One frustrating aspect of our discussion about the compatibility of science and religion was the amount of effort expended arguing about definitions, rather than substance. When I use words like "God" or "religion," I try to use them in senses that are consistent with how they have been understood (at least in the Western world) through history, by the large majority of contemporary believers, and according to definitions as you would encounter them in a dictionary. It seems clear to me that, by those standards, religious belief typically involves various claims about things that happen in the world -- for example, the virgin birth or ultimate resurrection of Jesus. Those claims can be judged by science, and are found wanting.

Some people would prefer to define "religion" so that religious beliefs entail nothing whatsoever about what happens in the world. And that's fine; definitions are not correct or incorrect, they are simply useful or useless, where usefulness is judged by the clarity of one's attempts at communication. Personally, I think using "religion" in that way is not very clear. Most Christians would disagree with the claim that Jesus came about because Joseph and Mary had sex and his sperm fertilized her ovum and things proceeded conventionally from there, or that Jesus didn't really rise from the dead, or that God did not create the universe. The Congregation for the Causes of Saints, whose job it is to judge whether a candidate for canonization has really performed the required number of miracles and so forth, would probably not agree that miracles don't occur. Francis Collins, recently nominated to direct the NIH, argues that some sort of God hypothesis helps explain the values of the fundamental constants of nature, just like a good Grand Unified Theory would. These views are by no means outliers, even without delving into the more extreme varieties of Biblical literalism.

Furthermore, if a religious person really did believe that nothing ever happened in the world that couldn't be perfectly well explained by ordinary non-religious means, I would think they would expend their argument-energy engaging with the many millions of people who believe that the virgin birth and the resurrection and the promise of an eternal afterlife and the efficacy of intercessory prayer are all actually literally true, rather than with a handful of atheist bloggers with whom they agree about everything that happens in the world. But it's a free country, and people are welcome to define words as they like, and argue with whom they wish.

But there was also a more interesting and substantive issue lurking below the surface. I focused in that post on the meaning of "religion," but did allude to the fact that defenders of Non-Overlapping Magisteria often misrepresent "science" as well. And this, I think, is not just a matter of definitions: we can more or less agree on what "science" means, and still disagree on what questions it has the power to answer. So that's an issue worth examining more carefully: what does science actually have the power to do?

I can think of one popular but very bad strategy for answering this question: first, attempt to distill the essence of "science" down to some punchy motto, and then ask what questions fall under the purview of that motto. At various points throughout history, popular mottos of choice might have been "the Baconian scientific method" or "logical positivism" or "Popperian falsificationism" or "methodological naturalism." But this tactic always leads to trouble. Science is a messy human endeavor, notoriously hard to boil down to cut-and-dried procedures. A much better strategy, I think, is to consider specific examples, figure out what kinds of questions science can reasonably address, and compare those to the questions in which we're interested.

Here is my favorite example question. Alpha Centauri A is a G-type star a little over four light years away. Now pick some very particular moment one billion years ago, and zoom in to the precise center of the star. Protons and electrons are colliding with each other all the time. Consider the collision of two electrons nearest to that exact time and that precise point in space. Now let's ask: was momentum conserved in that collision? Or, to make it slightly more empirical, was the magnitude of the total momentum after the collision within one percent of the magnitude of the total momentum before the collision?

This isn't supposed to be a trick question; I don't have any special knowledge or theories about the interior of Alpha Centauri that you don't have. The scientific answer to this question is: of course, the momentum was conserved. Conservation of momentum is a principle of science that has been tested to very high accuracy by all sorts of experiments, we have every reason to believe it held true in that particular collision, and absolutely no reason to doubt it; therefore, it's perfectly reasonable to say that momentum was conserved.

A stickler might argue, well, you shouldn't be so sure. You didn't observe that particular event, after all, and more importantly there's no conceivable way that you could collect data at the present time that would answer the question one way or the other. Science is an empirical endeavor, and should remain silent about things for which no empirical adjudication is possible.

But that's completely crazy. That's not how science works. Of course we can say that momentum was conserved. Indeed, if anyone were to take the logic of the previous paragraph seriously, science would be a completely worthless endeavor, because we could never make any statements about the future. Predictions would be impossible, because they haven't happened yet, so we don't have any data about them, so science would have to be silent.

All that is completely mixed-up, because science does not proceed phenomenon by phenomenon. Science constructs theories, and then compares them to empirically-collected data, and decides which theories provide better fits to the data. The definition of "better" is notoriously slippery in this case, but one thing is clear: if two theories make the same kinds of predictions for observable phenomena, but one is much simpler, we're always going to prefer the simpler one. The definition of theory is also occasionally troublesome, but the humble language shouldn't obscure the potential reach of the idea: whether we call them theories, models, hypotheses, or what have you, science passes judgment on ideas about how the world works.

And that's the crucial point. Science doesn't do a bunch of experiments concerning colliding objects, and say "momentum was conserved in that collision, and in that one, and in that one," and stop there. It does those experiments, and then it also proposes frameworks for understanding how the world works, and then it compares those theoretical frameworks to that experimental data, and -- if the data and theories seem good enough -- passes judgment. The judgments are necessarily tentative -- one should always be open to the possibility of better theories or surprising new data -- but are no less useful for that.

Furthermore, these theoretical frameworks come along with appropriate domains of validity, depending both on the kinds of experimental data we have available and on the theoretical framework itself. At the low energies available to us in laboratory experiments, we are very confident that baryon number (the total number of quarks minus antiquarks) is conserved in every collision. But we don't necessarily extend that to arbitrarily high energies, because it's easy to think of perfectly sensible extensions of our current theoretical understanding in which baryon number might very well be violated -- indeed, it's extremely likely, since there are a lot more quarks than antiquarks in the observable universe. In contrast, we believe with high confidence that electric charge is conserved at arbitrarily high energies. That's because the theoretical underpinnings of charge conservation are a lot more robust and inflexible than those of baryon-number conservation. A good theoretical framework can be extremely unforgiving and have tremendous scope, even if we've only tested it over a blink of cosmic time here on our tiny speck of a planet.

The same logic applies, for example, to the highly contentious case of the multiverse. The multiverse isn't, by itself, a theory; it's a prediction of a certain class of theories. If the idea were simply "Hey, we don't know what happens outside our observable universe, so maybe all sorts of crazy things happen," it would be laughably uninteresting. By scientific standards, it would fall woefully short. But the point is that various theoretical attempts to explain phenomena that we directly observe right in front of us -- like gravity, and quantum field theory -- lead us to predict that our universe should be one of many, and subsequently suggest that we take that situation seriously when we talk about the "naturalness" of various features of our local environment. The point, at the moment, is not whether there really is or is not a multiverse; it's that the way we think about it and reach conclusions about its plausibility is through exactly the same kind of scientific reasoning we've been using for a long time now. Science doesn't pass judgment on phenomena; it passes judgment on theories.

The reason why we can be confident that momentum was conserved during that particular collision a billion years ago is that science has concluded (beyond reasonable doubt, although not with metaphysical certitude) that the best framework for understanding the world is one in which momentum is conserved in all collisions. It's certainly possible that this particular collision was an exception; but a framework in which that were true would necessarily be more complicated, without providing any better explanation for the data we do have. We're comparing two theories: one in which momentum is always conserved, and one in which it occasionally isn't, including a billion years ago at the center of Alpha Centauri. Science is well equipped to carry out this comparison, and the first theory wins hands-down.

Now let's turn to a closely analogous question. There is some historical evidence that, about two thousand years ago in Galilee, a person named Jesus was born to a woman named Mary, and later grew up to be a messianic leader and was eventually crucified by the Romans. (Unruly bloke, by the way -- tended to be pretty doctrinaire about the number of paths to salvation, and prone to throwing moneychangers out of temples. Not very "accommodating," if you will.) The question is: how did Mary get pregnant?

One approach would be to say: we just don't know. We weren't there, don't have any reliable data, etc. Should just be quiet.

The scientific approach is very different. We have two theories. One theory is that Mary was a virgin; she had never had sex before becoming pregnant, or encountered sperm in any way. Her pregnancy was a miraculous event, carried out through the intervention of the Holy Ghost, a spiritual manifestation of a triune God. The other theory is that Mary got pregnant through relatively conventional channels, with the help of (one presumes) her husband. According to this theory, claims to the contrary in early (although not contemporary) literature are, simply, erroneous.

There's no question that these two theories can be judged scientifically. One is conceptually very simple; all it requires is that some ancient texts be mistaken, which we know happens all the time, even with texts that are considerably less ancient and considerably better corroborated. The other is conceptually horrible; it posits an isolated and unpredictable deviation from otherwise universal rules, and invokes a set of vaguely-defined spiritual categories along the way. By all of the standards that scientists have used for hundreds of years, the answer is clear: the sex-and-lies theory is enormously more compelling than the virgin-birth theory.

The same thing is true for various other sorts of miraculous events, or claims for the immortality of the soul, or a divine hand in guiding the evolution of the universe and/or life. These phenomena only make sense within a certain broad framework for understanding how the world works. And that framework can be judged against others in which there are no miracles etc. And, without fail, the scientific judgment comes down in favor of a strictly non-miraculous, non-supernatural view of the universe.

That's what's really meant by my claim that science and religion are incompatible. I was referring to the Congregation-for-the-Causes-of-the-Saints interpretation of religion, which entails a variety of claims about things that actually happen in the world; not the it's-all-in-our-hearts interpretation, where religion makes no such claims. (I have no interest in arguing at this point in time over which interpretation is "right.") When religion, or anything else, makes claims about things that happen in the world, those claims can in principle be judged by the methods of science. That's all.

Well, of course, there is one more thing: the judgment has been made, and views that step outside the boundaries of strictly natural explanation come up short. By "natural" I simply mean the view in which everything that happens can be explained in terms of a physical world obeying unambiguous rules, never disturbed by whimsical supernatural interventions from outside nature itself. The preference for a natural explanation is not an a priori assumption made by science; it's a conclusion of the scientific method. We know enough about the workings of the world to compare two competing big-picture theoretical frameworks: a purely naturalistic one, versus one that incorporates some sort of supernatural component. To explain what we actually see, there's no question that the naturalistic approach is simply a more compelling fit to the observations.

Could science, through its strategy of judging hypotheses on the basis of comparison with empirical data, ever move beyond naturalism to conclude that some sort of supernatural influence was a necessary feature of explaining what happens in the world? Sure; why not? If supernatural phenomena really did exist, and really did influence things that happened in the world, science would do its best to figure that out.

It's true that, given the current state of data and scientific theorizing, the vast preponderance of evidence comes down in favor of understanding the world on purely natural terms. But that's not to say that the situation could not, at least in principle, change. Science adapts to reality, however it presents itself. At the dawn of the 20th century, it would have been hard to find a more firmly accepted pillar of physics than the principle of determinism: the future can, in principle, be predicted from the present state. The experiments that led us to invent quantum mechanics changed all that. Moving from a theory in which the present uniquely determines the future to one where predictions are necessarily probabilistic in nature is an incredible seismic shift in our deep picture of reality. But science made the switch with impressive rapidity, because that's what the data demanded. Some stubborn folk tried to recover determinism at a deeper level by inventing more clever theories -- which is exactly what they should have done. But (to make a complicated story simple) they didn't succeed, and scientists learned to deal.

It's not hard to imagine a similar hypothetical scenario playing itself out for the case of supernatural influences. Scientists do experiments that reveal anomalies that can't be explained by current theories. (These could be subtle things at a microscopic level, or relatively blatant manifestations of angels with wings and flaming swords.) They struggle to come up with new theories that fit the data within the reigning naturalist paradigm, but they don't succeed. Eventually, they agree that the most compelling and economical theory is one with two parts: a natural part, based on unyielding rules, with a certain well-defined range of applicability, and a supernatural one, for which no rules can be found.

Of course, that phase of understanding might be a temporary one, depending on the future progress of theory and experiment. That's perfectly okay; scientific understanding is necessarily tentative. In the mid-19th century, before belief in atoms had caught on among physicists, the laws of thermodynamics were thought to be separate, autonomous rules, in addition to the crisp Newtonian laws governing particles. Eventually, through Maxwell and Boltzmann and the other pioneers of kinetic theory, we learned better, and figured out how thermodynamic behavior could be subsumed into the Newtonian paradigm through statistical mechanics. One of the nice things about science is that it's hard to predict its future course. Likewise, the need for a supernatural component in the best scientific understanding of the universe might evaporate -- or it might not. Science doesn't assume things from the start; it tries to deal with reality as it presents itself, however that may be.

This is where talk of "methodological naturalism" goes astray. Paul Kurtz defines it as the idea that "all hypotheses and events are to be explained and tested by reference to natural causes and events." That "explained and tested" is an innocent-looking mistake. Science tests things empirically, which is to say by reference to observable events; but it doesn't have to explain things as by reference to natural causes and events. Science explains what it sees the best way it can -- why would it do otherwise? The important thing is to account for the data in the simplest and most useful way possible.

There's no obstacle in principle to imagining that the normal progress of science could one day conclude that the invocation of a supernatural component was the best way of understanding the universe. Indeed, this scenario is basically the hope of most proponents of Intelligent Design. The point is not that this couldn't possibly happen -- it's that it hasn't happened in our actual world. In the real world, by far the most compelling theoretical framework consistent with the data is one in which everything that happens is perfectly accounted for by natural phenomena. No virgin human births, no coming back after being dead for three days, no afterlife in Heaven, no supernatural tinkering with the course of evolution. You can define "religion" however you like, but you can't deny the power of science to reach far-reaching conclusions about how reality works.