Randal: I never said these mathematical patterns are arbitrary. Just as a human architect has her reasons, so does God.
Justin: As you've been quick to admit throughout our extended conversation, God is not like humans. We shouldn't be so quick to import contingencies of human creativity to the divine. In other words, yes, your architect, if she likes rosettes, may repeatedly create rosettes. But we can't just pretend that positing the creative activity of a particular architect as the explanation of those rosettes has any explanatory power unless we also happen know that she really is particularly fond of that design.
In the same way, without independent reasons for thinking that God is fond of the kinds of general complexities you're actually referring to, then positing her creative activity lacks the guts we typically look for in a good explanation.
Randal: Justin, it pains me to say this, but that's simply not true.
Justin: Ah, but it pains me even more.
Randal: You don't need to know why an architect utilizes a particular design motif to know that he or she utilizes it. I can be familiar with the major motifs in Gaudi's architecture, for example, without knowing why he included these motifs. Similarly, one can reasonably conclude that God utilized particular design motifs in creation without knowing why he did so.
Justin: It is certainly true that we don't need to know exactly why some designer created a feature to know that a designer did, in fact, create it. That said, if one wants to posit God as an explanation of some group of patterns or motifs, then you need a reason why God would create those rather than something entirely different.
Randal: My point is that those types of patterns are not surprising on theism, but they are on atheism. Now I want to come back to your atheist rejoinder in which you seek to offer your own explanation of these recurring patterns. You say that all you need are some simple laws that can explain the repeating patterns of the Fibonacci sequence and pi (and the golden ratio and who knows what else). That's very helpful, just so long as you can explain what those simple laws are and why they should obtain rather than some other laws. If you can't do that, then your rejoinder is nothing more than a promissory note to have faith that an explanation consistent with atheism shall be forthcoming in the future. And I hope you'll forgive me if I don't, as yet, have that much faith.
Justin: Your argument, as you've stated above, is not about pi or the Fibonacci sequence in particular being repeated in nature. Rather, you're interested in why in general complex mathematical patterns like them are repeated in nature.
But what about your lack of trust in science either already having or coming up with some future explanation for these repeated mathematical patterns?
Here I'll quote the Sith Lord and Supreme Commander of the Imperial fleet himself: “I find your lack of faith disturbing.”
Randal: Chastised for lack of faith? Well now, that's something you don't hear from an atheist every day!
Justin: Yes, it might sound strange coming from an atheist, but, remember, at the beginning of this dialogue we chose to define faith as roughly equivalent to trust. And, well, if there are strong reasons for trusting that some proposition is true, then it may be rational to accept it as true.
Randal: Hold on, it isn't that you and I agreed together to define faith as roughly equivalent to trust. Rather, I pointed out there are two common definitions of faith, with trust being one of them. Anyway, I'm just heartened to hear an atheist chastising me for lack of faith!
In the absence of a clever Jedi rejoinder to the Sith Lord, let me offer a couple more sober responses.
Let me start by illustrating how weak your appeal to faith is by presenting an analogy. Imagine if the prosecutor in a murder trial provided evidence that the DNA of the accused was found on the murder weapon. That's exactly the kind of evidence one would expect if the defendant were guilty, and so it would seem to support the prosecution's case. Now imagine if all that the defense said in rebuttal was that they had faith that in the future forensics will one day show that kind of DNA evidence to be unreliable. That wouldn't get very far with the jury! Courts depend on evidence and argument. They don't ask juries to defer to faith in the absence of evidence. And, yet, that's what you're asking here. You ask us to defer to the hope that my argument will eventually be defeated by the advance of science.
Justin: Yes, of course. If he stopped there, I agree his comments would rightly be met with confusion or scorn.
For that reason, I need to have room to provide my reason for saying we can rationally have trust in science's ability to explain some observation. Given the one-way trend of scientific explanations replacing supernaturalistic explanations, we have good probabilistic reasons for thinking that it will be a mere matter of time. So, if it really is the case that we don't know the answer to some scientific question, historical precedent makes it rational for us to think one will eventually be found without any appeal to supernatural forces. At the very least, the dismal record of explanation-based theistic research programs should lead us to be dubious about theism's future explanatory success.
You seem to suggest, though, that we would need such a hope to defeat your argument. I must disagree here. I think it's clear by now that you've failed to argue that theism would lead us to expect complex mathematical patterns more than atheism, and so your argument really does boil down to a God-of-the-gaps argument. That is to say, you've claimed to have found a place of scientific ignorance, and you've plugged in a hypothesis with no explanatory power with respect to complex mathematics. With all due respect, this just isn't a very good argument.
Randal: I haven't invoked, as you say, a “theistic research program” any more than you've invoked an “atheistic research program.” I've simply argued that theism better explains one aspect of the natural world just as you've denied this. The problem is that it seems that you now want to exclude appeal to divine explanations a priori because of their alleged poor track record. In that case, I must wonder why you even entered into this conversation in the first place. Whatever issue I might raise, you can just defer to your unshakeable faith that science will explain it eventually. Atheists sometimes chide Christians for having superficial “God-did-it” explanations. Well it seems like you're going for a “science-will-do-it” equivalent.
Justin: I agree that you have not invoked an entire theistic research program. I've never claimed otherwise. Your attempt at explaining observations in the world by positing a particular kind of explanation (the creative powers of God) is just the latest in a long, unsuccessful history. When comparing different explanations, this stain of a historical precedent about theistic explanations in general should count for something.
Randal: The stain of history? Yikes, I hope that washes out.
Justin: I'm not sure why you think I've attempted to exclude divine explanations a priori. I believe we've walked through a number of arguments while comparing the explanatory merits of theism. The historical precedent to which I am referring is nothing like an a priori dismissal; rather, it's recognizing that a track record should count.
Randal: You talk about a track record, but which track record? I'm not proposing theistic explanations of nature, for therein lies the realm of natural science. Rather, I'm offering an explanation in philosophy, and specifically metaphysics, and appeals to God have a rich and honorable place in metaphysical explanation.
Anyway, you're quite mistaken to think that identifying one of your hoped-for pattern-generating natural laws would address my challenge. It wouldn't. Let's assume for a moment that science does uncover laws that explain how it is that, for example, flower petal numbers tend to conform to the Fibonacci sequence. As I said, even in this case you'd still need to explain why these physical laws obtain rather than some other physical laws. In other words, you'd merely have pushed the question back a step. In that case, the question would shift to this: why is the world structured with physical laws that manifest complex mathematical patterns throughout nature?
/> In short, the problem remains.
Justin: Yeah, I don't agree with that at all. One does not need to explain the purported explanation in order to show that it is the better of the two on offer.
But let's look closer at the piece of evidence you've brought up repeatedly, so that we can address it once and for all. You point to the number of flower petals as being Fibonacci numbers and say this is somehow an interesting fact about nature that demands an explanation. Cell biologist Todd Cooke of the University of Maryland observes,
The numbers 2, 3, and 5 (and their multiples) are frequently alleged to disclose the involvement of the Fibonacci sequence in a given process because they are taken to represent unique Fibonacci numbers as opposed to other “non-Fibonacci” numbers. It follows from this allegation that any structure appearing in a group of five, such as the digits on the human hand or the petals on a rose flower, can be interpreted as being a manifestation of the Fibonacci sequence. But the first six positive integers are either components or multiples of the primary Fibonacci sequence; thus, a small group must be composed of at least 7 units before it appears to be unrelated to the primary Fibonacci sequence.7
Science writer Philip Ball writes, “Even if we consider numbers up to 21, only four (7, 11, 17, 19) are not Fibonacci numbers or multiples of them. No wonder we see Fibonacci numbers everywhere!”8
Randal: In the first passage you quote, Todd Cooke is not rebutting the presence or significance of Fibonacci sequences in nature. He's merely challenging the attempt to find Fibonacci sequences in phyllotactic patterns (that is, the arrangement of petals, leaves, and branches). That does nothing to explain the extraordinary presence of Fibonacci sequence patterns in everything from seashells to spiral galaxies. And of course it also says nothing about other recurring mathematical patterns, like pi and the golden ratio. It is also incorrect to suggest that I placed particular stock in that one particular example.
But I assume you're after something more ambitious than a quibble over one example. Are you attempting to generalize Cooke's point by claiming that all instances of recurring mathematical patterns in nature are nothing more than the projection of these patterns onto nature—patterns that really only exist in our minds?
Justin: You're right that he isn't challenging the idea that Fibonacci numbers show up in nature. Rather, he is challenging the notion that this particular example suggests anything beyond ordinary natural forces. As Ball notes, to some degree, it's actually quite difficult to avoid Fibonacci numbers.
Needless to say, I'm not interested in generalizing the problem with this example over all of the examples you've claimed, nor am I qualified, as a nonexpert, to play whack-a-mole with every post hoc numerological assertion one could make about “designs” in our world. However, given that it was the example you cited a number of times now, I figured it was one you found particularly interesting.
Randal: Hmm, that's an interesting take on the matter, given that I placed no special emphasis on that particular example. And I'm not so sure about your general characterization either. Whack-a-mole is a game children play at Chuck E. Cheese's. But I take it we're engaged in a serious discussion of a range of phenomena that are supposedly surprising on atheism but not on theism.
Justin: While whack-a-mole may be fun at your best friend's eighth birthday party, it's considerably less so in the context of an argument.
Randal: Sorry, I don't have any eight-year-old friends. And note that I didn't accuse you of playing whack-a-mole when you introduced a range of examples of cosmic hostility that you wanted me to explain. So I'm not sure why you think I'm playing whack-a-mole when I offer a range of evidential examples to support my thesis!
Justin: What your argument consists of is a broad claim about complex mathematics in nature, for which you have several examples. Given that I am not an expert in biochemistry or any of the other possibly relevant fields, I can't really speak as to whether these claims represent genuine mysteries among relevant scientific experts. To be quite frank, I doubt they do.
That said, if the history of theistic explanations is to shed any light on this conversation, it is that this general gap-filling strategy is probably a dead end.
Randal: Decrying this argument as mere “gap-filling” appears to me to be nothing more than an attempt to tar me with a rhetorical brush. You're still not grappling with the force of the argument. As I said, the argument includes the need to explain laws of nature that are fine-tuned to reflect these complex recurring numerical patterns. Being an expert in biochemistry or any other field of natural science is not going to help you with a metaphysical explanation, given that scientists begin with the laws of nature such as they are. Thus, the discovery of a natural law to account for the genesis of these patterns would merely invite the follow-up question of whether natural laws that generate recurring high-level mathematical patterns in nature are more to be expected on theism or atheism.
WHY EXPLANATIONS NEED NOT HAVE THEIR OWN EXPLANATION
Randal: So, once again, it looks like we're stalled.
But even so, I'm not ready to leave the topic behind just yet. At the outset of this conversation I said that I wanted to approach the issue from a couple of angles. The analogy of an architectural motif is only the first. So are you okay if we leave this specific argument behind and move onto my related argument?
Justin: I'm fine with that. Though I do think it's important to repeat that one does not need to give a more fundamental explanation of a proposed explanation in order to show that it is a better explanation.
Randal: Right, you did say that.
Justin: Philosopher Gregory Dawes writes,
Richard Dawkins, for instance, writes that to explain the machinery of life “by invoking a supernatural Designer is to explain precisely nothing.” Why? Because it “leaves unexplained the origin of the designer.”…Dawkins apparently assumes that every successful explanation should also explain its own explanans. But this is an unreasonable demand. Many of our most successful explanations raise new puzzles and present us with new questions to be answered.9
In the same way, one could posit an earthquake to explain why the pictures have fallen off the shelf. It serves as a plausible explanation regardless of the fact that it hasn't addressed the antecedent issue of why that earthquake happened in that place and at that time.
Randal: I agree with all that. And I'm especially heartened by your taking a dig at Richard Dawkins's shoddy reasoning in The God Delusion. His central argument against God is not a good one, and that's one reason why.
The example is spot on. An earthquake would provide a good explanation for pictures falling off a shelf, and you don't need to explain what caused the earthquake before you can say that the earthquake caused the pictures to fall. Indeed, to require such a thing would quickly lead to an infinite regress of explanations, which is absurd. So on that much we agree.
That said, I need to ask, how is atheism relevantly analogous to the earthquake? I see perfectly well how an earthquake would explain the fallen pictures. But how does atheism explain the complex, recurring numerical patterns we find throughout nature? If I understand you correctly, to this point you've stated that at least some of these patterns (e.g., some instances of the Fibonacci sequence) are not in need of explanation and the rest will one day be explained by science. But I don't see appeals to hoped-for future explanations as having any present explanatory value analogous to the earthquake hypothesis.
Justin: That's only been one part of my answer.
Randal: Oh good, I was getting worried.
Justin: My position here is that the natural world as we know it probably explains these issues by way of known scientific processes. Again, I'm not in a position to say with supreme confidence whether the myriad examples you've provided are genuine mysteries to the relevant scientific communities.
But again, I doubt it.
I've also consistently said that, even if they are mysteries, consistent historical trends
suggest that they are likely to have an explanation in the future and that God-of-the-gaps arguments like this one fall in time. This pessimistic attitude toward your argument is not unfounded. While these patterns in nature may be interesting, I've not been given a substantive, non-ad-hoc reason why this is more to be expected on theism than on an atheistic hypothesis.
So yes, another stand-off it is.
THE MATHEMATICAL BLUEPRINT ARGUMENT
Randal: Fair enough, though it is simply confused to label a metaphysical argument like this as God-of-the-gaps. Beyond that, I could repeat why I still think you're wrong, and you could reply by reiterating why you think I'm wrong, but that would probably get boring after a while. So let's just move on to my second argument. This is a broader argument, which shifts away from isolated mathematical patterns to the extraordinary degree to which mathematics generally maps onto physical reality. And, once again, I'd like to build my case on a thought experiment.
Justin: Alright, let's hear it.
Randal: So imagine walking in the rough high country when you come upon a curious arrangement of rocks. Their unusual placement is suggestive of design, but the appearance is not itself sufficient to warrant that conclusion, and so you withhold judgment. However, as you study the formation more closely you discover the extraordinary fact that at noon on the winter solstice the sun shines directly through a hole in the peak of the highest obelisk and lands directly in the middle of a circle of rocks right in the center of the formation. It is fair to say that this discovery would constitute a remarkable fit between the rock structure and astronomical phenomena, a fit that would cry out for an intelligent explanation.
An Atheist and a Christian Walk into a Bar Page 18