Science, it is often said, is restricted in principle to the search for natural causes and the rejection of the supernatural; call this intrinsic methodological naturalism (IMN). Here, following the work of Boudry et al. , I argue that this view is misguided and damaging. We have not precluded supernatural claims from discussion. On the contrary, we have investigated them and found them wanting, as I show here using both historical and present-day examples.
“I have no need of that hypothesis.” So, according to legend, said the great astronomer and mathematician Piere-Simon, marquis de Laplace, when asked by Napoleon why he had not mentioned God in his book. If so, Laplace was not referring to the hypothesis that God exists, but to the much more interesting hypothesis that He intervenes in the material world. And Laplace’s point was not, fundamentally, philosophical or theological, but scientific.
The planets do not move round the Sun in circular orbits, but in elliptical pathways, as Newton had explained using his laws of motion, combined with his inverse square law for gravitational attraction. There is one small problem, however. The planets are attracted, not only to the Sun, but to each other, perturbing each other’s pathways away from a perfect ellipse. These perturbations are not trivial, and in fact it was the perturbation of the orbit of Uranus that would lead to the discovery of Neptune. Newton himself surmised that they could, eventually, render the entire system unstable so that God would need, from time to time, to intervene and correct it. Laplace devoted much of his career to developing the mathematical tools for estimating the size of the perturbations, and concluded that the Solar System was in fact stable. So Newton’s hypothesis of divine intervention was redundant, and it was this hypothesis that Laplace was supposedly referring to.
There is an irony here. As Henri Poincaré was to show a century later, a system of three or more gravitationally interacting bodies is potentially chaotic. Under certain circumstances, an initially minute difference in starting conditions can lead to an ever increasing divergence of outcomes, so that eventually planets can adopt highly elongated orbits, or even be thrown out of their solar systems altogether. Modern computer simulations  show that over the long term the solar system is indeed chaotic, with the possibility that Mercury may leave the Solar System, and that in some 3.5 billion years Mercury’s instability could be transferred to the other inner planets, including Earth, leading to the possibility of collision.
Stephen Hawking has commented  on Laplace’s remark, in much the same spirit as I am suggesting, but going much further:
I don’t think that Laplace was claiming that God didn’t exist. It is just that He doesn’t intervene, to break the laws of Science. That must be the position of every scientist. A scientific law is not a scientific law, if it only holds when some supernatural being decides to let things run, and not intervene.
A similar point of view had been put forward by Richard Lewontin, in his uncomfortably perceptive review  of Sagan’s Demon Haunted World, a review that I consider required reading for those defending science because of its all too rare recognition of creationism as a complex social problem:
Perhaps we ought to add to the menu of Saganic demonology, just after spoon-bending, ten-second seat-of-the-pants explanations of social realities.
I cannot do justice to Lewontin’s complex reasoning by brief truncated quotations. It is clear, however, that he uses two very different arguments in rapid succession:
Nearly every present-day scientist would agree with Carl Sagan that our explanations of material phenomena exclude any role for supernatural demons, witches, and spirits of every kind, including any of the various gods from Adonai to Zeus … We also exclude from our explanations little green men from Mars riding in spaceships, although they are supposed to be quite as corporeal as you and I, because the evidence is overwhelming that Mars hasn’t got any …
It is not that the methods and institutions of science somehow compel us to accept a material explanation of the phenomenal world, but, on the contrary, that we are forced by our a priori adherence to material causes to create an apparatus of investigation and a set of concepts that produce material explanations, no matter how counter-intuitive, no matter how mystifying to the uninitiated. Moreover, that materialism is absolute, for we cannot allow a Divine Foot in the door … To appeal to an omnipotent deity is to allow that at any moment the regularities of nature may be ruptured, that miracles may happen.
The first paragraph is one that I can accept and advocate in its entirety. We reject supernatural causes in the same way that we reject implausible material explanations, because the evidence tells us that they don’t exist. The second, a statement and defense of IMN, is of a very different kind. Science, he says, is committed in advance to exclusively material explanations, and the reason for doing so is, again, to exclude divine intervention.
Leave aside for now the problem of defining “materialism,” on which more later. Leave aside also the deliberately provocative anti-religious language, inconvenient though that be for coalition builders. After all, Lewontin has, and is entitled to, his own agenda here. Leave aside for the moment even the possibility that miracles need not disrupt the normal business of science, as long as they are sufficiently rare. Hawking has followed Lewontin into the trap that awaits all those who would legislate the metaphysical out of existence. They lay themselves open to the charge that they are, themselves, arbitrarily introducing yet another metaphysical rule.
So, alas, does the National Science Teachers Association, whose commitment to IMN is quoted with approval by the National Academy of Sciences: 
Science is a method of explaining the natural world. It assumes the universe operates according to regularities and that through systematic investigation we can understand these regularities. The methodology of science emphasizes the logical testing of alternate explanations of natural phenomena against empirical data. Because science is limited to explaining the natural world by means of natural processes, it cannot use supernatural causation in its explanations. Similarly, science is precluded from making statements about supernatural forces because these are outside its provenance. Science has increased our knowledge because of this insistence on the search for natural causes. [Emphasis added]
This is very bad. We slide from an innocent-seeming description of the domain of science as the “natural” world, through the uncontroversial idea of testing explanations against each other, to the non sequitur of the sentence I have highlighted. There is an illusion of logic, based on an assumed dichotomy between the natural and the supernatural, but this is mere wordplay. We are given no other reason for this leap, even though it could have been justified, as Hawking and Lewontin justify their own exclusion of the supernatural, by reference to the assumption of regularity. As I will show, the claim that “science is precluded from making statements about supernatural forces” is simply untrue. Time and again, science has refuted the appeal to the supernatural by providing alternatives — if this is not “making statements about supernatural forces”, what is?
Natural and supernatural
Can we even make a meaningful distinction between the natural and the supernatural? I was initially inclined to say no. If something occurs, it’s part of nature. It is a law of nature that water doesn’t turn into wine, but if you believe that the miracle of the wedding feast of Cana really happened, then you need to modify the law to say “Water doesn’t turn into wine, except when Jesus tells it to.” Maarten Boudry persuaded me that this was not a helpful line to take. Like all attempts to define a problem out of existence, it is logically unassailable, but useless. It denies us access to the very distinction that we should be clarifying.
The question, however, is more difficult than it seems. After all, we do not know everything that there is to be known about nature. The limits of natural explanation have been extended in the past, by invoking action at a distance (gravity, then other forces), intrinsic randomness (quantum mechanics), and more recently particle entanglement (quantum mechanics again). Presumably they will be in the future, in ways yet undreamt of. So the fact that something cannot be explained by today’s science need not force us to invoke the supernatural. What would, then? Boudry and Taner Edis [1c] have suggested a test for what they call unphysical causation, but it is highly technical, with their criterion based on demonstrated access to uncomputable numbers (I will not attempt to reproduce their argument). However, they suggest some examples. What, for instance, if Lourdes started producing undeniable miracles in large numbers, including the regrowth of amputated limbs, but only for devout Catholics? What if all organisms were found to contain an identical section of DNA, whose diffraction pattern spelt out the message “© Yahweh 4004 BC”?
Some case histories
Searching for messages is not a new idea. There are cottage industries within both Christianity and Islam, producing evidence that the authors of the Bible or the Qur’an are referring to scientific facts unknown by mere mortals when these books were first written. For instance, does the reference to the “circle of the earth” in Isaiah 40:22 imply that the author knew that the earth goes round the sun? Do the numerous biblical references to God stretching out the heavens show an awareness of the expanding universe? Mohammed is said to have “split the moon”; is this a reference to its formation by accretion? Few of us would find these examples convincing. What of the “Bible code” claim, which put three successive books on the best-seller list, that computer searching of the Hebrew text according to certain counting rules reveals messages hidden there for us? This was debunked  by showing that normal secular writings would also confess to similar secrets when subjected to similar torture.
Present-day science does indeed make statements highly relevant to the existence or otherwise of supernatural forces. To raise the stakes to their utmost, some consider the Universe to be fine tuned for life, and regard this as scientific evidence for a purposeful Creator. Others regard it as yet another argument from ignorance, since it may well be that the Universe is not really all that special, or that there are as yet unknown constraints of some kind on the relevant physical constants, or that quantum fluctuations will generate such a superabundance of Universes that some, statistically, are bound to have the required properties. While it may be premature to test these suggestions, they are part of a clearly scientific agenda . The suggested causes would be “natural” by any standards, but if established would have the effect of making the appeal to a supernatural Creator unnecessary. Science would then have made a clear statement about the purported supernatural force responsible for fine tuning, exactly as it did about the purported supernatural force responsible for the stability of the Solar System, namely that there was, in Laplace’s words, no need for that hypothesis.
Two other examples spring to mind. First, the argument from Intelligent Design as applied to the mammalian eye. This fails, because the mammalian eye is in one crucial detail very poorly designed. The nerve endings, and the blood supply, run in front of, rather than behind, the photosensors, partly occluding them and giving rise to each eye’s blind spot. It does not have to be that way, since the octopus eye is built the right way round. At this point, the defender of design has two options. He can admit defeat, or at least accept that the Designer’s options are restricted by our evolutionary history. So in this case the argument from design is refuted or, at any rate, enfeebled. Or he can argue, as Behe does in Darwin’s Black Box, that the refutation fails because we do not know the Designer’s full intent. At this point, we lose interest because the argument from design has become so well immunized against observation, to borrow a term from Maarten Boudry’s PhD thesis Here be Dragons , that it has ceased to be science. In neither case have we referred to the supernatural nature of the argument as the reason for dismissing it.
Secondly, there is a version of theistic evolution in which the Creator intervened at the level of quantum mechanical indeterminacy to set in course one mutation rather than another, and used this to ensure the evolution of intelligent humans. I first heard this suggestion from Alvin Plantinga , and if I understand Ken Miller’s Finding Darwin’s God correctly I think that on this topic, for once, he and Plantinga would agree. Certainly there is nothing here that violates the laws of physics and chemistry, since the chance breakdown of one single radioactive atom at one moment rather than the next may well disrupt a growing chain of DNA, and a single mutation may well have far-reaching consequences . Were such a mutation to have happened under the Creator’s guidance, that would be supernatural causation par excellence.
I would argue against this on the grounds that there is little or no evidence of a bias towards beneficial mutations, and that since intelligence has emerged independently in cephalopods, cetaceans, parrots, velociraptors (if cerebral capacity is anything to go by), and simians, the emergence of such little intelligence as we have requires no special explanation. Now you may regard my argument as mistaken, banal, or ill-informed, but I do not see how you can describe it as outside the domain of science.
It is only after the Bible Code claims have been convincingly shredded that we can decide that claims of this kind are not worth our time and trouble. It was only after exhaustive card-guessing experiments had failed to reveal any evidence for ESP (and after the published evidence for its reality was found to be faulty if not fraudulent) that people decided it was just not worth their while to continue in that direction. It was only after spiritualists had repeatedly been exposed as fakes that scientists more or less stopped investigating them. For a while, even such distinguished scientists as Alfred Russel Wallace took their pretensions seriously. However, nowadays such investigations are undertaken more to unmask fraud and protect the public than in the hope of new discoveries. (In this endeavor, scientists have been joined by professional magicians, from Houdini to James “the amazing” Randi, illustrating to my mind the artificiality of separating off “science” from other kinds of factual enquiry.) Much the same, but with less emphasis on fraud, can be said about hunting for ghosts. In this century, there have been several studies of the effects of intercessory prayer on recovery from illness. No effect (or in one case, a small negative effect, tentatively attributed to the added stress of the situation), and a recommendation  from Cochrane Reviews, which collate data from clinical trials, that no further work of this kind be undertaken. In each of these cases, the scientific search has been abandoned, not because of some overarching principle about the nature of science, but because plain experience showed it to be pointless. A priori rejection of the supernatural had nothing to do with these decisions, which were based purely on experience. Experience that would never have been attained if scientists really were debarred from submitting the supernatural to investigation.
In all these examples, we do indeed use scientific reasoning to discuss the claims of supernaturalists, so IMN is untrue. It was untrue in the 18th century when science explored solar system stability; it was untrue in the 19th when natural selection rendered Paley’s watchmaker redundant; it was untrue in the 20th when claims of extrasensory perception were scientifically examined and found wanting; and it is untrue in the present century as we prepare to grapple with such problems as the origin of our Universe and its appearance of being fine-tuned for the emergence of life. To propagating IMN is to propagate a falsehood.
The appeal to intrinsic naturalism is unnecessary
One argument for IMN is that in its absence the possibility of invoking supernatural explanations may discourage the search for natural ones. This is a purely pragmatic argument, and I cannot imagine it having any real effect. Those who prefer supernatural explanations invoke them anyway. Millions of Americans believe humans to have arisen through a special supernatural act, but this is not for lack of a naturalistic explanation. Intelligent Design creationists argue that undirected evolution cannot possibly generate new information, or that protein sequences are too improbable to have arisen naturally. Young Earth creationists, a separate group (although in the UK the two strongly overlap) point to anomalies in radiometric dating, or to polonium halos in rocks that did not contain polonium’s ultimate parent, uranium, and claim that these somehow cause the naturalistic account of earth’s geological history to unravel. This they do because of their prior commitment to mystification. Debunking their nonsense is a proper matter for science, and the talkorigins website has a page  listing numerous such claims and their rebuttals , although experience shows that mere refutation will not stop their proponents from repeating them. And there are important unsolved problems, such as the origin of life, which some claim as evidence for supernatural intervention, but I do not think that any scientist interested in the topic would be so easily fobbed off. In any case, defining their activities as unscientific would not make the supernaturalists disappear. On the contrary; they would (and do, see below) triumphantly hail such definitions as proof that we impose arbitrary limitations on our science.
So why do we tend to avoid problems whose solution would involve the supernatural? For practical, rather than for philosophical, reasons. Science, as P. J. Medawar pointed out in his devastating critique  of Koestler’s Act of Creation, is an extremely practical activity, and it is commonplace for lines of enquiry to be abandoned because they were getting nowhere (I can confirm this from bitter experience, as a sometime experimental chemist). Thus, as Boudry and colleagues remind us [1a], the Royal Academy of Sciences in Paris decided in 1775 to have nothing more to do with proposals to build a perpetual motion machine. This was many years ahead of the development of the laws of thermodynamics, which tell us that such a machine is impossible, but so much effort had been spent to so little effect that the Academy decided no more was warranted. Not because (as we might now be tempted to say) such a machine would require a supernatural mechanism, but because they didn’t think there was any chance of it working. If we turn aside, as we often do, from investigating this or that claim to supernatural agency, we do not do so on principle but because experience warns us that we would be wasting our time.
Our faith in the regularity of nature derives from our having lived and evolved in a world where it holds good, not from some special rule about the nature of science. It is confirmed, over huge reaches of space and time, by observation, and we can interpret the spectra of galaxies whose light has taken 12 billion years to reach us.
And that faith itself is subject to examination, and has its own limits. Careful measurement of these distant spectra led to the suggestion (since subjected to highly critical scrutiny)  that the constants of physics might have changed even in the fourth decimal place, a possibility that was enough to arouse the interest of The Economist . Thus the assumption of regularity is itself testable, and tested. On current thinking, the early Universe underwent a period of rapid inflation, in which space expanded at such a rate that the distance between points initially close together grew at a rate faster than the speed of light. Thus during this expansionary stage the laws of nature were very different from what they are today, and to describe it we must abandon the assumption of regularity altogether. And the state of the Universe before this stage may be to us in principle unknowable.
The appeal to intrinsic naturalism is damaging
We do, most of the time, practice a form of naturalism, but it is a form derived from experience (sometimes called Provisory or PMN), as opposed to the a priori injunction of IMN). Does this distinction matter, other than perhaps to professional philosophers? Yes, very much indeed. There is a war on, between the supporters of science as we know it, and the creationists and endarkeners who wish to replace it with what the Discovery Institute’s Institute for Science and Culture, in its notorious “Wedge document” , calls “the theistic understanding that nature and human beings are created by God.”
The unwarranted and inaccurate grafting onto the methods of science of the arbitrary rule that it must not traffic in the supernatural exposes a flank to its enemies, which they have been quick to exploit. The central argument of Phillip Johnson’s Defeating Darwinism by Opening Minds, which predates the Wedge Document, is that mainstream science (including, crucially, the study of human origins) is illegitimate because it arbitrarily excludes explanations that lie outside the limits of naturalism. His disciple Alastair Noble, director of the Glasgow-based, Centre for Intelligent Design, says in the Centre’s introductory video :
One of the key questions posed by the world around us is whether we are here by chance or by design. There is a strident strain of science which insists that all the design in the world is apparent, not real, and that natural selection acting on random mutations is sufficient to explain it all. That kind of science is derived from a view that the only explanations which are acceptable are those which depend purely on physical or materialist processes. That is not a scientific finding that is derived from the evidence. It is, in fact a philosophical position, and a biased one at that, which is brought to the actual evidence. It excludes other types of explanation which the evidence may merit.
Here the claim that mainstream science excludes design-based explanations a priori is used to bolster the common creationist tactic of misrepresenting the outcomes of its investigations, including evolution, as inputs. Going further downmarket, we come to the creationist claims that evolution science is a religion like any other, or that evolution and creationism differ only in their starting assumptions, and as long as the scientific community itself presents the rejection of the supernatural as an input rather than an output, we have scant grounds for complaint against such vulgarizations.
In short, IMN is untrue and carries a heavy rhetorical cost to science. But everything that can be accomplished by including IMN in our definition of science and then appealing to that definition as criterion, can be accomplished on its own merits by less circuitous means. So let’s cut out the middleman.
A simple alternative
Instead, I would appeal once more to Laplace, who took as examples such purported phenomena as animal magnetism, dowsing, and solar and lunar influences on mood :
We are so far from knowing all the agents of nature and their diverse modes of action that it would not be philosophical to deny phenomena solely because they are inexplicable in the actual state of our knowledge. But we ought to examine them with an attention all the more scrupulous as it appears more difficult to admit them, and it is here that the calculation of probabilities becomes indispensable, to decide to what point one must multiply observations or experiments, in order to obtain for the agents that they indicate a probability that outweighs the reasons we would otherwise have against admitting them.
Or, in the abbreviated form that has come down to us to us through Carl Sagan,
Extraordinary claims require extraordinary evidence.
That’s all we need.
I thank Maarten Boudry and Stephen Law for helpful discussions. Earlier versions of some of this material have appeared on 3 Quarks Daily and on my blog.
Paul Braterman spent most of his career in chemistry at Glasgow University (his present base) and the University of North Texas. He has published over 120 scientific papers and book chapters, and is on the committee of the British Centre for Science Education. During his career, Braterman has collaborated with NASA’s Astrobiology Institute, Jet Propulsion Laboratory, Scripps Institution of Oceanography, and the Sandia/UNM Materials Research Laboratory. His first non-technical book is From Stars to Stalagmites: How Everything Connects. He is writing a book on creationism in the classroom, and blogs on 3 Quarks Daily and at paulbraterman.wordpress.com.
 a) How not to attack intelligent design creationism: philosophical misconceptions about methodological naturalism, by Maarten Boudry, Stefaan Blancke and Johan Braeckman, Foundations Of Science (2010) 15:227; b) Grist to the mill of anti-evolutionism: the failed strategy of ruling the supernatural out of science by philosophical fiat, by Maarten Boudry, Stefaan Blancke and Johan Braeckman, Science & Education (2012) 211151-1165 ; c) Beyond Physics? On the Prospects of Finding a Meaningful Oracle, by Taner Edis and Maarten Boudry, Foundations of Science (2014), March.
 Large-scale chaos in the solar system, by J. Laskar, Astronomy and Astrophysics (2009) 287:L9-L12; Existence of collisional trajectories of Mercury, Mars and Venus with the Earth, by J. Laskar and M. Gastineau, Nature (2009) 459:817-819.
 Stephen Hawking, Does God Play Dice, 1999.
 Billions and Billions of Demons, by Richard Lewontin, New York Review of Books, January 9, 1997.
 Teaching About Evolution and the Nature of Science, 1998 but still current, and freely available here, p. 124.
 See e.g. Hidden Messages and The Bible Code, by Dave Thomas, Skeptical Enquirer 21.6, November / December 1997. My discussion refers to Michael Drosnin’s Bible Code books, rather than to the original statistical puzzle posed by Eliyahu Rips, who has dissociated himself from them.
 Capital letters for Creator and Designer because I do not wish to collude in the polite fiction that the Intelligent Design program is anything other than an argument for the existence of God. For a very recent discussion of the fine tuning and multiverse concepts by Coel Hellier on this site, see here, and references therein. Separate technical questions have been raised about the validity of the statistical argument from fine-tuning, but these do not affect my argument.
 Here be Dragons. Exploring the Hinterland of Science, by M. Boudry.
 Personal communication, ca. 2006.
 Consider the mutation that made Queen Victoria, grandmother of the last Tsarevich, a carrier of hemophilia, and what difference this might have made to Russian history.
 L. Roberts, I. Ahmed, S. Hall, and A. Davison, Intercessory Prayer for the alleviation of ill health, Cochrane Summaries, 9 November 2011.
 Mark Isaak (ed.), Index to Creationist Claims, TalkOrigins Archive, 5 November 2006.
 Alternating mutation and selection can and demonstrably does generate new information; protein sequences have considerable flexibility and do not arise in a single step; polonium halos in uranium-free rocks can be traced to the diffusion of radon; dating anomalies are exceptional and indeed informative, since they can be traced to heating episodes and other post-depositional events; and so on.
 New Statesman, 19 June 1964, reprinted in Pluto’s Republic, OUP 1984.
 Michael T. Murphy, John K. Webb, and Victor V. Flambaum, Revision of VLT/UVES constraints on a varying fine-structure constant, arXiv:astro-ph/0612407v3, 11 November 2007.
 Ye cannae change the laws of physics, The Economist, 31 August 2010.
 The Discovery Institute’s Wedge document.
 Available at http://www.c4id.org.uk/
 Pierre Simon marquis de Laplace, Essai philosophique sur les probabilités, 1814, p. 50.