A Refutation of Bruce Gordon’s “Argument From The Incompleteness of Nature”

By R.N. Carmona

Before setting out to formulate Gordon’s “Argument From The Incompleteness of Nature,” a general note is in order. After years of dealing with the more common arguments for God, e.g., the Kalam Cosmological, Moral, Fine-Tuning, Teleological, Ontological arguments, I began to notice that such arguments collapse when the complexity of the facts are analyzed. For instance, P1 of the Moral Argument states that “If God does not exist, objective values and duties do not exist.” This has proved to be the most controversial premise of the argument, but analyses of what is meant by objective, values, and duties lead us in directions where we can apprehend morality along these lines without God being necessarily involved. What I’m noticing now about more complex Theistic arguments is that they collapse when the simplicity of the facts are put on the table, i.e., when simple considerations are taken into account. This also applies to Gordon’s argument. To see what I mean, it will be necessary, first and foremost, to frame Gordon’s argument.

G1 “Quantum mechanics reveals a genuine ontological indeterminacy and incompleteness present in nature” (Gordon, Bruce L.. The Necessity of Sufficiency: The Argument From The Incompleteness of Nature. Two Dozen (or so) Arguments for God: The Plantinga Project, Edited by Walls, Jerry L. & Dougherty Trent. Oxford: Oxford University Press, 2018. 420. Print.)

G2 “Since all physical cause-and-effect relations are local, however, the completeness of quantum theory implies the causal-ontological incompleteness of physical reality: the universe is shot through with mathematically predictable non-local correlations that, on pain of experimental contradiction, have no physical explanation” (Gordon, 421)

G3 “Quantum theory raises fundamental questions about the coherence of material identity, individuality, and causality that pose a prima facie problem for naturalistic metaphysics” (Gordon, 423)

G4 (By way of inference) it is probable that all naturalistic interpretations of quantum mechanics contain conceptual shortcomings (Gordon, 423-429)

GC1 Therefore, “a theistic variant of the Copenhagen interpretation brings metaphysical completion to quantum theory so as to resolve the fundamental puzzle” (Gordon, 423)

GC2 Therefore, “God’s existence and continuous activity is the best explanation for the reality, persistence, and coherence of natural phenomena, and the account of divine action best meeting this explanatory demand is a form of occasionalist idealism” (Gordon, 436)

Gordon also condenses his argument as follows:

Now, in quantum physics we are confronted with a situation in which material causality falls irremediably short of explanatory demand, for there is no collection of physical variables jointly sufficient to the explanation of irreducibly probabilistic quantum outcomes. On pain of postulations to the contrary refuted by experimental violations of Bell inequalities, an ontological gap exists in the causal structure of physical reality that no collection of material causes can be offered to fill. So if a prior commitment to metaphysical naturalism constrains us, no non-naturalistic (transcendent) explanation is available to bridge this gap, and we must embrace the conclusion that innumerable physical events transpire without a sufficient cause, that is, for no explanatorily sufficient reason. In short, Copenhagen orthodoxy, framed in a purely physical context, entails a denial of the principle of sufficient reason (PSR) understood as the general maxim that every contingent event has an explanation. (425)

Right away, one can see how G1 through G3 hold insofar as scientific ignorance remains the case. But first, it will be useful to take note of what motivates Gordon to think that there is any truth to these premises. His primary motivations are informed by what he thinks is the inability of physicists to solve the measurement problem and that, at least from what he interprets is a fault of naturalism, quantum interpretations violate the Principle of Sufficient Reason (PSR) and/or are metaphysically implausible. If Gordon can draw his conclusions by way of induction, by ruling out particular interpretations yet to be offered on the basis of the shortcomings of six more general interpretations, then a naturalist has more warrant to rule out Theism by way of induction, by highlighting the many failures of Theism to square with scientific facts and its many more failures to offer sound philosophical arguments. God was once a local deity, intimately involved in matters far more mundane than quanta. It was widely believed that God created the Earth, not via the gradual work of physical laws, but as intimately as a potter forms his vase. Christians of the past even set out to prove God’s involvement in the world. Donald Prothero gives us a prime example:

Other geologists and paleontologists followed Cuvier’s lead and tried to describe each layer with its distinctive fossils as evidence of yet another Creation and Flood event not mentioned in the Bible. In 1842, Alcide d’Orbigny began describing the Jurassic fossils from the southwestern French Alps and soon recognized 10 different stages, each of which he interpreted as a separate non-Biblical creation and flood. As the work continued, it became more and more complicated until 27 separate creations and floods were recognized, which distorted the Biblical account out of shape. By this time, European geologists finally began to admit that the sequence of fossils was too long and complex to fit it with Genesis at all. They abandoned the attempt to reconcile it with the Bible. Once again, however, these were devout men who did not doubt the Bible and were certainly not interested in shuffling the sequence of fossils to prove Darwinian evolution (an idea still not published at this point). They simply did not see how the Bible could explain the rock record as it was then understood.

Prothero, Donald.  Evolution:  What the Fossils Say and Why it Matters.  New York:  Columbia University Press, 2007. 56-57. Print.

Going over the litany of examples throughout history is not necessary because Theism’s lack of explanatory success informs the behavior of today’s Theists. Therefore, it suffices to point out that Theists have gone from asserting that God is intimately involved in every aspect of reality, in addition to positing that the Bible renders an infallible account of many historical events, including a global flood, to relegating God to the outskirts of human knowledge where the refulgence of science remains unfelt, as hidden somewhere before the Big Bang, active solely in quantum phenomena that evade the experiences of even the most devout believers, and as grounds for some explanation of human consciousness that allows for the continuance of consciousness after death, i.e., a philosophy of mind that entails the existence of the soul, e.g., Cartesian dualism, Aristotelianism hylomorphism, panpsychism. Gordon’s argument is a prime example of this retreat to the far reaches of scientific ignorance, hoping with all his might that he will find God at the fringes of reality. If naturalism has pushed Theism this far, then it is safe to say that Theism is teetering on the edge, that any argument Theists put forth now are highly likely to fail, and that it is only a matter of time before Theism plunges into the abyss.

Before exposing glaring issues with Gordon’s conclusion, I will go over issues with his analysis of the many worlds interpretation (MWI) and the Ghirardi-Rimini-Weber spontaneous collapse interpretation (GRWI). Then I will provide an overview of two interpretations that circumvent the measurement problem and one its entailments, the observer effect. Prior to that, there are already issues with his analysis of the PSR that sound suspiciously like Plantinga’s EAAN or worse, Lewis’ Argument Against Naturalism. Gordon states:

Suppose, among all of the events that happen in the universe, there are countless many that happen without cause or reason. If this were true, we would have no principled way of telling which events were caused and which were not, for events that appeared to have a cause might, in fact, lack one. Our current perceptual states, for example, might have no explanation, in which case they would bear no reliable connection to the way the world is. So if the PSR were false, we could never have any confidence in our cognitive states. (425)

It is important to note that scientists are only concerned about causes inasmuch as they have explanatory power. If a cause does no explanatory work, then it does not help them to get a better understanding of a given phenomenon. Think of Nancy Cartwright’s $1,000 bill descending in St. Stephen’s Square. Scientists simply do not care to arrive at a model that accurately predicts where the bill will land and more precisely, about its exact movements through the air prior to landing. This particular example, that involves any number of difficult to quantify variables, e.g., bird droppings hitting the bill on the way down, dust particles slightly changing the bill’s trajectory, wind speeds, does not help scientists better understand drift, free fall, etc. Physicists already have general principles that help them understand how, for instance, a basketball succumbs to the magnus effect. A disposition of the ball, in particular its shape, makes it susceptible to this effect whereas the dispositions of the bill guarantee that it will drift wildly during the entirety of its descent to the ground.

Any event appearing to be caused does not immediately invite scientific scrutiny. Only events that do explanatory work or are suspected of having some explanatory power over a given effect, specifically in relation to a theory or model, are worth examining. In any case, it does not follow from the possibility that the PSR is false that our perceptual states have no explanation or cause. Therefore, that we can have no confidence in our perceptual states is completely non sequitur. Neuroscientists, cognitive scientists, and psychologists have done plenty of work to show that our perceptual states do have explanations, regardless of whether the PSR is true or not. Thus, if the PSR turns out to not be the case, our perceptual states are not among events lacking a cause or an explanation.

A general note of relevance is in order. Gordon’s citations are mostly decades old, which any peer reviewer in philosophy would immediately be suspicious of. Of the Many Worlds Interpretation, Gordon states: “So which way of building the universal wavefunction is to be preferred? This difficulty, known as the “preferred basis problem,” reveals that the branching process itself is completely arbitrary from a mathematical standpoint and therefore, from the abstract point of view presupposed by the MWI, not reflective of any physical reality” (427). Setting aside the non sequitur, “not reflective of any physical reality,” his primary authority informing this statement, namely David Wallace in 2003, no longer considers preferred basis to be an issue. Gordon would know that if he had read Wallace’s 2010 paper “Quantum Mechanics on Spacetime I: Spacetime State Realism,” in where he states:

We might sum up the objection thus: wave-function realism requires a meta-physically preferred basis… This objection is probably most significant for Everettians, who generally regard it as a virtue of their preferred interpretation that it requires no additional formalism, and so are unlikely to look kindly on a requirement in the metaphysics for additional formalism. Advocates of dynamical-collapse and hidden-variable theories are already committed to adding additional formalism, and in fact run into problems in QFT for rather similar reasons: there is no longer a natural choice of basis to use in defining the collapse mechanism or the hidden variables. We are not ourselves sanguine about the prospects of overcoming this problem; but if it were to be overcome, the solution might well also suggest a metaphysically preferred basis to use in formulating a QFT version of wave-function realism.

Wallace, David, and Christopher G. Timpson. “Quantum Mechanics on Spacetime I: Spacetime State Realism.” The British Journal for the Philosophy of Science, vol. 61, no. 4, 2010, pp. 697–727. https://arxiv.org/pdf/0907.5294.pdf. Accessed 1 Feb. 2021.

Lev Vaidman, Professor at the School of Physics and Astronomy in Tel Aviv, corroborates this: “due to the extensive research on decoherence, the problem of preferred basis is not considered as a serious objection anymore” (Vaidman, Lev, “Many-Worlds Interpretation of Quantum Mechanics”, The Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.), Fall 2018, https://plato.stanford.edu/archives/fall2018/entries/qm-manyworlds/).

Gordon raises a second difficulty for the MWI: “The second difficulty lies in its treatment of quantum probabilities” (Ibid.). Worse than using outdated sources is Gordon’s misrepresentation of a source that actually disagrees with his statement. Simon Saunders, in “Chance in the Everett interpretation,” actually states: “To conclude: there is no good reason to think EQM is really a theory of over-lapping worlds. If questions of overlap of branches are to be settled by appeal to the underlying mathematics, in terms of vector space structure, then there is at least one natural mereology in terms of which worlds that differ in some feature, since orthogonal, are non-overlapping” (Saunders, Simon (2010). Chance in the Everett interpretation. In Simon Saunders, Jonathan Barrett, Adrian Kent & David Wallace (eds.), Many Worlds?: Everett, Quantum Theory & Reality. Oxford University Press.). Saunders attempts to “solve the problem without introducing additional structure into the theory” (Vaidman, Ibid.) and yet Gordon tells his reader to “see Saunders et al. 2010 for extensive polemics regarding it” (Ibid.). This is an egregious level of malpractice that can only be explained by his desperation to prove his belief in God.

Turning now to his analysis of GRWI, the prospects for his argument do not improve. Gordon states of GRWI: “The problem is that it cannot be rendered compatible with relativity theory or extended to the treatment of quantum fields in this form” (Ibid.); “the theory remains radically non-local and has the additional drawback of eliminating the possibility of particle interactions and thus any physics of interest” (Ibid.); and “there are no versions of the theory in which the collapse is complete, with the consequence that all “material” objects have low- density copies at multiple locations, the presence and effect of which linger forever in the GRWI wavefunction” (Ibid.). The first and third concerns are not an issue for GRWI. The first issue simply restates the more general difficulty physicists have had with reconciling quantum mechanics and general relativity; this would then be an issue for the entire enterprise of quantum mechanics, so we would essentially be tossing the bath water, baby and all! The third issue is an appeal to ignorance. That there is currently no version of GRWI offering a collapse that is complete does not mean that scientists ought to give up on the search for a version containing a complete collapse. This leaves the second concern, which is addressed in Tejinder Singh’s 2018 paper “Space and Time as a Consequence of GRW Quantum Jumps,” where he deploys GRWI to solve the measurement problem. Singh states:

This classical metric is in turn produced by classical bodies, according to the laws of general relativity. And classical bodies are themselves the result of GRW localisation. Thus it is not reasonable to assume space to exist prior to the GRW quantum jumps. Rather, it seems quite intuitive that space results from GRW collapses taking place all over the universe. Space is that which is between collapsed objects. No collapse, no space. This also helps us understand why the GRW jumps take place in space: it is because space in the first place is created because of these jumps.

Singh, Tejinder. “Space and time as a consequence of GRW quantum jumps.” TZeitschrift für Naturforschung A73 (2018) 923. https://arxiv.org/pdf/1806.01297.pdf. Accessed 1 Feb. 2021.

Singh considers Hilbert space as more fundamental than classical space, so these GRW jumps occurring in Hilbert space give rise to the classical fabric of space we are accustomed to. He posits that the wave function is contingent on the configuration space where the particle moves through time, to potentially infinite degrees of freedom. This then results in a complete collapse of the wave function. Gordon’s hasty conclusion no longer holds if Singh has succeeded in offering a version of GRWI containing a complete collapse of the wave function.

This is setting aside the fact that Gordon overlooked what many consider an updated or even upgraded version of MWI, namely the Many Interacting Worlds Interpretation (MIWI). The MIWI differs from the MWI in that all quantum phenomena are the result of an inter-universal repulsive force acting on worlds in close proximity to one another, thus explaining any dissimilarity between them. Michael Hall, et. al. conclude that the MIWI can reproduce quantum interference phenomena, in addition to offering advantages with respect to computational modeling. They note that on the de Broglie–Bohm Interpretation, the wave function denoted by Ψ, even when it is a very large value allows computer modeling to focus on high density regions in configuration space, specifically regions where calculation errors have to be corrected to analyze convergence given norms of angular momentum (see Hall, Michael J. W., Deckert, Dirk-André, and Wiseman, Howard M.. Quantum Phenomena Modeled by Interactions between Many Classical Worlds. Physical Review X, 2014; 4 (4) DOI: 10.1103/PhysRevX.4.041013).

There is also the Lindgren-Liukkonen Interpretation (LLI), championed by two quantum physicists that take Ockham’s Razor seriously. Given this, their quantum interpretation is a statistical interpretation that solves the observer effect. In other words, there is no logical reason, to their minds, why the results of a measurement are dependent on an observer. They dispense with the notion of a conscious observer changing the result of measurements. The LLI shows that any epistemological and ontological issues that stem from the uncertainty principle are solved given that the uncertainty principle is a fixed property of stochastic mechanics (see Lindgren, Jussi and Liukkonen, Jukka. The Heisenberg Uncertainty Principle as an Endogenous Equilibrium Property of Stochastic Optimal Control Systems in Quantum Mechanics. Symmetry, 2020; 12 (9): 1533 DOI: 10.3390/sym12091533

Gordon not only failed to rule out enough interpretations of quantum mechanics to make his conclusion more likely, but he failed to rule out the best defenses of, at least, two of the interpretations he is skeptical about. The larger issue for Gordon is that even if he managed to rule out say, twenty interpretations in quantum mechanics, his conclusion simply does not follow and if it did, there are simple considerations that render it untenable. Recall: “God’s existence and continuous activity is the best explanation for the reality, persistence, and coherence of natural phenomena, and the account of divine action best meeting this explanatory demand is a form of occasionalist idealism” (Gordon, 436). It follows from this that God’s existence and continuous activity is the best explanation for the reality, persistence, and coherence of viruses, diseases, natural disasters, and pretty much any undesired consequence a Theist can imagine. Clearly, Gordon does not want to admit these natural phenomena into his conclusion, choosing instead to special plead for any cases he thinks suit his argument. In other words, one of his concerns fits better on his foot: Suppose, among all of the events that happen in the universe, there are countless many that happen without God’s continuous activity, e.g., pretty much all the bad stuff. If this were true, we would have no principled way of telling which events were caused by his activity and which were not, for events that appeared to have been caused by God, in fact, were not. It is far more probable therefore, that God has no hand in any event in the natural world, not even granting a retreat into the quantum realm.

Ultimately, if a Theist wants to continue to assert that God has a hand in the unification of quantum and classical phenomena, they need to take a different route than Gordon has. Gordon severely undermines his own project by using outdated sources, being completely unaware of the fact that one of the authors of one of his primary sources changed their mind and actually proved the opposite of what seemed to lend a hand to Gordon’s argument, and overlooking a number of interpretations that may provide a stable and complete collapse of the wave function, thus solving quantum paradoxes, like the measurement problem and related observer effect. More damning to such arguments is that if a personal, loving deity saw fit to retreat to the far reaches of metaphysical reality, then he can have no desire to be known or detected by even people who are hopelessly devoted and attached to him. Quanta lies so far outside of the everyday experience of human beings that the idea that God is asking us to pursue him into the microcosms of the quanta is, quite frankly, nonsensical. It makes more sense that retreats like Gordon’s, into profoundly metaphysical territory, has everything to do with Theism’s failure to square with science, in addition to offering philosophical arguments or proofs that are sound or, at the very least, cogent and without controversy. This is precisely the prognosis for Theism and the relentless advances of science and philosophy, closely in tow, do not look poised to provide any remedy. Gordon’s argument, while complex, completely collapses in the face of simple considerations, which is a happy irony given his claims about the quantum wave function.


  1. Pepee

    Great post, and i have 5 questions on this
    1) What do you think about G2 is the all physical cause-effect relations are local? And if “yes” then is prove nature is incomplete?
    2) can any QM phenomena used to refute G2
    3)what do you think about gordon’s other articles?
    Gordon, Bruce L. (2010) “Inflationary Cosmology and the String Multiverse,” in Robert J. Spitzer, S.J. New Proofs for the Existence of God: Contributions of Contemporary Physics and Philosophy. Grand Rapids: Eerdmans, pp. 75-103.

    _______. (2011a). “A Quantum-Theoretic Argument against Naturalism,” in Bruce L. Gordon and William A. Dembski, eds., The Nature of Nature: Examining the Role of Naturalism in Science. Wilmington: ISI Books, pp.179-214.

    _______. (2011b) “Balloons on a String: A Critique of Multiverse Cosmology,” in Bruce L. Gordon and William A. Dembski, eds., The Nature of Nature: Examining the Role of Naturalism in Science. Wilmington: ISI Books, pp.558-601.

    _______. (2013a) “In Defense of Uniformitarianism,” Perspectives on Science and the Christian Faith, vol. 65, no. 2, pp.79-86.
    4) What do you think about whole of “TWO DOZEN” book
    5) What do you think about Leon and Smith’s QM-based arguments for atheism


    • R.N. Carmona

      1) G2 contains a non sequitur. I do not think non-local correlations have no physical explanation. So no, I don’t think locality implies that nature is incomplete.

      2) I think that the two interpretations I summarized refute G2, especially the LLI.

      3) I cannot comment on Gordon’s other articles since I haven’t read them.

      4) As for the whole “Two Dozen (Or So) Arguments” book, I think that some of the arguments have been refuted. Given that I have read, at least, the gist of some of the arguments, they are not convincing. The Argument From Too Many Arguments is an egregious misuse of Bayes Theorem. Poston does not include evidence against Theism in variable e, which requires all evidence for and against a position. Deductive arguments, even where valid, are not evidence. Sound arguments are evidence. In any case, Poston’s ~83% probability that Theism is true is woefully overstated, especially given that arguments for all other positions aside from Theism are not accounted for and that the 20+ arguments in the book are not shown to be sound.

      In general, by simple induction, my skepticism of ALL Theistic arguments is warranted. None have been convincing and more importantly, sound to lead me to believe that any of the new arguments or new iterations of older arguments will succeed where the older arguments failed. I think that if Theism had any explanatory power, the evidence hitherto would have confirmed as much. That is far from the case, hence recent retreats to deeply metaphysical territory; I have no reason to believe a personal god that wants to be known and who loves us is requiring us to chase him into the quanta and modal aspects of logic. God would therefore, show no concern for people who simply have no interest in quantum mechanics and metaphysics (both of which having a tendency to exclude women and the poor, which includes a great deal of minorities who simply don’t have exposure to STEM and philosophy or the opportunities and means to pursue careers in these areas). So, it would seem, God only wants to save (mostly) White, affluent men. Excuse my candor, but this is precisely why I am begrudgingly an ally of philosophical atheism; a huge part of me wants to move on into much more interesting aspects of philosophy knowing full well that the god of these elitist academics, apart from being utterly incongruous with the god of Christianity, doesn’t exist. I have no desire to entertain the idea of a god that is discovered only by people who are mostly male, affluent, and who have a high enough IQ to have a good grasp of the jargon involved in these arguments — which excludes even a number of Theists who only cling to these arguments because they purport to confirm their predilections. It has been clear to me from a number of conversations that a lot of Theists cannot even begin to understand arguments as complex as Gordon’s. Everyday people simply do not have the means to understand general physics, relativity, quantum mechanics, and predicate logic and pertinent areas in philosophy. This is probably the most important thing I’ll say all week, so hopefully you’ve understood what could be considered an argument from elitism against god’s existence, or something like that.

      5) What is the title Leon and Smith’s paper? It sounds interesting, even though the same applies in the other direction. At least, on atheism, hyper academic arguments like that aren’t necessary to ground the proposition, god does not exist.


  2. Pepee

    1/2)some QM phenomena şike Quantum entaglement and smith’s simultaneous causation thesis used to explain Jon-local correlations with local correlations.
    5)there are 4 different arguments, first two are smith&grünbaum’s arguments other two is leon’s arguments links:


    Liked by 1 person

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