On metabiology, natural law and divine action

I’d like to pick up on a remark made by our friend Darek Barefoot on a recent thread:

God may be working outside the pattern of lawlike regularities in countless irregular nudges of the genetic code, but given how many of these nudges there seem to have been it becomes difficult to distinguish them from lawlike regularities.

There’s actually quite a lot worthy of discussion there. For example, on an occasionalist metaphysics God’s nudges, like the lawlike regularities, and everything else for that matter, would constitute all that happened anyway. Lawlikeness would be entirely dependent on God’s desire to act consistently, and irregularities on his choice to vary things.

In concurrentism too lawlike events would also be God’s actions, in that he would be the first mover of them, though their regularity would be a true feature of the natures with which they were endowed. Only in “mere conservationism” (and materialism, of course) would predicable events be in any sense autonomous of God’s ongoing activity – they would (in conservationism) instead be the result of his forward provision, more or less detailed.

For most Christian philosophers and theologians of the past, then, the division into “natural” and “supernatural”,  or into “law”, “chance” and “absolute fluke”, is actually one of human convenience – God has never asked us to distinguish them, but rather to attribute all things to him. He doesn’t owe us watertight science.

But the issue with evolution isn’t that at all: it’s that the process hasn’t been reduced to lawlike events at all. If one is talking about “nudging”, one is concerned with the nudging of apparently stochastic mutations, fortuitous factors in the environment and – in many cases – the infinitesimal probabilities said by Pauli to be indistinguishable from miracle. As I said in that previous post, if anything the presence of organised complexity with such low contingency is actually more characteristic of intelligent “nudging” than it is either of lawlike processes or statistical contingency.

The lack of a mathematical footing to evolution was what prompted mathematician Gregory Chaitin to initiate the research programme of metabiology, its aim summarised by the title of his 2012 book Making Biology Mathematical. He is one of those using evolutionary algorithms to study evolution, and to cut a very complex story short (for the sake of reaching broad conclusions) he found it necessary to build into his algorithms the concept of a Halting Oracle. This is also called a “Turing Oracle”, not so much because Turing invented it, but because he proved it was impossible:

We shall not go any further into the nature of this oracle apart from saying that it cannot be a machine.

It’s a mathematical tool only, for the analysis of what cannot be computed, either mechanically or biologically. Chaitin describes its role in his model:

You’re allowed to ask God or someone to give you the answer to some question where you can’t compute the answer, and the oracle will immediately give you the answer, and you go on ahead.

The input of “magic” information like this is justified to make the model work (it will not do so without even when modelling intelligent design!), but one thing is not disputible either by critics, supporters or Chaitin himself: it makes the model non-Darwinian. If anything, Chaitin’s work models variation rather than Darwinian evolution – and it requires intelligent input, as he openly affirms.

Indeed, in passing it must be said that all evolutionary algorithms import information via oracles of one kind or another – in some, for example, a “Hamming Oracle” is used, simply illustrated by Richard Dawkins’ “METHINKSITISAWEASEL” programme: if your changed letter matches the target phrase (the hidden information) it’s retained.

Now what Chaitin says about the limitations of his “toy” model is interesting. If one made it more like the real world by modelling what is actually believed to happen there, it would become progressively less computable. So you can (probably even in theory) have a mathematical model that isn’t truly Darwinian, or a more-or-less Darwinian model that isn’t mathematical. Neither will put evolution on a law-like footing.

Meanwhile, the state of play is that you can only make any model work by supplying information along the way – appearing to confirm Gödel’s logical conclusion from decades back that nowt comes from nowt, and Pauli’s that teleology cannot be kept out.

We have, then, a rather curious set of circumstances:

  • Practically, actual Darwinian processes have not been reduced to law – especially mathematical law – and it may be impossible to do so.
  • Darwinian processes, unless new types of laws of emergence appear (despite the first difficulty), depend largely on gaining organised complexity by non-lawlike processes of very low probability, which logicians like Gödel (and philosophers like Étienne Gilson) believe to be intrinsically impossible, and which in any case are formally indistinguishable from miracle.
  • Validation of the mechanisms of random mutation and natural selection, above the microscale, as the sole or predominant means of speciation, remain unobserved and contestible after 150 years. Disconfirmatory evidence, additional and alternative mechanisms all weaken its plausibility.
  • The central case that evolution is a lawlike process without the need for the input of information has not come remotely near definitive demonstration.
  • …And don’t even mention the origin of life. Chaitin: “Now let me mention, by the way, that this model has life in it from the beginning. This model does not talk about the origin of life, because I already have a universal programming language here at the beginning.”

It seems to me that a theory which is intuitively eminently plausible and comprehensible becomes less prone to confirmation the more closely it is subjected to scrutiny. One does not have to be unduly skeptical (or even particularly religious), and still less stupid, to treat it as one would any other internally consistent but non-rigorous theory.

But, to put it in a more theologically-orientated way, the assertion that evolution is an entirely natural process (whether that means materialistically natural or natural in the “divine frontloading” sense) rests mainly on faith in its plausibility rather than either logical necessity or empirical demonstration. It doesn’t even begin to be a scientific claim.

To the Christian, I must re-affirm, the difference is only one of “How God did it.” Lawlike evolution is no less teleological and divine than law-like procreation. Special creation is no more intrinsically unlikely for life than for the cosmos. And some combination of the two is unproblematic – if one believes that John the Baptist or Jeremiah the prohet were born naturally but yet according to God’s election.

However, the theist who tries to make God the author of an ateolological process loses both his cake and the satisfaction of eating it, and becomes logically incoherent along the way.

I agree with Darek that the evidence of teleology in the creation itself makes the actual process of secondary importance. It only matters to me because … well, because truth matters. But also because the kind of creation we inhabit inevitably tells us something about the kind of God we have.

If he’s the God of Deism in nature, he’s likely to be the God of Deism in religion, too. If he were entirely capricious, neither the world nor the faith would be good places to be. If he’s the Logos of the Father … that’s where things get interesting, up close and personal.

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About Jon Garvey

Training in medicine (which was my career), social psychology and theology. Interests in most things, but especially the science-faith interface. The rest of my time, though, is spent writing, playing and recording music.
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10 Responses to On metabiology, natural law and divine action

  1. Jon

    I believe it was the composer Ravel who once said that true argument must begin with agreement and then proceed to differences over detail. So here. We are surely in broad agreement.

    A couple of observations. First, I doubt that scientific weather modeling could ever be mathematically grounded in the way being demanded of “natural selection.” I use scare quotes because we are talking about dynamic interactions of organisms with environment and each other, the combinatorics of which are too staggeringly dense to be untangled.

    The second I put as a question: Is a medical researcher entitled to consider mutations leading to birth defects to be, to a significant extent, chance events? Not that these mutations occur outside of natural law nor that probability cannot be invoked, but that the network of causes in particular cases (even setting aside QM uncertainty) is far too dense to be traced? I believe most of us would forgive researchers for so designating such events.

    With a postitive answer assumed, I must return to Exod 4:11, which I take as profound truth. Does God individually appoint the deaf and blind in some very real sense? Always adding the disclaimer that God does revel in deafness or blindness or Tay-Sachs or other impairment but that he incorporates them into his good purpose toward a good end. If so, then God works in purposeful ways by means of process that from a scientific standpoint is understandably characterized as “chance” and which is to outward appearance “undirected.”

    Reasoning along these lines leaves me untroubled by the stochastic element presumed in neo-Darwinism. I need not stand on my head to award unconscious processes some kind of self-creative freedom. Nor need I doubt God’s purposeful action to the extent that a process is nested within a law-like framework or incorporates a stochastic element in scientific terms.

    For those who wish to contest the neo-Darwinian model of evolution, contest away. But at all costs avoid giving the impression that the case for God’s creative sculpting of nature depends upon the success of that effort.

    • Avatar photo Edward Robinson says:


      I replied to your last comment under “Frontloading, Maths, and Logic” — which I mention in case you want to have a look at what I said there.

      Regarding the above, there is a difference between a broadly lawlike framework that “incorporates a stochastic element” and a process which is wholly or almost wholly stochastic. For example, the human immune system makes use of randomness, but the use made of randomness is tightly circumscribed by the overall working of the system. But according to neo-Darwinism, all immune systems (human and otherwise) arose due to randomness.

      To make an analogy from the non-random world, there is a difference between saying that a grandfather clock works strictly in accord with the laws of physics, and saying that the grandfather clock came to be purely through the action of the laws of physics. So the immune system may make use of randomness, but it does not follow that the very first immune system arose due to randomness.

      Another example, from the world of randomness: smoke alarms sometimes use radioactive materials. But radioactive decay is supposedly random. So the smoke alarm makes use of a random physical process to accomplish a rationally determined end, i.e., making a noise to alert the homeowner to smoke. But no one proposes that smoke alarms were put together by a random physical processes.

      The problem with many if not most varieties of theistic evolution (and I’m not rejecting theistic evolution itself in saying this) is that they do not make crystal clear that the random element is supervised in such a way as to achieve rationally determined ends. And when you try to pin TE/EC proponents down on this — does God do anything in particular, or does he just light off the Big Bang and watch the random combinations of atoms and molecules do whatever they happen to do — they get squirmy, evasive, irritated, and quickly change the topic or abandon the discussion (as can be found in the record virtually every time such questions have been raised on BioLogos). The degree to which God plans, programs, rules over, controls, or determines the goals of the evolutionary process is not something they wish to talk about with clarity. They prefer to keep that subject as murky and indefinite as possible. They must have something to hide, or they wouldn’t be acting in this way.

      And this is why — as I argued in my last column — TE has hit a ceiling in American popular support. Its only potential for growth is found in the evangelical world, and it’s precisely the evangelicals who are leery of TE because TE avoids clarity in this area.

      One can try to justify TE vagueness by all kinds of stratagems. One can speak of the mysterious nature of God’s providence, etc. I find all such answers evasive, confused, and cowardly. After all, such answers are never resorted to by TEs in the case of other scientific theories. For example, if I ask a TE how God controls the motion of the planets, the TE will give me a very clear answer: through the laws set forth in Newton’s (or Einstein’s) physics. And I am quite happy with that answer. But when I ask a TE how God controls the outcomes of evolution, the mystery-mongering starts. The theory of gravity apparently requires no mystification to work God into the picture, whereas the theory of evolution does. This is highly suspicious.

      But even if such dance-around-the-question answers were intellectually legitimate answers, they would not convince the majority of evangelicals. The evangelical culture of the USA has always been a plain-speaking, direct-talking culture, not an oblique, allusive, nudge-nudge-wink-wink-guess-what-I-mean-but-won’t-say culture. Evangelicals demand straightforward answers. The TE leaders simply have to come clean on the question whether God is fully in charge of the results of evolution, or not.

      As far as anyone can tell, a good number of them, especially the biologists, think that God is not actually in charge of everything, that he has given nature its freedom and accepts the results that nature puts out, as long as it somehow or somewhere spits out some creature capable of fellowship with him, even if that is a smart dinosaur or smart octopus rather than a human being. That’s the impression one comes away with after reading Venema, Falk, or Ken Miller, not to mention a score of their groupies who post on BioLogos and elsewhere around the internet. And they know that’s the impression they create, because they have been confronted with this characterization of their view a hundred times or more; yet, given a hundred chances, in many different forums, they won’t dispel this characterization by explicit statements to the contrary. It’s therefore reasonable to infer that this characterization in fact reflects the actual position of these TEs.

      • Ed

        Most of the people I’ve known on a personal basis have been conservative US evangelicals, of various denominations. As a group they never get near the type of philosophical distinction you are talking about. There are few reasons why it matters little to the evangelical community at large how the TEs on Biologos interpret God’s role in evolution.

        The first reason is that any suggestion that human beings in any way descended from apelike creatures is too repellent for evangelicals to consider. You can insert miracles liberally. You can have God guiding the process in the most direct way imaginable. It makes no difference. An apelike brutish being as human forebearer is so intrinsically repugnant to them that they will go nowhere near it. Under any circumstances I can imagine.

        The second reason is that the Bible says the world was made in six days. Simple enough. And there is a genealogy taking us back from Abraham to Adam in a couple of thousand years or so. There’s no room for evolution. Sure, there are old earth evangelicals but they are always on the sidelines and always on the defensive.

        Third is the matter of evidence. Evidence for an old earth? Evidence for common descent (read as “man from a monkey”)? To dyed-in-the-wool evangelicals the strength of a person’s faith is measured by how much evidence they are willing to reject in order to cling to the plain, simple statements of Scripture. Piling up more evidence simply challenges them to have more faith.

        There are plenty of evangelical academics who differ, but the regular church-attending, self-identifying US evangelicals are not interested in the ideas of academics of any stripe. It’s a community that chooses its own ideological leadership by popular acclaim, and the leaders it chooses are the John MacArthurs and Ken Hams.

        Sure, there are intellectual evangelicals who parse scientific-philosophical distinctions like the one you’re talking about, but if you think the evangelical community as a whole has any interest in or understanding of such issues you are mistaken.

        Finally, how many scientists deny that evolution takes place according to the laws of physics and chemistry? It is process with a dense web of interactions, chaotic in something like the way weather is chaotic. The interactions are too complex to support precise, simple predictive strategies. That is not the same as saying that evolution is generally conceived as occurring outside the laws of nature.

        • Avatar photo Edward Robinson says:


          I, too, have spent a good deal of time interacting with conservative evangelicals, and evangelicals of all kinds. I concede many of your points. Still, I think you have not seen what I am driving at. Let me try to clarify.

          The evangelical community in the USA can be divided, for the purpose of analysis, into conservative, moderate, and liberal.

          The liberal evangelicals are already mostly onside with BioLogos and theistic evolution; indeed, TE in its modern form (the past 20 years) is the creation of liberal evangelicals.

          The “conservative” evangelicals, as you say, are not going to be onside with BioLogos or TE because they take Genesis with fairly rigid literalness and the very idea of human evolution is repugnant to them. These people are not part of BioLogos’s “target market.” Everyone at BioLogos knows that Ken Ham is not going to accept TE. Arguing with Ham etc. is a waste of energy.

          The “moderate” evangelicals are those who are at least in principle open to non-literal readings of parts of Genesis, but only if those non-literal readings preserve what for them are core Christian truths . Thus, for example, one might say that the important thing about Genesis 1 is that God created everything, not the actual description of how he created everything. From the fact that God created everything, we owe him gratitude, we know he is omnipotent, we know his will is sovereign, we know that man’s existence was determined in advance by divine choice, etc. Or in Genesis 2, the conversation with the serpent might not be meant literally, but only figuratively, but the Fall is still a real event with real consequences for the human race.

          The question I’m addressing is why BioLogos is doing so miserably at winning over these moderate evangelicals. The answer to me is clear: (1) BioLogos is very slippery on whether the whole Bible is true (even after allowing for figurative meanings in some cases). For moderate evangelicals, denial of that is a deal-breaker. (2) BioLogos will not clearly affirm God’s sovereignty over the process of evolution, God’s advance plan for particular results of evolution. It will not even confirm that man and only man was the highest goal of evolution, and that God made absolutely sure that man (rather than an intelligent octopus or porpoise) was the end result of the process.

          It looks as if many TEs, on BioLogos and elsewhere, are teaching that God rolled the Darwinian dice and then nature took over from there. And by the very nature of Darwinian theory, it is not possible for any given starting position to guarantee any fixed ending position. So it looks as if God is not sovereign, not providential, not in control.

          No moderate, Bible-believing evangelical, however much he may be open to the “common descent” part of evolution, is going to accept an account of the divine involvement of evolution like that.

          This is why BioLogos is spinning its wheels. Who is converting to BioLogos-TE? Mainly, other faculty members at liberal divinity colleges and liberal arts colleges run by evangelical denominations. In other words, the liberal intelligentsia is spreading its message mainly among the liberal intelligentsia. The people in the pews are unmoved.

          I grant you that the target market of moderate evangelicals for TE is not large. But that is all that TE has got! Nobody on the planet cares about BioLogos or TE except Protestant evangelicals. Mainsteam Protestant churches accepted evolution long ago, so the message of BioLogos is for them redundant. Catholics have their own ways of handling evolution, and don’t care if BioLogos lives or dies. Atheists like Dawkins and Coyne see TE as a contemptible halfway house between real science and outmoded religion. If TE is to grow in numbers and in social influence, it to grow within the Protestant evangelical world. And to do that, it has to sound convincingly Biblical (not fundamentalist, but at least Biblical) and convincingly in line with confessional Protestantism on questions such as sovereignty, omnipotence, providence, the Fall, etc. It has failed to do that. And in particular, it is shooting itself in the foot by not stating where it stands on God’s control over the evolutionary process.

          Your last paragraph makes no sense to me. It doesn’t address any claim that I made. Perhaps you misunderstood what I was arguing, but until I know what you mean, I can’t respond to it.

          • Ed

            I simply feel that the “target market” you have identified, that of moderate evangelicals who are sensitive to philosophical distinctions in interpretation of evolution, is so miniscule that it would be unrealistic to think Biologos or anyone else will move survey numbers by addressing it, whether convincingly or not.

            As for my last paragraph, I addressed this on the later thread. If you are still in the dark about it, my apologies.

            • Avatar photo Edward Robinson says:

              Thanks for coming back on this, Darek.

              Well, if you are right, you have just in effect predicted the death of TE/EC as a movement, because it is ONLY the evangelical Christian world that has any interest in TE/EC, and the evangelical world (at least, about 80% of it) will continue to reject all versions of evolution for as long as TE/EC refuses to state directly that God determines and controls all evolution’s outcomes. An evolutionary process that is neither guided nor preprogrammed will be (rightly, I add) rejected by evangelicals as materialistic and atheistic.

              On the other hand, if the TE leaders were to turn around and say: “We think God is silently steering the process by introducing favorable mutations” or “We think God set up life at the beginning so that the outcomes of evolution, in particular man, were inevitable” they would win over many evangelicals. But as they won’t say either of those things, or anything else like that, they are doomed to rejection. That’s the reality of evangelical faith, and if Falk, Giberson, Haarsma, Venema, etc. can’t figure that out, they aren’t particularly perceptive of the sociology of American religion, and therefore (like any salesman who doesn’t take the time to learn the attitudes of the people he’s selling to), they will fail.

              As for your “explanation” of the paragraph that puzzled me, it isn’t an explanation at all. I don’t disagree with what you wrote in that paragraph; but it didn’t address anything that I was arguing for; it thus came across to me then, and still does now, as a non sequitur. It is as if you were mentally arguing against some other combatant and forgot that you were arguing with me instead, and responded to arguments someone else had used, rather than to what I was saying. But I’m content never to know the literary origins of your paragraph. Best wishes.

        • Avatar photo GD says:

          “…… how many scientists deny that evolution takes place according to the laws of physics and chemistry? It is process with a dense web of interactions, chaotic …”

          This is spot on – indeed it is probably the main reason why some suggest ‘additions’, such as emergence, complexity, or a hierarchy of laws yet to be discovered, to account for the entire planetary system and the great interdependence.

          I agree the interactions are extremely complex, but this imo is a big reason to ditch the naïve Darwinian outlook and seek a far more satisfying and intellectually robust outlook. I for one do not see any anti-religious content in such an endeavour.

    • Avatar photo Jon Garvey says:


      First off, I hope I made it clear that God could work through law, stochastic events or any other combination … provided those means are sufficient to exexute his chosen outcomes. So “Does evolutionary theory work?” is a somewhat different question to “Does God work through evolutionary theory?” If the first is true, the second is too. My own gut feeling is that we have a good idea why we can’t predict the weather – evolution is much more of a black box, with a lot more theoretical problems, and a pile of metaphysical baggage that never seems to go away.

      But the key theological issues hinge not on confirming or disconfirming Darwinism, but on rewriting theology on the basis of metaphysics drawn from the theory (eg, since we can’t predict its outcomes, God can’t either and prefers not to).

      As you rightly say, the commonest kind of stochastic events are either unpredictable events of deterministic laws, or chaotic events which are probably deterministic if one could measure accurately enough (though some disagree on that). I’ve know doubt that both are transparent to the omnisicient Lord.

      Then there are the materially indeterminate events like quantum events, which may well have effects at the molecular scales evolutionary change works at. These states don’t seem to be written into the original creation – at least both R J Russell and J Polkinghorne see them as a way God could act in the world without “interfering” with science at the level of information.

      Once more, apart from your useful Exodus text (haven’t spotted that before to add to my store of “universal providence” quotes) there are specific Scriptural statements that chance is governed by providence. The question in the context of our conversation is whether that government happens “naturally” by the design of the cosmos or by some kind of direct providence. Myposition is that the former (a) suggests an unfashionably deterministic physics and (b) is not really required by any theological consideration

      I’ve recently been increasingly unable to find good reasons why God should prefer the former, and a number of Scriptural ones for supposing he is both transcendent (the Creator of secondary causes) and immanent (the Governor of his household) in nature.

      But the agreement is what I take away – give me a Universe governed by God’s detailed providence and I’ll run with any science, whislt reserving the right to put forward my own opinions!

  2. Please amend my sentence in the previous post to read that God does NOT revel in impairment.

  3. Lou Jost says:

    So many things wrong with this post…

    First, as I mentioned in comments on your earlier post on Godel, we know that evolution is not impossible in principle. Every genetic algorithm that solves a new problem refutes this claim. The premises of evolution show how the coding space (DNA) becomes correlated with the external world; complexity is generated by a stochastic process that interacts with the external world. That’s where the “information” comes from.

    I don’t know what you mean by a lack of mathematical footing in biology. If you mean that we should be able to mathematically predict precise outcomes of evolution, you are right, we aren’t there, and that seems to be impossible even in principle. But we can make local predictions. Why should we expect to be able to do more? I don’t see people complaining that physics doesn’t have an answer for why there are exactly eight (or nine) planets in the solar system, or why a large asteroid hit earth 65 Mya instead of 55 Mya. Does that mean physics has a lack of mathematical footing? Of course not.

    “Meanwhile, the state of play is that you can only make any model work by supplying information along the way – appearing to confirm Gödel’s logical conclusion from decades back that nowt comes from nowt, and Pauli’s that teleology cannot be kept out.”

    Again, the correlations/complexity of organisms has its origin in the complexity of the environment. No magic needed, and no logical problems. And no, there is no teleology in this.

    “…[low-probability events]… in any case are formally indistinguishable from miracle.”

    There is no good evidence that evolution depends on anomalously-low-probability events. Yes, many of the twists of evolution depend on rare mutations, but other rare mutations may have done just as well or better. There is quite a bit of genetic evidence for multiple, independent, distinct innovations that serve the same functions. The fact that variation depends largely on mutation is not invoking the miraculous. (And while on the subject, much variation depends on novel combinations of existing genes rather than mutations creating completely new ones.)

    “Validation of the mechanisms of random mutation and natural selection, above the microscale, as the sole or predominant means of speciation, remain unobserved and contestible after 150 years. Disconfirmatory evidence, additional and alternative mechanisms all weaken its plausibility.”

    Yes, there are more sources of variation than random mutation. So? Darwin would be very pleased to hear about polyploid speciation, gene duplications leading to new functions, etc. All of these new things further undercut the argument of Pauli and IDers that there could not have been enough time for naturalistic evolution to produce the observed diversity and degree of adaptation.

    “The central case that evolution is a lawlike process without the need for the input of information has not come remotely near definitive demonstration.”

    Who says evolution occurs without input of information? The “information” source is the environment.

    As for origin of life, you got me there. I have no idea. But there are reasonable ideas floating around.

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