Sunday, August 9, 2020

Mathematical Argument for God Debunked?

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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)

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)

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.”


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.