Justin: I should briefly interject here as I'm highly skeptical of this design inference.
Randal: Why am I not surprised?
Justin: A small grouping of rocks casting a shadow on another at a time on which humans have imposed meaning is, well, going to be as frequent as our imagination's ability to attach meaning to ultimately meaningless astronomical happenings. Perhaps I've got a fence post out front whose shadow points toward the exact center of my neighbor's garage door at ten a.m. on the anniversary of his college roommate's fifth marriage. I'm not sure this “calls out” for an explanation.
But I'll shut up and let you make your broader point.
Randal: No need to shut up in this case. After all, I share your skepticism on the fencepost. As for the scenario I painted, if the sun shone through the hole in that obelisk at 3:41 p.m. on a Tuesday, folks would rightly dismiss it as insignificant. But the winter solstice is not merely significant because we arbitrarily imbue it with meaning. It's the lowest excursion on the celestial sphere relative to the celestial equator. If the sun shone through the hole at noon on the winter solstice, that is precisely the kind of fine-grained significant connection to the natural world that would suggest intentional design to the archaeoastronomer.
Justin: Do you see the lowest excursion on the celestial sphere relative to the celestial equator to be something of objective significance? I sure don't, so it doesn't seem designed at all. That said, feel free to continue to make your point.
Randal: Well, I'll let you take up that complaint with the archaeoastronomers, since they certainly do find the solstice to be astronomically significant. Indeed, my scenario is based on a real place, which warrants precisely this kind of design inference—the Newgrange prehistoric monument in Ireland. So your quibble really is with experts in the field.
Justin: Sure, it has significance in a particular field. I'm just saying it's no more special objectively than any other astronomical happening.
Randal: The point I'm making is not limited to the methods of archaeoastronomy. The general lesson is that we all look for finely tuned patterns that are indicative of intelligence. I want to argue that this same principle can be applied to the relationship between the physical world and mathematics. And that was Wigner's point in the famous paper with which I launched this discussion. Just as the rock structure maps onto astronomical reality with an extraordinary fit, so our physical universe maps onto mathematical reality with an extraordinary fit. And just as intelligence is the best explanation of the former, so I believe it is the best explanation of the latter.
Justin: Okay, I think I see where you're going here. It's another design inference. Unfortunately, it's another toward which I am quite dubious. You regard the universe as mapping onto mathematical reality. But why endorse that view rather than one that holds that the concepts at play in mathematics map onto our physical reality after the fact—or some other option entirely?
Randal: Let me start by noting that some instances of mathematical mapping are not surprising and thus do not require an explanation. For example, Euclid's algorithm enables us to calculate the greatest common divisor between two numbers. It turns out that we can use the algorithm throughout nature, but this isn't surprising given that Euclid's algorithm is logically necessary so it must apply to any physical universe.
Justin: Okay, sure. Go on.
Randal: But other cases of mathematical mapping are not like that. For example, consider the fact that we can use calculus to map the path of a baseball that is hit by a bat. So long as we have the right initial variables (the height at which the ball was hit, the angle, the initial velocity of the ball, the wind speed, and so on) we can predict the trajectory of the ball with dizzying accuracy.
Justin: Right. Assuming we know both the initial conditions and the number and degree of the forces acting upon it, these things are pretty predictable.
Randal: Yes, but the really important point is that this mapping of the baseball's trajectory is not like Euclid's algorithm. You see, there is nothing logically necessary about the laws of nature being what they are such that a baseball must assume this trajectory when hit.
Justin: Oh, okay. I think I see what you're getting at.
Randal: Nonetheless, we find mathematics provides a powerful tool to plot the ball's course, a fit reminiscent of my analogy of the rock formation to the winter solstice. The natural world is describable in the language of mathematics, and yet it need not have been the case. Once we realize there is no logical or metaphysical necessity here, this particular fit becomes a cause for wonder, as Albert Einstein conceded when he famously observed, “The most incomprehensible thing about the physical world is that it is comprehensible.”10
Justin: So, this is just an argument about there being regularities in nature?
Randal: No, this is an argument based on the fact that the physical world is richly describable in the language of mathematics. As I said, there is no logical necessity that the natural world be describable mathematically, and yet it is. This calls out for explanation, and a mind is precisely the kind of explanation that accounts for the phenomenon.
Justin: Well, hear me out. Imagine a universe quite different from our own, with regular laws quite different from our own. With those regular physical laws acting on your baseball, we would likely still be able to map the trajectory mathematically. With that in view, it matters little that the laws we happen to have are not, as you've mentioned, logically necessary.
This is why I ask whether your argument is really about why we have any regularities. Am I completely off base here?
Randal: Hmm, off base on a baseball illustration. Clever!
So you think Wigner and Einstein were confused to find this mathematical describability to be a surprising fact?
Justin: I'm not saying that at all. I'm saying the particular argument I've been given here isn't something I find terribly compelling.
Randal: Okay, but what is your basis for claiming that natural regularities in other possible worlds would likely be describable in the language of mathematics? To be honest, it seems to me that you're trying to avoid the problem I've presented rather than offer a response to it.
Justin: This question just seems bizarre to me. Can you imagine a possible world in which the language of mathematics, a language we invent, is useless to us with regard to describing things? Assuming we exist and are capable of some kind of mathematics, why would we be incapable of creating mathematical concepts and using them to describe the interesting relationships in the world around us?
Randal: Remember, I pointed out that some degree of mathematical mapping (e.g., Euclid's algorithm) occurs in every physical world. So that clearly does not require an explanation.
The issue is the complex and contingent nature of mathematical mapping that we find in nature. I started with calculus and a mundane baseball example, but that's only the beginning. More than a century ago, Einstein's Special Theory of Relativity predicted the phenomenon of time dilation, that is, that time was not absolute and thus that it could slow down under some circumstances. This extraordinary prediction was confirmed in a 2014 experiment in which lithium ions were accelerated in a particle accelerator to one-third the speed of light.11 Let me say it again: a 2014 experiment of dizzying sophistication in a particle accelerator confirmed the predictions of complex mathematical equations written out a century before.
Justin: Yes, that prediction was first confirmed back in 1938 in the Ives-Stilwell experiment. In 2014, however, scientists have confirmed this prediction again but with unprecedented precision!
Given a robust theoretical framework for how some aspect of the physical universe operates, predictions based on that framework will be able to be tested in increasingly precise ways as new methods are devised.
Science is pretty rad.
Randal: Science is indeed amazing, though I must admit that I stopped calling anything rad around the same time that grunge music became popular.
Justin: Ouch!
>
Randal: It could've been worse. At least you didn't say science is groovy.
Look, the philosophical question before us is which of these two views, theism or atheism, best explains this highly complex mathematical structure in nature. As I've said, this kind of extraordinary fit of mathematical description and prediction to physical reality cannot be explained by trivial logical necessity. So what does explain it?
I've offered an explanation that appeals to mind: just as an intelligent civilization might build a structure that maps onto complex astronomical processes, so God created a world that maps onto a rich mathematical structure. But it seems you don't even want to concede that Wigner and Einstein were right to be amazed.
Justin: Let me again put my puzzlement toward your line of inquiry in the form of a question. What would a physical world not describable by some basic mathematical concepts even look like?
Perhaps you are more imaginative than I and can imagine an actual physical world resembling something like, oh, I don't know, those “worlds” found in the lithographic prints of Dutch artist M. C. Escher.
Randal: I do like M. C. Escher. In fact, I think I have an old Escher calendar somewhere.
Justin: Who doesn't?
Randal: But I'm not thinking about that here. I've already noted that every possible world would map onto some basic mathematical concepts. But the special theory of relativity is not a basic mathematical concept. We're dealing with an extraordinary degree of fit here. As I've said, that degree of rational, mathematical structure in nature is not surprising on theism but it is on atheism.
Justin: Well, that's not at all obvious. To be clear, I think you are right to appeal to a mind when thinking about the relationship between mathematics and the sciences, but I think you've got the direction of explanation backward.
I think the precision with which the predictions of Einstein's equations were confirmed is in large part because of the effort spent on creating various systems of mathematics capable of representing the physical world with increasingly impressive precision.
Randal: Well sure, mathematicians like Einstein worked hard at discovering the nature of the world by way of complex mathematical calculations that were confirmed a century later by way of empirical observation. But how is that a rebuttal to my argument?
Justin: But, Randal, he didn't just pull the math out of thin air. With scientific theories, we impose various systems of mathematics onto our prior accumulated observations and come up with elegant explanations that both fit the data and make predictions about future observations. Sometimes these predictions are rather counterintuitive. The relations may get very complex, but the basic idea here isn't that different from predicting the basic trajectory of your baseball while knowing the relevant variables.
Randal: Sure, but how is that supposed to provide a rebuttal to what I've argued? You're merely redescribing the very phenomenon you need to explain!
Justin: There looks to be no substantive explanatory role for God to play in this process, and I suspect that is part of the reason why she is largely absent from physics departments.
The argument here, while of no obvious relevance to the God question, does provide incredibly powerful evidence for the intelligence, conceptual clarity, and creativity of physicists and mathematicians.
Randal: Your quip that God does not provide an explanatory role in physics departments suggests that you haven't understood my argument. I'm not appealing to God as a physical explanation but rather as a metaphysical one. We're doing philosophy here, not science, so we shouldn't expect to find God as an explanation in physics departments.
Justin: My response didn't distinguish between physical and metaphysical explanations because I've argued that positing God here is unsuccessful on both counts.
Randal: Okay, but I've never appealed to God as a physical explanation so, unless you're just trying to get a rhetorical advantage, it simply isn't relevant to say that God is absent from the physics department. That said, we do agree, at least, on the great intelligence of physicists and mathematicians. (As the saying goes, be grateful for small mercies!)
But, as I've pointed out, these very physicists and mathematicians, folks like Einstein and Wigner, recognize that they are discovering the mathematical structure of the world, and they are left in awe of that structure. I've provided a philosophical explanation for that structure. Just as an archaeoastronomer would appeal to mind to explain the fit of physical structure to astronomical events and processes, so I've appealed to mind to explain the fit of mathematical structure to physical events and processes.
Justin: I see no explanatory reason to posit God as a response to these issues, and you see God as the best explanation for this correspondence between our mathematical concepts and the physical world. Here I think we end in yet another stalemate with respect to this argument.
Randal: So yet again I'm persuaded that I won, and you're persuaded that you won. This is starting to get predictable. Perhaps we should ask somebody to serve as a tiebreaker to decide which of us is right. How about I give my mom a call? We can both share our arguments and she can decide who wins.
Justin: That won't be necessary, Randal. I gave your mom a rundown of the arguments over a nice candlelit dinner last night. She found my arguments difficult to resist and now calls herself an atheist.
You left yourself wide open for that one.
Randal: Hah! My parents called me last night laughing that some weirdo came up to them at the mall food court yesterday trying to convince them that atheism was true. When my mom politely said she was a theist the guy got really excited, thinking she said atheist.
So that was you, eh? Good to know. But hey, don't look so disappointed. You've got one more try to convince me of something.
Justin: I suppose then that it is my turn yet again to offer up another argument in favor of atheism and against theism.
Randal: I think you're right! I hope you've got something really good to bring our meandering conversation to a memorable conclusion.
Justin: I hope I don't disappoint.
Randal: Yeah, and I hope you do. I want to win this one. So what you got?
PRELIMINARY COMMENTS ON GOD, EVIL, AND SUFFERING
Justin: There is one such argument (or family of arguments) that I suspect is familiar to nearly every person who has ever pondered the specific concept of God we have been struggling with throughout this exchange. These arguments, as with my other arguments, are seen as problems for theism. These problems come in many different logical structures and names, but they all appeal to some fact or facts about the existence of or nature of suffering in the actual world.
Randal: Ah, I was wondering when the venerable problems from evil and suffering would make an appearance. And let me say at the outset that this is a big problem for any theist. And while the intellectual side of the problem of evil and suffering is bad enough, from a personal perspective the experience of evil and suffering is far worse. Nothing can shake a person's belief in God like the shattering experience of deep pain, suffering, and loss.
Justin: Unfortunately, when it comes to the problem of our experience of pain and suffering, the atheist is no better off than the theist. That's true even if, as I'll attempt to argue, the atheist does enjoy a considerable advantage with respect to the intellectual problem.
Randal: Interesting. I agree that everybody suffers, if that's what you mean. At the same time, I do believe that theism has one significant advantage straight out of the gate in that it provides hope for a final deliverance from suffering that atheism doesn't offer. And that belief in a hopeful future in turn conveys psychological benefits that can help ameliorate the degree of suffering a person will endure.
Justin: While I agree that some religious versions of theism offer a final deliverance, that compensation hardly serves as a justification. Moreover, it's not clear to me that this is true in terms of the bare theism being discussed in this book. After all, theism does not entail that there
would be any kind of life after death.
Though, admittedly, life after death is more probable on theism than on atheism.
Randal: No doubt. And you're right to point out that our relatively barebones definition of theism doesn't include life after death. But it does include God's maximal power and perfect goodness, and those attributes together provide a significant ground for hope. So whether or not one agrees with Immanuel Kant's famous claim that a just God would secure an afterlife where justice is satisfied, one can hopefully agree that, all things being equal, it is better for those who suffer that a maximally good and just being exists than not.
But by no means am I claiming this eliminates the problem. Either way, I admit that we theists do face a challenge here.
Justin: Oh, I see what you're saying, and I think I agree.
Randal: Awesome! Since we agree, how about we end the chapter right now on that high note of common accord?
Justin: And rob patient readers of the spectacle that is a theist dealing with variations on the age-old problem of suffering? I wouldn't dare!
Randal: Oh blarg!
EVOLUTION AND ATHEISM: A MATCH MADE IN HEAVEN?
Justin: Now, the specific argument that I want to press here for this last exchange is similar to my other arguments in that it seeks to draw out a particular set of facts that hold true in the actual world but that are better explained on the assumption that no God exists (as defined) than on the assumption that God does exist.
Randal: Sounds fine to me. Just let me buckle my seatbelt in preparation for the rocky road that lies ahead.
Okay, I'm ready to go. You may fire when ready!
Justin: This argument, inspired by the work of Paul Draper, centers around a few basic facts.
Randal: Excellent. Arguments are always better when they start with facts.
Justin: The first fact to which the argument appeals is the fact that evolution is the way by which the variety of living things on earth has come about. The second fact is about the relationships between pain and pleasure and the biological goals of survival and reproduction. Together, I think they provide a powerful argument for atheism.
An Atheist and a Christian Walk into a Bar Page 19