The no-miracles argument

The no-miracles argument is the claim that the empirical success of mature scientific theories would be a miracle — an extraordinary cosmic coincidence — if those theories were not at least approximately true descriptions of the world. It is the single most influential positive argument for scientific realism: the view that our best scientific theories provide approximately true accounts of both the observable and unobservable features of reality. The argument appeals to a common-sense intuition — that the best explanation for why something works is that the beliefs guiding it are roughly correct — and applies it to science as a whole.^{1, 4}

The argument has generated one of the most sustained debates in twentieth- and twenty-first-century philosophy of science, pitting scientific realists against a variety of anti-realist opponents: constructive empiricists who hold that the aim of science is empirical adequacy rather than truth, social constructivists who deny that scientific theories track a mind-independent reality, and instrumentalists who regard theoretical claims about unobservable entities as useful fictions rather than truth-candidates. The no-miracles argument stands at the centre of this debate because it offers what realists consider their strongest reason for thinking that scientific theories do more than merely "save the phenomena."^{4, 6}

Origins and formulation

The intuition behind the no-miracles argument is older than its canonical formulation. J. J. C. Smart articulated an early version in Philosophy and Scientific Realism (1963), arguing that it would be a "cosmic coincidence" if a theory's claims about unobservable entities were radically false yet the theory still managed to yield correct predictions about observable phenomena. Smart's point was that the predictive success of theories like atomic physics and molecular biology is naturally explained by the hypothesis that atoms and molecules actually exist as the theories describe them, and unnaturally explained by any hypothesis that denies this.⁵

The argument received its most influential and widely cited formulation from Hilary Putnam in 1975. In the introduction to his Mathematics, Matter and Method, Putnam stated the core claim succinctly: "The positive argument for realism is that it is the only philosophy that doesn't make the success of science a miracle." Putnam argued that scientific theories characteristically make novel predictions — predictions of phenomena that were not part of the data used to construct the theory — and that this novel predictive success is inexplicable unless the theories' theoretical claims are at least approximately true. If the theory's claims about electrons, genes, tectonic plates, or gravitational waves were wholly false, it would be an astonishing coincidence that the theory's predictions kept turning out to be correct.¹

The argument is a form of inference to the best explanation (IBE), also known as abductive inference. It proceeds roughly as follows: the observable fact to be explained is the empirical success of science; the candidate explanations are (a) that the theories are approximately true and (b) that the theories are false but happen to yield correct predictions; explanation (a) is vastly more plausible than explanation (b); therefore, scientific realism is the best explanation of science's success. The strength of the argument depends on whether IBE is a legitimate form of inference and whether there are alternative explanations of scientific success that do not require approximate truth.^{4, 10}

Novel predictive success

The most compelling cases for the no-miracles argument involve novel predictions: cases where a theory predicts a phenomenon that was not known at the time the theory was formulated, and the prediction is subsequently confirmed by experiment or observation. Novel predictions are significant because they cannot easily be explained by the hypothesis that the theory was merely "fitted" to known data. If a theory predicts something entirely unexpected and the prediction turns out to be correct, the realist argues, the most natural explanation is that the theory has latched onto some feature of reality that is responsible for the predicted phenomenon.^{9, 15}

Stathis Psillos, in Scientific Realism: How Science Tracks Truth (1999), catalogues numerous examples. Fresnel's wave theory of light predicted the "Poisson bright spot" — a bright point at the centre of the shadow of a circular disc — which was subsequently confirmed experimentally by Arago in 1818. The prediction followed from the mathematics of wave diffraction and was so counterintuitive that Poisson had originally proposed it as a reductio of Fresnel's theory. The general theory of relativity predicted the bending of starlight by the sun, confirmed during the 1919 solar eclipse. Dirac's relativistic quantum mechanics predicted the existence of the positron, confirmed by Anderson in 1932. In each case, the theory predicted a phenomenon that no one had reason to expect on any other grounds, and the prediction was confirmed.^{15, 9}

The realist contends that these cases are difficult to explain without positing that the theories are at least approximately true. If Fresnel's account of light as a wave phenomenon were wholly wrong, why would the mathematics of his theory generate a correct prediction about a previously unknown optical phenomenon? The anti-realist must either provide an alternative explanation of novel predictive success or argue that such success is less impressive than it appears.⁴

Constructive empiricism and van Fraassen’s response

The most influential anti-realist response to the no-miracles argument was advanced by Bas van Fraassen in The Scientific Image (1980). Van Fraassen defends constructive empiricism, the view that the aim of science is not truth but empirical adequacy: a theory is empirically adequate if and only if what it says about observable things and events is true. On this view, a theory can be accepted as empirically adequate without any commitment to the truth of its claims about unobservable entities such as electrons, quarks, or gravitational fields.⁶

Van Fraassen challenges the no-miracles argument on two fronts. First, he questions the legitimacy of applying inference to the best explanation at the meta-level. The no-miracles argument asks us to infer the approximate truth of scientific theories as the best explanation of their success. But IBE is itself a rule of inference whose validity is precisely what is at issue between realists and anti-realists. The anti-realist who does not accept IBE as a general rule of inference is not rationally compelled to accept the no-miracles argument, since the argument presupposes the very form of reasoning that the anti-realist rejects. This objection has been influential but is also circular in a sense: if IBE is a legitimate form of inference, then the no-miracles argument goes through; if it is not, the realist loses not just this argument but many other arguments that rely on abductive reasoning.^{6, 10}

Second, van Fraassen offers a selectionist explanation of scientific success as an alternative to the realist explanation. Just as Darwinian evolution explains the "fit" between organisms and their environments without positing a designer, van Fraassen suggests that the success of scientific theories can be explained by a process of selection: theories that fail to make correct predictions are abandoned, and only the successful ones survive. The success of current theories is thus not miraculous but tautological — we observe only the survivors of a process that eliminates failures. Critics of this response argue that it confuses the survival of theories with their success at novel prediction: the selectionist account explains why existing theories are empirically adequate (they would have been discarded if they were not), but it does not explain why they successfully predict novel phenomena that were not part of the selection process.^{6, 4}

The pessimistic meta-induction

The most damaging objection to the no-miracles argument is Larry Laudan's pessimistic meta-induction, presented in his 1981 paper "A Confutation of Convergent Realism." Laudan argues that the history of science provides a long list of theories that were empirically successful — they made correct predictions, were widely accepted by the scientific community, and guided successful research programmes — yet are now regarded as fundamentally false. If past empirical success did not guarantee approximate truth, the pessimistic meta-induction asks, why should we believe that present empirical success guarantees it?²

Laudan's list of successful-but-false theories includes the crystalline spheres of ancient astronomy, the humoral theory of medicine, the phlogiston theory of combustion, the caloric theory of heat, the electromagnetic ether, and the optical ether (luminiferous ether) that was central to nineteenth-century physics. In each case, the theory was empirically successful by the standards of its time: it made correct predictions, explained known phenomena, and was fruitful in generating new research. Yet each theory posited entities (phlogiston, caloric fluid, the ether) that we now believe do not exist. The realist must explain how these theories could have been empirically successful if their central theoretical claims were false — and if success can coexist with radical falsity in these cases, the inference from success to approximate truth appears to be unreliable.²

Laudan's argument directly attacks the premise of the no-miracles argument. The realist claims that success would be a miracle without approximate truth; Laudan replies that the historical record shows many cases where success occurred without approximate truth, so the alleged miracle has actually happened repeatedly. The no-miracles argument, Laudan contends, simply ignores the base rate of false-but-successful theories in the history of science.^{2, 4}

Realist responses to the pessimistic induction

Scientific realists have developed several strategies for responding to Laudan's challenge. The most common is the divide-and-conquer strategy, pursued in detail by Psillos. The strategy argues that not all components of a successful theory are equally responsible for its success. In the case of the caloric theory of heat, for example, the theory's successful predictions about heat conduction and specific heats depended on certain mathematical structures and empirical regularities that were preserved in the kinetic theory that replaced it; the successful predictions did not depend on the existence of caloric fluid as a material substance. The realist can therefore maintain that the parts of past theories that were responsible for their empirical success have been approximately preserved in successor theories, even if other parts (including claims about specific unobservable entities) were abandoned.^{15, 9}

This response requires the realist to specify, in a principled and non-ad-hoc way, which parts of a theory are "responsible for" its success and which are idle. Critics argue that this is difficult to do prospectively: for any current theory, we cannot know in advance which parts will be retained and which abandoned, so the divide-and-conquer strategy may amount to a retrospective rationalisation rather than a genuine predictive criterion.^{2, 4}

Ian Hacking, in Representing and Intervening (1983), offers a different realist strategy that shifts the focus from theories to entities. Hacking argues that we have strong reason to believe in the existence of unobservable entities when we can manipulate them as tools in experimental investigation. We believe in electrons not because electron theory makes successful predictions, but because we can spray electrons from an electron gun to investigate other phenomena. "If you can spray them, they are real," Hacking writes. This entity realism is more modest than theory realism: it commits us to the existence of certain unobservable entities without committing us to the truth of any particular theory about them.⁷

Structural realism

John Worrall's structural realism, proposed in his 1989 paper "Structural Realism: The Best of Both Worlds?", represents the most influential attempt to chart a middle course between the no-miracles argument and the pessimistic meta-induction. Worrall observes that when one scientific theory is replaced by another, what is typically preserved is not the theory's claims about the nature of unobservable entities but its mathematical or structural content. Fresnel's theory of light described light as vibrations in a material ether; Maxwell's electromagnetic theory abandoned the ether but preserved the mathematical equations that described the behaviour of light. The structural continuity between the two theories explains why Fresnel's theory was empirically successful without requiring that its claims about the ether were approximately true.³

Structural realism thus concedes the force of the pessimistic induction at the level of ontology — the specific entities posited by successful theories may not exist — while insisting that the mathematical structure of successful theories does track the structure of reality. The no-miracles argument, on this view, is correct about structure: it would be a miracle if the structural content of successful theories were entirely wrong. But it overreaches when it infers the approximate truth of theories' claims about the nature of unobservable entities.^{3, 14}

Structural realism has been developed in two directions. Epistemic structural realism, Worrall's original position, holds that structure is all we can know about the unobservable world; there may be entities with intrinsic natures that underlie the structure, but these are epistemically inaccessible. Ontic structural realism, defended by James Ladyman and others, makes the stronger claim that structure is all there is: the world itself is fundamentally structural, and the notion of objects with intrinsic properties is metaphysically misguided. Both versions preserve the core intuition of the no-miracles argument while accommodating the historical evidence that motivates the pessimistic induction.¹⁴

The base rate fallacy objection

P. D. Magnus and Craig Callender, in their 2004 paper "The Miracle Argument and the Base Rate Fallacy," raised a distinct objection to the no-miracles argument by arguing that it commits a statistical fallacy. The argument reasons from the fact that a theory is empirically successful to the conclusion that it is probably approximately true. But the strength of this inference depends on the base rate of approximately true theories among all possible theories. If the prior probability that a randomly selected theory is approximately true is very low, then even a test (empirical success) with a high hit rate can yield a low posterior probability of truth — because most of the theories that pass the test will be false positives.⁸

The analogy is to medical screening: a test that is 95% accurate for a disease with a 1% prevalence rate will generate more false positives than true positives. Similarly, if the space of possible theories is vast and only a tiny fraction are approximately true, then the fact that a theory is empirically successful may not raise the probability of its truth as much as the no-miracles argument assumes. Magnus and Callender argue that the no-miracles argument fails to specify the relevant base rate and therefore cannot establish that empirical success provides strong evidence for approximate truth.⁸

Realists have responded by arguing that the base rate objection misconstrues the argument. The no-miracles argument is not a statistical inference over the entire space of possible theories but an inference to the best explanation applied to specific, mature, well-confirmed theories. The relevant comparison is not between a successful theory and a randomly chosen theory but between a theory that makes surprising, novel, precise predictions and one that does not. When the base is restricted to theories that pass demanding empirical tests (including novel prediction), the realist argues, the proportion of approximately true theories is much higher than Magnus and Callender assume.^{4, 15}

Relevance to science-religion debates

The no-miracles argument has implications beyond the philosophy of science, particularly for the relationship between science and religion. If scientific realism is correct — if the success of science is best explained by the approximate truth of scientific theories — then this constrains the space of plausible metaphysical views. Theories that conflict with well-established scientific findings (young-earth creationism, geocentrism, vitalism) are not merely empirically inadequate but approximately false, and the success of the theories that replaced them provides positive evidence for this conclusion.⁴

The argument also bears on the question of whether supernatural explanations can compete with scientific ones. If inference to the best explanation is a legitimate form of reasoning — as the no-miracles argument presupposes — then it applies across domains: we should accept whichever explanation best accounts for the evidence, whether natural or supernatural. Some theistic philosophers have argued that this legitimises supernatural explanations in cases where natural explanations are inadequate. But most defenders of the no-miracles argument contend that the track record of science provides cumulative evidence that natural explanations are systematically more successful than supernatural ones, and that this asymmetric track record itself constitutes an argument for methodological naturalism.^{7, 10}

Contemporary status

The no-miracles argument remains the centrepiece of the case for scientific realism, but the debate it has generated has revealed that the argument is less straightforward than Putnam's original formulation suggested. The pessimistic meta-induction has shown that the inference from success to truth is historically fallible; structural realism has shown that the argument may establish less than full-blown realism about theoretical entities; and the base rate objection has raised questions about the argument's logical form. At the same time, no anti-realist has provided a fully satisfying alternative explanation of novel predictive success, and the realist intuition — that there must be some connection between a theory's getting things right and the world's being roughly the way the theory says — continues to exert powerful philosophical force.^{4, 14, 15}

The debate has also clarified what is at stake. The no-miracles argument is not an argument for the infallibility of science, for the truth of any particular theory, or for the claim that science will eventually converge on a final true theory. It is an argument that the best explanation of science's distinctive empirical success is that science is doing something right — that its methods are truth-tracking in a way that rivals such as astrology, homeopathy, and folk psychology are not. Even critics of the argument typically grant this much, differing only on whether "doing something right" requires the strong metaphysical commitment of approximate truth or can be cashed out in weaker terms such as empirical adequacy or structural accuracy.^{4, 6, 13}