The no-miracles argument (NMA) — the explanationist argument that the best explanation of the predictive success of science is that our mature theories are approximately true — is the central argument for scientific realism, and it has long been charged with epistemic circularity: it presupposes the approximate truth of the very background theories that make its explanatory inference trustworthy. K. Brad Wray's 2018 critique of J. D. Trout's contingency-based variant of the NMA sharpened this charge into a self-defeat argument: Trout's own principle that the sense of understanding is unreliable unless background theories are approximately true applies reflexively to Trout's historical explanation of the rise of modern science, and Wray argued that Trout's argument for realism and the related explanation of the success of science are self-defeating — that Trout inadvertently undermines his own argument in the course of arguing against the traditional realist strategies for explaining the success of science. The open question that critique leaves is whether the explanationist inference from success to approximate truth can be justified without epistemic circularity, and what should replace it if it cannot, together with the linked dimensions of the critique bearing on it: independent, non-circular grounds for the approximate truth of the background theories presupposed by explanationist inference; the adequacy of the survey of historically plausible explanations against unconceived alternatives; whether quantitative historical indicators such as discovery rates can be disambiguated from sociocultural and institutional causes so as to evidence epistemic improvement; and the availability of alternative justificatory strategies for realism. Bayesian and deductive reformulations (Sprenger and Hartmann 2019; Golemon and Graber 2023), continued defenses of the traditional argument (Park 2021; Ganson 2020), and new anti-realist arguments (Rowbottom 2019) all leave the core circularity problem open, and a 2023–2026 Synthese exchange (Golemon and Graber; Lee; Golemon) shows non-explanationist alternatives actively contested and unresolved. The problem remains open.

Background

Scientific realism is the position that our best scientific theories are approximately true — true enough in their claims about both observable and unobservable entities (electrons, fields, genes) that their observational consequences are not accidental — and that mature science progresses toward a more accurate picture of the world. The classic argument for realism is the no-miracles argument (NMA), usually attributed to Hilary Putnam: the novel predictive and instrumental success of science would be a miracle — an inexplicable coincidence — unless successful theories were at least approximately true, so approximate truth is the best explanation of success. The NMA is thus an instance of inference to the best explanation (IBE), the mode of reasoning in which one infers that, of the candidate hypotheses considered, whichever would best explain the evidence is likely true. An explanationist defense of realism is any defense that rests on such an explanatory inference from success to truth; approximate truth is the notion that a theory, while strictly false, captures the world well enough in its central claims to be credited as truthlike. The two standing objections to this strategy are the pessimistic induction — Larry Laudan's catalogue of past theories (phlogiston, caloric, ether, Bohr's atom) that were empirically successful in their day yet are now judged false, suggesting that success does not imply truth — and the problem of unconceived alternatives, P. Kyle Stanford's argument that scientists have recurrently failed even to conceive of the serious alternatives that later replaced their theories, so the 'best explanation' among those currently conceived need not be true. A further, formal objection from Bayesian confirmation theory holds that the NMA commits a base-rate fallacy by ignoring the prior proportion of true theories among those science selects. The circularity charge is older and more structural: to trust an explanatory inference one must already trust the background theories that tell one what counts as a good explanation, and if the inference is being used to establish that background theories are true, the justification goes in a circle. The debate over whether this circularity is vicious, benign, or avoidable is the locus of the present problem.

J. D. Trout's book Wondrous Truths: The Improbable Triumph of Modern Science (Oxford University Press, 2016) added a distinctive variant. Drawing on cognitive science of explanation, Trout holds that the felt 'sense of understanding' — the subjective satisfaction an explanation produces — is generated largely by processing fluency and congruence with background assumptions, and is therefore an unreliable guide to truth unless the background theories are already approximately true. His historical claim is that the rise of modern science in seventeenth-century Europe was caused, contingently and largely by luck, when Boyle, Newton, and their contemporaries happened to hit upon the corpuscular hypothesis (the doctrine that matter consists of corpuscles with a few stable properties), a theory close enough to the truth that subsequent scientific methods — which merely refine approximately true background theories — could generate enduring success. Trout explicitly acknowledges and dismisses the charge that this reasoning is circular.

K. Brad Wray's 2018 discussion note in Studies in History and Philosophy of Science Part A argues that Trout's defense is self-defeating: by Trout's own principle, the sense of understanding by which we accept Trout's historical explanation is unreliable, because we lack approximately true background theories about the causal structure of historical scientific change; and the historical and quantitative evidence Trout cites (a rise in the rate of scientific discoveries beginning in mid-sixteenth-century Europe) cannot be disentangled from sociological and institutional alternative explanations of the same pattern. Wray adds that, in the process of arguing against the traditional realist strategies for explaining the success of science, Trout inadvertently undermines his own argument. The critique generalizes: these structural problems — self-defeating circularity, an insufficiently surveyed space of candidate explanations, and inadequate historical evidence — are not specific to Trout but afflict explanationist defenses of realism generally, including the canon in Stathis Psillos's Scientific Realism: How Science Tracks Truth. The open question left by that critique, together with the linked dimensions of the critique bearing on it, is: what independent, non-circular grounds (empirical, methodological, or conceptual) could secure the approximate truth of the background theories invoked in explanationist inference; how to delimit the space of historically plausible explanations so that IBE is trustworthy despite unconceived alternatives; whether quantitative historical indicators such as rates of discovery can be disambiguated from sociocultural and institutional causes so as to serve as evidence of epistemic improvement rather than merely increased scientific activity; and what alternative justificatory strategies for realism (other than explanationism) can avoid the self-undermining problems identified here while still accounting for empirical success and continuity across theory change.

Problem Statement

The problem, raised by Wray's (2018) critique of Trout's contingency-based defense of scientific realism — a critique arguing that Trout's argument for realism and the related explanation of the success of science are self-defeating, and that Trout inadvertently undermines his own argument in the course of arguing against the traditional realist strategies for explaining the success of science — is to settle whether the inference from the empirical success of science to the approximate truth of successful theories can be justified without epistemic circularity, that is, without presupposing the approximate truth of the background theories that make the explanatory inference trustworthy and without relying on the felt sense of understanding whose unreliability, absent approximately true background theories, is the source of the self-defeat objection; and, if it cannot, what should replace it.

Part of this question is whether a worked-out non-circular grounding for the inference from success to approximate truth can be given, or whether the circularity involved can be shown not to be vicious so that the self-defeat charge fails; the other part is, if no such grounding is available, what the consequences for scientific realism are and what should replace explanationism, including whether a developed alternative justificatory strategy for scientific realism can avoid the self-defeat/circularity problem while still accounting for the empirical success of mature science and for continuity across theory change.

Wray's connected criticisms are linked dimensions of the critique bearing on this question, not four independent questions: (1) what independent, non-circular grounds — empirical, methodological, or conceptual — could secure that the background theories invoked in explanationist inferences (including in historical explanations of the success and rise of science, such as Trout's appeal to the lucky discovery of approximately true corpuscular/Newtonian background theories) are approximately true, where a non-circular grounding is one that does not itself rest on explanationist inference or on the felt sense of understanding; (2) whether the space of historically plausible explanations of scientific success and of the rise of modern science has been adequately delimited so that inference to the best explanation is trustworthy in the presence of unconceived alternatives — including the reflexive case, where the reasoning doing the delimiting itself lacks approximately true background theories; (3) the extent to which quantitative historical indicators of scientific success (such as rates of discovery) can be disambiguated from sociocultural and institutional causes (changes in the societal role and support of science, growth in the number of scientists) so as to serve as evidence of epistemic improvement rather than merely increased scientific activity; and (4) what alternative justificatory strategies for realism (other than explanationism) can avoid the self-undermining problems identified here while still accounting for empirical success and continuity across theory change.

References

  1. K. Brad Wray, "A new twist to the No Miracles Argument for the success of science", Studies in History and Philosophy of Science Part A 69:86–89 (2018). DOI 10.1016/j.shpsa.2018.02.002, https://doi.org/10.1016/j.shpsa.2018.02.002
  2. J. D. Trout, Wondrous Truths: The Improbable Triumph of Modern Science, Oxford University Press (2016). ISBN 9780199385072, DOI 10.1093/acprof:oso/9780199385072.001.0001, https://doi.org/10.1093/acprof:oso/9780199385072.001.0001
  3. Hilary Putnam, Mathematics, Matter and Method: Philosophical Papers, vol. 1, Cambridge University Press (2nd edition 1979; first edition 1975). DOI 10.1017/cbo9780511625268, https://doi.org/10.1017/cbo9780511625268
  4. Larry Laudan, "A Confutation of Convergent Realism", Philosophy of Science 48:19–49 (1981). DOI 10.1086/288975, https://doi.org/10.1086/288975
  5. Stathis Psillos, Scientific Realism: How Science Tracks Truth, Routledge (1999; electronic edition 2005). DOI 10.4324/9780203979648, https://doi.org/10.4324/9780203979648
  6. P. Kyle Stanford, Exceeding Our Grasp: Science, History, and the Problem of Unconceived Alternatives, Oxford University Press (2006). ISBN 9780195174083, DOI 10.1093/0195174089.001.0001, https://doi.org/10.1093/0195174089.001.0001
  7. K. Brad Wray, Resisting Scientific Realism, Cambridge University Press (2018). DOI 10.1017/9781108231633, https://doi.org/10.1017/9781108231633
  8. Nicholas Maxwell, review of J. D. Trout, Wondrous Truths: The Improbable Triumph of Modern Science, Acta Baltica Historiae et Philosophiae Scientiarum 5(2):108–115 (2017). DOI 10.11590/abhps.2017.2.05, https://doi.org/10.11590/abhps.2017.2.05
  9. Olin M. Robus, "How Newton got lucky" (review of J. D. Trout, Wondrous Truths), Metascience 26:91–94 (2017). DOI 10.1007/s11016-016-0143-0, https://doi.org/10.1007/s11016-016-0143-0
  10. Antonio Clericuzio, review of J. D. Trout, Wondrous Truths: The Improbable Triumph of Modern Science, Isis 109:155–156 (2018). DOI 10.1086/696559, https://doi.org/10.1086/696559
  11. Jan Sprenger and Stephan Hartmann, "Scientific Realism and the No Miracles Argument", in Bayesian Philosophy of Science, Oxford University Press (2019), pp. 81–106. DOI 10.1093/oso/9780199672110.003.0003, https://doi.org/10.1093/oso/9780199672110.003.0003
  12. Darrell P. Rowbottom, "A methodological argument against scientific realism", Synthese 198:2153–2167 (published online June 2019). DOI 10.1007/s11229-019-02197-7, https://doi.org/10.1007/s11229-019-02197-7
  13. Seungbae Park, "In Defense of the No Miracles Argument", in Embracing Scientific Realism, Synthese Library, Springer (2021), pp. 1–22. DOI 10.1007/978-3-030-87813-9_1, https://doi.org/10.1007/978-3-030-87813-9_1
  14. Keith Dyck, "On No-Miracles and the Base-Rate Fallacy", Philosophy of Science 90:761–776 (2023). DOI 10.1017/psa.2023.80, https://doi.org/10.1017/psa.2023.80
  15. Luke Golemon and Abraham Graber, "A deductive variation on the no miracles argument", Synthese 201, article 81 (2023). DOI 10.1007/s11229-023-04078-6, https://doi.org/10.1007/s11229-023-04078-6
  16. Kok Yong Lee, "A critical examination of Golemon and Graber's deductive No-Miracle Argument", Synthese 206, article 40 (2025). DOI 10.1007/s11229-025-05144-x, https://doi.org/10.1007/s11229-025-05144-x
  17. Luke Golemon, "An inductive no-miracles argument", Synthese 207, article 180 (2026). DOI 10.1007/s11229-026-05548-3, https://doi.org/10.1007/s11229-026-05548-3
  18. Sergio Aramburu, "Teorías científicas "aproximadamente verdaderas": Un análisis semántico", Revista Colombiana de Filosofía de la Ciencia 24:293–323 (2024). DOI 10.18270/rcfc.4472, https://doi.org/10.18270/rcfc.4472
  19. Dorit A. Ganson, The Explanationist Defense of Scientific Realism, Routledge (2020). ISBN 9781003023357, DOI 10.4324/9781003023357, https://doi.org/10.4324/9781003023357