by Jerry Bowyer
Vern Poythress is by any reasonable standard a deeply and widely educated man. He has six academic degrees, a B.S. from CalTech and a PhD from Harvard in mathematics. An M Div, ThM, M Litt, and a ThD in various theological disciplines from Westminster Seminary, Cambridge University and the University of Stellenbosch respectively. He now teaches New Testament (and on occasion: philosophy of science and philosophy of language) at Westminster. He publishes books, popular articles and journal articles on a broad range of topics.
We sat down across a Skype connection recently to discuss Poythress’ recent book Chance and the Sovereignty of God, theology, probability theory, finance, economics and the information theory which makes that Skype connection possible.
The standard modern culture-war revolves around God vs. the mathematical sciences. Take your choice: Faith or physics. Then there are the voices of mutual toleration, which attempt to leave room for science among the faithful and for faith among the scientific. Poythress, though, taps into a different tradition entirely, one which is seldom heard in modern debate: That God and science are neither enemies, nor partners, but rather that God is the necessary foundation for mathematics and therefore of every science which uses it.
The argument is that mathematical laws, in order to be properly relied upon, must have attributes which indicate an origin in God. They are true everywhere (omnipresent), true always (eternal), cannot be defied or defeated (omnipotent), and are rational and have language characteristics (which makes them personal). Omnipresent, omnipotent, eternal, personal… Sounds like God. Math is an expression of the mind of God. Sound strange? It isn’t. Modern natural science was created by people who said that they were trying to “think God’s thoughts after Him.”
It occurred to Poythress that this argument applies to the ‘laws’ of mathematics, but what about the mathematics of what is allegedly outside the law, the mathematics of chance? Does chance kill the laws of math and with them, the need for their Lawgiver?
For Poythress, chance is not chaos, it is simply missing knowledge. To say that in a fair coin toss there is a 50% chance of heads is to say more about our knowledge (particularly the lack thereof) than it does about whether the laws of math applied. Fifty/fifty simply means that out of the two options we have no knowledge which we can use to favor one outcome or the other. The outcome is not random, not chaotic: it’s just unknown. For Poythress, the Calvinist, the outcome is known by God and even determined by Him. It’s not chance to Him, it’s plan. With our limited knowledge, however, it looks like chance. If we knew enough, we’d know the outcome of the toss and we’d know it with 100% certainty.
The ingenious insight behind modern probability theory is that even our zone of ignorance still has a structure and an order to it. Probability and statistical theory model what we don’t know. They help us predict our lack of prediction. The paper by W.S. Gossett on which pretty much all statistical analysis is based is about creating a ‘prediction’ of the ‘standard error’ of ‘the mean.’ It’s about predicting our errors. The zone of uncertainty is not a zone of lawless chaos, but is instead a realm of higher mathematical laws.
You can listen to the entire interview here) or read a partial transcript below (edited for clarity).
JERRY BOWYER: Are your insights simply a matter of the idea that theism provides the necessary theoretical foundation of statistics so only theists can do probability and statistics consistently? You know, in other words, only theists can consistently use these models and have it be consistent with their world view? Or does it go further; does the antithesis go farther such that Christians would actually do the mathematical operations differently or use them differently?
VERN POYTHRESS: Right. Well, I do believe that the foundations are not simply theism but specifically the Christian God. And I touch on that in areas where I talk about the one and the many. And that’s all over the place because their regularity depends on many events, right? But the many events illustrate the regularity so that the two are correlative with one another and each makes sense only in terms of the other. I believe that has its origin in the one and many and divine nature. So obviously, I want to say there’s a clear distinction between God, the creator, and everything that he’s created, but he shows his character in the things that he’s made. So I would argue that it’s not a bare theism but actually Christian theism that explains that.
BOWYER: I think you’re saying unless you have some sense of plurality, unless you have, say, for instance, a triune understanding of God, you will have trouble not collapsing into monism in your philosophy, and monism is a pretty lousy foundation for mathematics because in the end it comes down to one plus one plus one plus one equals one.
POYTHRESS: One, yeah—you never get beyond one.
BOWYER: You never get beyond one, right, okay. All right. I got that. Very good point.
So that having been said, whether it’s theism or specifically Christian or triune theism—would someone who is practicing from that world view practice differently? Would they do different equations?
POYTHRESS: Right, I think it’s an excellent question. And you may know I have another book —Redeeming Mathematics is the title—where I discuss the fact that there can actually be differences at a high level in mathematics, that not everybody accepts the same mathematical truths. But that is a kind of subtle thing. And I think at the level we’re talking about, with most use of probability and statistics, what we’re seeing is that everybody secretly relies on God; even the atheist does.
And I’ve got another book, “Redeeming Science,”; its introductory chapter is about that. But actually there’s one chapter in the book on chance. Let me see if I can single it out. Yeah, chapter 17 is where I go through ‑‑
BOWYER: Theistic foundations for probability?
POYTHRESS: Yeah. Where I go through the various attributes of God as manifested in the regularities involved in probability. So everybody depends on that.
BOWYER: So there has to be unity, but there also has to be diversity.
POYTHRESS: Yeah. Yeah.
BOWYER: And there also—and symmetry. In other words, you throw a die, one-sixth probability is in symmetry with a one-sixth probability of getting two, which is in symmetry with a one-sixth probability, et cetera, et cetera. So you have unity, diversity, symmetry.
POYTHRESS: Yes. I’m saying everybody really secretly relies on God, but they won’t admit it. And what happens is that the regularities, the lawful regularities of the entirety of probability theory and the entirety of its application in various realms in life depends on these lawful regularities. They’re there, but the person who doesn’t believe in God, says he doesn’t believe in God, he still relies on those, but he thinks of those regularities as impersonal. So they’re just there. They’re kind of a cosmic mechanism. And you know, I argue that that really doesn’t work because the features of the regularities include personal aspects.
BOWYER: What do you mean the features of the regularity include personal aspects?
POYTHRESS: Well, let’s take the very simple one, that the heads will come up half the time, right? Well, that’s already a statement about regularity. It’s a general statement, and it’s rational, and it’s language-like. And those two features, rationality and language-likeness, are characteristic only of persons. What I think people often don’t recognize is they think of the world—because of the influence of materialistic philosophy—they think of the world as matter in motion. Or even if they’re dealing with human society—it’s regularities that have no further explanation other than they’re just there.
But if you look at the character of what we expect the regularities to be, we expect them to be always the case. That’s the feature of eternality: everywhere the case. That’s the feature of everywhere present. It’s characteristics of God. And everybody relies on that.
BOWYER: And all-powerful. There’s no force in the universe that can turn two plus two into something other than four.
POYTHRESS: Into something else, that’s right.
POYTHRESS: So everybody relies on that, and it’s actually revelatory of God. It’s divine nature. It’s divine—it’s characteristics of God that are being revealed there that people are relying on.
But the classic way of getting around it is to think of these lawful things as impersonal because then you’re not responsible morally to them; they’re just there, and if they’re mechanical, they’re basically inferior to you as a person rather than being God ruling the universe. So there is a spiritual motivation for not admitting that these regularities are of a personal character, that it’s God speaking personally and specifying everything about the world. And he’s faithful to himself, which is why we can—and people rely on it so much, but they think of it just as a mechanism. But it’s God’s faithfulness.
So I’m reinterpreting the entire world in terms of the meaning that it has when you realize that God governs it. But it’s not a reinterpretation in a vacuum as if I’m just saying, well, let’s see what we could say if we assume that God is there, but that these are actually the character of these regularities –they have the attributes of God, including language-like character and rationality. Those two things reveal that they’re personal.
BOWYER: You’re not running that world view as a hypothesis; you are taking that world view as the only sure foundation for the very idea of hypothesis and hypothesis testing.
POYTHRESS: Yeah, that’s right.