Chapter 15: The No-Miracles Argument

The classic statement of the no-miracles argument comes from Hilary Putnam in Mathematics, Matter and Method (1975):

“The positive argument for realism is that it is the only philosophy that doesn’t make the success of science a miracle. That terms in mature scientific theories typically refer (this formulation is due to Richard Boyd), that the theories accepted in a mature science are typically approximately true, that the same term can refer to the same thing even when it occurs in different theories — these statements are viewed by the scientific realist not as necessary truths but as part of the only scientific explanation of the success of science, and hence as part of any adequate scientific description of science and its relations to its objects.”

The argument has a clear abductive structure — it is an inference to the best explanation (IBE):

The argument is especially compelling when theories make novel predictions — predictions about phenomena the theory was not designed to accommodate. When Mendeleev’s periodic table predicted the existence and properties of then-unknown elements (gallium, germanium, scandium), and these predictions were confirmed, this seemed powerful evidence that the periodic table was “onto something real.” When general relativity predicted the precession of Mercury’s perihelion with extraordinary accuracy, or when the Higgs boson was found at roughly the predicted mass, these successes cry out for explanation.

The anti-realist must either deny that such successes require explanation or offer an alternative explanation. Van Fraassen takes the first route: the success of science no more requires explanation than the survival of organisms requires a designer. Just as evolutionary processes produce organisms “adapted” to their environments without any miraculous intervention, so the social process of science selects for empirically adequate theories without any need for truth.

Richard Boyd developed the no-miracles argument into a more sophisticated form. Boyd’s argument focuses not just on the predictive success of individual theories but on the instrumental reliability of scientific methodology. Scientists use background theories to design experiments, calibrate instruments, interpret data, and judge which new theories are worth pursuing. This methodology is remarkably reliable — it regularly produces successful theories. Boyd argues that the best explanation of this methodological reliability is the approximate truth of the background theories.

Boyd’s argument proceeds in stages:

Critics charge that Boyd’s argument is circular: it uses IBE (inference to the best explanation) to justify realism, but IBE is a form of inference whose reliability is precisely what is at issue. If the anti-realist rejects IBE as a guide to truth about unobservables, then using IBE to argue for realism begs the question. Boyd responds that some circularity is unavoidable in the justification of fundamental epistemic principles, and that his argument exhibits only a benign “track record” circularity, not a vicious logical circularity.

The most powerful challenge to the no-miracles argument is Larry Laudan’s pessimistic meta-induction, presented in his 1981 paper “A Confutation of Convergent Realism.” Laudan attacks the realist’s central assumption: that empirical success is a reliable indicator of approximate truth.

“The history of science furnishes vast evidence of empirically successful theories that were subsequently rejected, and whose central theoretical terms are now taken not to refer.”

The argument has a simple inductive structure:

Laudan’s Historical List

Laudan provides a now-famous list of theories that were once empirically successful yet are now considered fundamentally false:

Each of these theories had genuine empirical successes — they made accurate predictions, guided fruitful research, and were accepted by the scientific community of their day. Yet we now believe their central theoretical terms (“phlogiston,” “caloric,” “ether”) fail to refer. If success did not indicate truth for these theories, why should we trust it as an indicator of truth for our current theories?

The meta-induction is “pessimistic” because it leads to a gloomy conclusion about our epistemic situation. It is a “meta-induction” because it is an induction over the history of science itself — an induction about the reliability of induction from success to truth.

P.D. Magnus and Craig Callender (2004) raised a subtle but powerful objection to the no-miracles argument: it commits a base rate fallacy. The no-miracles argument reasons that if a theory is approximately true, it is very likely to be empirically successful. Therefore (by IBE), an empirically successful theory is probably approximately true. But this inference is fallacious unless we know the base rate of approximately true theories.

Consider an analogy. A highly reliable medical test returns a positive result. Should you believe you have the disease? Not necessarily — it depends on the base rate of the disease in the population. If the disease is extremely rare, even a very reliable test will produce mostly false positives. Similarly, even if approximate truth reliably produces success, the probability that a successful theory is approximately true depends on what fraction of theories are approximately true to begin with.

The realist argues: P(success | truth) is high. But the NMA needs P(truth | success) to be high, and by Bayes’ theorem:

If the prior probability of a theory being approximately true — P(truth) — is low, then P(truth | success) can be low even when P(success | truth) is high. The NMA simply assumes that P(truth) is not negligibly small, but this is precisely what is at issue in the realism debate.

The realist might respond that the base rate objection proves too much: if we take it seriously, it undermines all instances of IBE, not just the NMA. Since IBE is a legitimate and widely used form of inference across science and everyday life, we should not abandon it based on abstract base rate worries. The debate continues over whether this response is adequate.

John Worrall’s structural realism offers a direct response to the pessimistic meta-induction. Worrall argues that Laudan’s list is misleading because it focuses on changes in ontology (what entities are posited) while ignoring structural continuity (what mathematical relations are preserved). When we look carefully at the history of science, we find that the mathematical structure of successful theories is typically preserved through theory change, even when the ontology changes dramatically.

Worrall’s key example is the Fresnel-to-Maxwell transition. Fresnel’s equations for the reflection and refraction of polarized light survived almost intact in Maxwell’s electromagnetic theory. The ontology changed (from mechanical ether to electromagnetic field), but the structure was preserved. This pattern, Worrall argues, is typical:

This pattern of structural preservation explains both the success of past theories (they got the structure approximately right) and their eventual replacement (they got the ontology wrong). It vindicates the no-miracles intuition at the structural level while conceding the pessimistic meta-induction at the ontological level.

Critics ask whether structural continuity is always genuine or sometimes artificial — imposed by the historian seeking patterns. Hasok Chang has argued that the continuity between Fresnel and Maxwell is less straightforward than Worrall suggests, and that in many cases the “structural preservation” involves significant reinterpretation of the equations’ meaning and domain of application.

The realism debate shows no signs of resolution, but it has become considerably more nuanced. Several developments characterize the current landscape:

Perhaps the deepest lesson of the debate is that the relationship between success and truth is more complex than either naive realism or blanket anti-realism suggests. Science does seem to be getting something right about the world — the convergence of independent methods, the stunning accuracy of novel predictions, and the power of technology all point in that direction. But what exactly science gets right, and how to articulate this in a way that withstands historical counterexamples, remains one of philosophy’s most challenging open questions.

Many philosophers have argued that the no-miracles argument is most compelling when applied to novel predictions — predictions about phenomena that were not known when the theory was formulated, or were not used in constructing the theory. The success of a theory in accommodating data it was designed to fit is relatively unsurprising; the success of a theory in predicting previously unknown phenomena is what truly demands explanation.

Several notions of novelty have been distinguished:

Timothy Lyons has argued for a “deployment realism” focused specifically on novel predictive success. The no-miracles argument is strongest, Lyons contends, when applied to theories that have generated successful novel predictions — not merely theories that are empirically adequate with respect to already-known data. This narrows the scope of the NMA but makes it more defensible.

However, Peter Lipton has raised a concern: if we restrict the NMA to novel predictions, we may weaken it excessively. Many theories that we want to count as approximately true do not make strikingly novel predictions but rather explain and organize existing data in illuminating ways. Darwin’s theory of evolution by natural selection, for instance, was primarily an explanation of known facts about biogeography, comparative anatomy, and embryology, rather than a source of novel predictions. Yet it would be strange to deny realism about natural selection on this basis.

Realists have developed several strategies for responding to Laudan’s challenge:

Each response has its strengths and weaknesses, and the anti-realist has rejoinders to each. The debate has become increasingly refined, with both sides developing more nuanced positions that acknowledge the partial validity of the other’s arguments.