, and rots the mind. To be fair Woodford does say this in his video he might be missing something (15:54 to 15:57). He is, but to be fair to Woodford again, I don’t think the argument from mathematics was argued as strongly or as clearly as it could have been in a number of cases, including the video Woodford responded to. I think the argument from the universe’s mathematical order becomes clearer when you contrast our universe with the way physical reality conceivably could have been like, that is, it could conceivably have been more like a randomized hard drive and a lot less like software running elegant mathematical algorithms directing everything in a more orderly fashion.

The Pseudohumility of Christianity?

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Stephen Woodford has a YouTube channel called Rationality Rules and he posted a video titled The Pseudohumility of Christianity attacking the humility of Christianity.

Arguments Against Christian Humility

Christianity encourages its adherents to practice humility, e.g. Matthew 23:12 and Philippians 2:3. So what’s the issue? At around 4:53 Woodford says, “The issue is that these verses are predicated upon sheer arrogance, and here is where my rant starts.”

He says that Christians believe there is one perfect God and that we’re created in his image (true so far), “which is a not-so-subtle way of saying we are, or close to, perfect.” What? Why think that? Exactly what it means to be created “in the image of God” is unclear and is debated among theologians (we are like God in some ways, having mind, will, and emotions—perhaps it means this). Woodford provides no evidence or argument for his particular exegesis nor does he cite any theologian who adheres to it; he gives only his word for this uncharitable interpretation. What should be needless to say is that Christianity teaches we are far from perfect, so far in fact that it is while we were enemies of God that Christ died for us (Romans 5:10), which is quite far from perfect indeed.

At around 5:15 to 5:34 Woodford recognizes an alternate interpretation for being made in the image of God: us being created above animals and Woodford says this “stinks of hubris.” But does it? My parents chose that I exist because they wanted a child to love and care for, and presumably they valued me over any animal. Does this belief “stink of hubris”? After all, it’s not as if I did anything to deserve it. In a way it could be said that God “chose” us insofar as he created humans and we have greater value than animals, and Woodford seems to think this justifies his claim that it “stinks of hubris,” but this doesn’t seem to follow.

At around 5:41 Woodford says that “most Christians believe that the universe was created for us in mind.” So? It doesn’t follow that most Christians believe that the universe was created only for us in mind; after all there’s an awful lot more to the universe than just us! (To say nothing of the untold legions of angels that also exist in reality!) At around 5:45 he also adds that most Christians believe that “we are a vital part in a grand divine plan.” Well, we are a part and we are “vital” in the sense that God loves us very much, but so what? It’s not as if we’re the only part of God’s plan; we could well be one of innumerable vital parts. At around 5:48 to 5:54 he notes the Christian belief that we have personal consciousnesses that outlast our bodies. Again, so? It’s not as if we’re the only beings who will outlast our bodies, e.g. angels. At around 5:55 to 6:08 he says many Christians believe they have a personal relationship with God (so?) and that God answers prayers (so?).

I could go on, but you get the gist. It’s true that in many ways God is nice to us. Woodford’s arguments fail largely because of a failure to ask why God answers prayers, gives humans an afterlife, makes us part of his divine plan, etc. Does God do so because we’re so awesome when we’re not? If so, then this is arrogance. But if instead it’s merely due to God being generous, then this doesn’t imply arrogance. So which is it? Well, consider again Romans 5:10: Christ died for us when we were still God’s enemies. The reason God is so nice to us is not because we’re so awesome and deserving. Indeed, part of the Christian faith is that we’re not deserving! It’s because God is so generous in his sacrificial love. We don’t deserve eternal life; rather it’s a gift from God, so teaches Christianity. Thus, a litany of nice things that Christians believe God does for us (which Woodford apparently believes are “extraordinarily arrogant tenants,” around 6:45 to 6:51) fails to constitute a good argument for arrogance; the conclusion just doesn’t follow.

Conclusion

I’ve seen multiple nontheists charge Christianity with arrogance, a claim often that they often supply with little to no evidence. After all, the Bible nowhere teaches that the universe was created just for us. Christianity teaches humility and explains why we have good reason to be humble; we are sinners in need of a savior, and it is while we were enemies of God that God sent his Son out of sacrificial love. It wasn’t because we deserved it. At around 7:01 to 7:06 Woodford says that “There is nothing humble about asserting the universe revolves around you.” He’s right, but he’s also wrong in thinking Christianity teaches anything of the sort; it doesn’t, and Woodford fails to provide sufficient evidence justifying this assertion (after all, for all we know there could be intelligent life in many other parts of reality whom God loves as well). Christianity suggests that, metaphorically speaking, the universe revolves around God, not us. We’re just fortunate to be in orbit.

Argument from Evil as an Internal Critique

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Introduction

Even if certain atheists reject moral objectivism, can such atheists still use the argument from evil as an internal critique of theism?

A Problem for Atheists Who Reject Moral Objectivism

As I wrote about in my article Rosenberg’s Argument from Evil Folly, there’s a big problem for the atheist in using the argument from evil if the atheist in question believes objective morality does not exist. People can have different ideas of what sorts of things are morally good. Suppose for example a theist has a standard of goodness such that it’s good that God permits the evil we see for certain reasons that are morally sufficient on this standard of goodness. Some atheists might say that if God adopted their standard of goodness, God would not permit the evil we see. But without an objective moral standard, there’s no objective fact of the matter about which standard of goodness God would adopt if he existed, and thus there’d be no objective fact of the matter whether God would permit evil if he existed, in which case the argument from evil would collapse under its own weight.

A Solution?

Another idea is to use the argument from evil as an internal critique. For example, couldn’t the atheist at least criticize the theist for having an inconsistency in the theist’s conception of goodness with respect to a perfectly good God allowing evil? That depends on the theist, but it’s relatively trivial to construct a view of goodness that is consistent with a perfectly good God allowing evil in the world. Suppose for example a hypothetical theist says that it is morally good for us humans to try to fight against evil (refraining from doing morally wrong actions, advancing medical technology, learning to share our food with the hungry, etc.) with the limited abilities that we have, with the obstacles we face etc. and that this is better than God making the evils any less bad, such that if God adopted this standard of goodness God would allow the evil we see (on this view, it’s good that God permits evil in the way that he does, but it’s not necessarily good that we humans permit evil; in a sense God and humans would have different responsibilities). Maybe this view of the hypothetical theist is wrong, but it’s not self-contradictory, and so there would be no inconsistency in this hypothetical theist’s conception of goodness with respect to a perfectly good God allowing evil.

There is another way an atheist who isn’t a moral objectivist could supply an internal critique. God is not only perfectly morally good, he is also all-loving. In the June 2020 debate on Capturing Christianity between Cosmic Skeptic and Inspiring Philosophy, Cosmic Skeptic said this at around 1:46:23:

Let’s not talk about good and evil because if they’re not objective maybe it’s unhelpful. But if you think that God is all-loving as a separate point then the question just reformulates itself. It’s not just a question about what’s loving and what’s not. It’s like we know facts about the universe. We know that children get cancer and we have to be committed to the view that that is loving; that it is loving to allow a child to get cancer. It’s the same problem as saying you have to accept that it is good or at least not evil for a child to get cancer. It would just be framed differently. Whatever the person believes, as you say Cameron that’s probably the best way to answer it, with any argument I ever make on any debate that I do, on any video I make, it’s always an argument of consistency—pretty much, most of the time. And that’s what I’m looking for here; is just consistency.[1]

Does it follow that if a loving God permits cancer, that it is loving to allow a child to get cancer? No. For starters, let’s ask this question: why assume that a loving God would not permit suffering? Presumably it’s because that if you love someone you value their well-being. It’s reasonable that loving someone implies valuing that person’s well-being, but the problem is that a morally good God might value other things as well, things that “interfere” with valuing one’s well-being.

To give an example of how valuing someone’s well-being can conflict with another value, suppose a loving and just judge is tasked with sentencing a man who has committed a heinous crime. The judge loves everyone including the man she is sentencing, so she values the man’s well-being, but on the other hand she also values punishing those who commit heinous crimes. So, the judge gives the man a long prison sentence to pay for his crime, even though she loves the man (by virtue of loving everyone) and values his well-being, and even though a lengthy prison sentence would decrease the man’s well-being.

Obviously the child Cosmic Skeptic has in mind hasn’t done anything wrong to deserve cancer, so the loving and just judge doesn’t work as analogy, but it does work to illustrate this point: values can conflict, including valuing someone’s well-being. If God is not just all-loving but also morally good, God could conceivably have other values that supersede the immediate well-being of humans. Imagine a hypothetical theist who believes God is all-loving but also believes that God is morally good, and that God adopts a standard of goodness such that it is good that God permits the observed suffering we see even though he loves us all, and that (at least in part) because God is all-loving our suffering in the mortal realm is finite and a pleasant everlasting life is available to every human who freely chooses God. This hypothetical theist grants it is not loving to permit suffering, but believes it is good that God permits the finite suffering we observe; God has values that supersede the immediate well-being of certain individuals. Again, maybe this view of the hypothetical theist is wrong, but it’s not self-contradictory, and so there would be no inconsistency in this hypothetical theist’s conception of goodness with respect to a perfectly good and all-loving God allowing evil.

Conclusion

The problem of evil fails as an internal critique not just against a morally good God but an all-loving and morally good God, at least tout court. It’s reasonable that an all-loving God would value our well-being. However, a theist could believe that while God values our well-being because he is perfectly loving, this is only one of the things that God values, and that other values could outweigh our immediate well-being such that an all-loving God who is also perfectly morally good would permit the evil we see.

I said that the problem of evil fails as an internal critique against an all-loving and morally good God tout court, but the problem of evil could succeed as an internal critique if the theist really did adopt a standard of moral goodness in which it is not good that God permits the evil we see. So in a way whether the argument from evil works as an internal critique depends on the theist. My objection is that the internal critique is not inherently successful; the theist could easily adopt a standard of moral goodness that evades the problem. Alternatively, the theist could say that while she knows some moral values (“moral values” in this case being “stuff that’s morally good”), she doesn’t necessarily know all the values, much less all values in conjunction with the appropriate weights for each value, such that for all she knows God has morally sufficient reasons for allowing the evil we see even if those reasons are beyond her ken (there are even more complications for whether to permit evil beyond knowing all the values and their appropriate weights, but for purposes of this blog article I’m mostly focusing on this).

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[1] I’ve lightly edited the quote to remove some filler words such as “um” and “right” for better flow.