# Inductivists who actually took Popper seriously **The philosophical literature contains roughly two dozen works that genuinely engage with Popper's arguments before responding — far fewer than one might expect given Popper's towering influence.** The best steelmanners share a common trait: intimate familiarity with Popper's actual texts, often from institutional proximity to the LSE or decades of sustained dialogue. The strongest engagements cluster in three traditions — Bayesian confirmation theory (Howson, Earman, Salmon), error-statistical methodology (Mayo), and post-Popperian philosophy of science (Lakatos, Worrall) — while the weakest tend toward polemics that substitute ridicule for argument. What follows is a comprehensive survey organized by quality of engagement, from gold-standard steelmanning down to flagged strawmen. --- ## The Bayesian vanguard: Howson, Earman, and Salmon The most sustained and faithful inductivist engagement with Popper comes from three Bayesian-adjacent philosophers who took his arguments seriously enough to spend careers responding. **Colin Howson** stands alone as the inductivist who most fully steelmanned Popper. Trained and employed at the LSE — Popper's own department — Howson had unmatched familiarity with Popperian philosophy. His solo work spans four decades of engagement. In "Must the Logical Probability of Laws Be Zero?" (*British Journal for the Philosophy of Science*, 1973), he removed what the BSPS called "an essential plank from Popper's falsificationist philosophy" by showing universal laws need not receive zero logical probability. His papers on the **Popper-Miller theorem** — particularly "On a Recent Objection to Popper and Miller's 'Disproof' of Probabilistic Induction" (*Philosophy of Science*, 1988) — represent the gold standard of philosophical engagement: Howson actually *defended* Popper and Miller's argument against a bad objection by Dunn and Hellman before offering his own independent critique. This willingness to protect an opponent's argument from weak attacks before presenting a stronger rebuttal is exactly what steelmanning means. Howson's major work, *Hume's Problem: Induction and the Justification of Belief* (Oxford University Press, 2000), develops the remarkable thesis that Bayesianism provides a logic of induction *without justifying induction* — partly vindicating Popper's Humean skepticism while showing probabilistic reasoning remains viable. Chapter 5, titled "Deductivism," engages Popper directly, arguing his rejection of Bayesian probability "was motivated by a desire to avoid what he thought to be a corollary of it, that knowledge is inductively based" — and that this was "mistaken." The book has been called "the reference work" for the Bayesian solution to Hume's problem. Howson and Peter Urbach's joint *Scientific Reasoning: The Bayesian Approach* (Open Court, 1989; 3rd ed. 2006) provides the canonical Bayesian alternative to Popper's program. Both authors were at the LSE, giving them insider knowledge of Popper's actual positions. The book argues that Popper's distinction between "corroboration" and "confirmation" is unsustainable because corroboration implicitly involves inductive reasoning, that Bayesian theory uniquely explains why novel predictions carry special evidential weight — something Popper acknowledged in practice but could not explain — and that his claim about zero probabilities for laws is false. The work is widely considered to give "a fair and accurate account of the anti-Bayesian views it criticizes." **Wesley Salmon** produced what many regard as the single most devastating inductivist challenge to Popper's program, sustained over three decades (1960s through 1990s). *The Foundations of Scientific Inference* (University of Pittsburgh Press, 1967) presented Popper's position with genuine respect before identifying its core difficulty. Salmon's dilemma is elegantly simple: Popper claims science functions purely deductively through falsification and corroboration, but corroboration is supposed to confer no confidence in future performance. So either corroboration implicitly involves inductive reasoning, or Popper's account gives no rational basis for relying on science. His famous formulation — **"modus tollens without corroboration is empty; modus tollens with corroboration is induction"** — has never been satisfactorily answered by Popperians. His follow-up "Rational Prediction" (*BJPS*, 1981) extended the critique by examining Popper's responses and Watkins's defense, pressing the question of why it is rational to rely on well-corroborated theories rather than consulting horoscopes. Christopher Hitchcock's introduction to the 50th anniversary edition calls Salmon's critique "one of the clearest, most incisive critiques" of Popper ever written. **John Earman's** *Bayes or Bust? A Critical Examination of Bayesian Confirmation Theory* (MIT Press, 1992) is notable for its intellectual honesty. Earman describes himself as a Bayesian "on Mondays, Wednesdays, and Fridays" while having doubts on other days. Chapter 4 is devoted to "quieting the doubts" raised by Popper, engaging with his specific technical arguments — including the charge that universal laws receive zero priors and the Popper-Miller argument that probabilification is never genuine inductive support — with precision rather than caricature. Earman acknowledges genuine difficulties for Bayesianism rather than pretending the program is complete, which makes his defense of it against Popper far more persuasive. Clark Glymour called it "a fine analysis of many issues facing modern theoretical statistics and the enterprise of confirmation theory." --- ## Mayo's error-statistical program: completing what Popper started **Deborah Mayo** occupies a unique position in this literature: she is perhaps the only philosopher whose entire research program is explicitly framed as *completing* Popper's project rather than refuting it. Her engagement is the most thorough steelmanning in the literature precisely because she credits Popper's core insight before showing where he went wrong. In *Error and the Growth of Experimental Knowledge* (University of Chicago Press, 1996), Mayo carefully distinguishes "naive" from "sophisticated" Popper, noting that Popper "did not assert that a single counter-example is enough to falsify a theory" and citing his requirement for "a reproducible effect which refutes the theory." She then argues that Popper's insight about severe testing was correct but he **"never made the error probability turn"** — he could not formally define what makes a test severe because he limited himself to deductive resources, refusing to embrace error probabilities lest he admit "a whiff of induction." Mayo provides the missing formal apparatus: a claim is severely tested when it passes a test that had a high probability of finding flaws if they existed, operationalized through Neyman-Pearson error probabilities. Her later *Statistical Inference as Severe Testing* (Cambridge University Press, 2018) states: "The severe testing perspective substantiates, using modern statistics, the idea Karl Popper promoted, but never adequately cashed out." Her essay "Critical Rationalism and Its Failure to Withstand Critical Scrutiny" (in *Rationality and Reality: Conversations with Alan Musgrave*, Springer, 2006) represents perhaps the sharpest single engagement. She quotes Popper's own formulation of the severity principle, steelmans it through Musgrave's best defense, and then systematically shows the critical rationalist position is a "bait and switch" — getting assent to intuitive severity claims but delivering tests incapable of doing their intended job. The remedy requires error probabilities, which Popper rejected. Reviewer Cosma Shalizi captured this beautifully: Mayo, "playing the Jacobin to Popper's Girondin, thinks she knows what the problem is: for all his can't-make-an-omelette-without-breaking-eggs rhetoric, Popper is entirely too soft on conjectures." --- ## Lakatos, Putnam, and Grünbaum: the Schilpp volume generation The 1974 Schilpp volume *The Philosophy of Karl Popper* (Open Court, 33 critical essays plus Popper's 236-page "Replies to My Critics") represents the single most concentrated dialogue between Popper and his critics. Three contributors stand out for quality of engagement. **Imre Lakatos** invented a steelmanning device that has become standard in philosophy of science. His "Falsification and the Methodology of Scientific Research Programmes" (in *Criticism and the Growth of Knowledge*, Cambridge University Press, 1970) distinguishes three "Poppers": Popper₀ (naive falsificationist — a straw figure he attributes to common misreadings), Popper₁ (the more nuanced philosopher as actually written), and Popper₂ (the "sophisticated methodological falsificationist" whom Lakatos identifies with himself). This tripartite distinction explicitly rescues Popper's strongest position from Kuhn's critique of the naive version before offering a radical revision. Lakatos argues individual theories cannot be meaningfully falsified in isolation — science progresses through competing *research programmes* with a "hard core" and a "protective belt" of auxiliary hypotheses. A programme is progressive if modifications predict novel facts, degenerating if they are merely ad hoc. His companion essay "Popper on Demarcation and Induction" (in the Schilpp volume, 1974) directly engages Popper on whether an inductive principle lurks behind trial-and-error learning. **Hilary Putnam's** "The 'Corroboration' of Theories" (Schilpp volume, pp. 221–240) opens with genuine respect — "Sir Karl Popper is a philosopher whose work has influenced and stimulated that of virtually every student in the philosophy of science" — before pressing a devastating historical counterexample. Newton's theory of universal gravitation was accepted not because it made novel risky predictions that were tested, but because it explained *already established phenomena* (planetary orbits, tides). On Popper's strict falsificationist account, accepting such a theory would seem irrational. Putnam detects **"an inductivist quaver"** in Popper's discussion of theory preference, arguing the logical structure of Popper's methodology is ultimately indistinguishable from inductivism. This essay is widely reprinted and remains one of the most cited critiques. **Adolf Grünbaum** produced what may be the most forceful inductivist challenge to Popper's entire program. His "Is Falsifiability the Touchstone of Scientific Rationality? Karl Popper versus Inductivism" (in *Essays in Memory of Imre Lakatos*, Reidel, 1976, pp. 213–252) and its expanded version "Popper vs Inductivism" (in *Progress and Rationality in Science*, 1978) contest Popper's historiography of inductivism, challenge whether falsifiability can serve as the touchstone of scientific rationality, and issue what Grünbaum calls "a new challenge to the cardinal arguments on which Popper rests his indictment of inductivism." His engagement is technically rigorous and takes Popper's specific arguments rather than caricatures as its target. --- ## The Carnap-Popper debate deserves reappraisal The debate between Carnap and Popper on probability and confirmation is often dismissed as two philosophers talking past each other — and Alex Michalos's scrupulously fair *The Popper-Carnap Controversy* (Martinus Nijhoff, 1971) showed they partly were, since they had different *explicanda*. But Carnap's reply in the Schilpp volume on his own philosophy (*The Philosophy of Rudolf Carnap*, Open Court, 1963) contains a technical argument that has been remarkably under-discussed. Carnap demonstrated that for sentences of the mixed-quantifier form "for all x there exists a y such that…" — which includes most laws of theoretical physics involving limit concepts — **falsification is essentially equivalent to verification**. This undermines Popper's foundational asymmetry between falsification and verification, which holds only for simple universal statements, not for actual physical laws. According to A.W. Carus, neither Popper nor any of his followers ever directly addressed this argument. Meanwhile, Jaakko Hintikka "effectively disproved Karl Popper's thesis that inductive logic is inconsistent" by developing systems where genuine universal generalizations can receive non-zero probabilities in infinite universes. Branden Fitelson has noted that "Popper should be given more credit for the shift that occurred in confirmation theory" toward increase-in-firmness measures, but "largely because of his nastiness in this dispute with Carnap, his contribution is not properly acknowledged." --- ## The deeper bench: Dorling, Jeffrey, Worrall, and others Several less well-known works deserve attention for the quality of their engagement. **Jon Dorling's** Bayesian Personalism papers — "Bayesian Personalism, the Methodology of Scientific Research Programmes, and Duhem's Problem" (*Studies in History and Philosophy of Science*, 1979) and "Bayesian Personalism, Falsificationism, and the Problem of Induction" (*Aristotelian Society Supplementary Volume*, 1981) — represent the most technically sophisticated attempt at reconciling Bayesianism with Popperian insights. Dorling noted that "the implications of Bayes' rule for scientific method often have a distinctly Popperian ring" and used concrete historical case studies to show Bayesian analysis resolves the Duhemian problem that plagues falsificationism. **Richard Jeffrey's** "Probability and Falsification: Critique of the Popper Program" (*Synthese*, 1975) argues conclusive falsification is as difficult as verification — a point that strikes at the heart of Popper's asymmetry thesis. Jeffrey also published a direct reply to the Popper-Miller theorem. **Isaac Levi's** decision-theoretic approach in *Gambling with Truth* (MIT Press, 1967) and his "Corroboration and Rules of Acceptance" (*BJPS*, 1963) occupies a unique middle ground, treating induction as a cognitive decision problem that borrows elements from both Popperian and Bayesian traditions. **John Worrall** — Lakatos's student at LSE and thus deeply steeped in Popperian philosophy — wrote "Why Both Popper and Watkins Fail to Solve the Problem of Induction" (in *Freedom and Rationality*, 1989), directly arguing corroboration smuggles in inductive elements. His structural realism can be read as an attempt to reconcile Popperian conjectural realism with the need for something like inductive support of structure across theory change. **Susan Haack's** *Evidence and Inquiry* (Blackwell, 1993) deserves special mention. Chapter 5, "The Evidence of the Senses: Refutations and Conjectures," provides one of the most detailed and fair critical examinations of Popper's epistemology in the literature. She engages directly with his conventionalist treatment of basic statements, quoting Popper carefully and identifying the core difficulty — that basic statements cannot be justified by experience in his system — before offering foundherentism as an alternative. Two recent works extend the tradition. **Jesús Zamora Bonilla's** "On Popper's Strong Inductivism (or Strongly Inconsistent Anti-Inductivism)" (*Studies in History and Philosophy of Science*, 2010) makes the technically sophisticated argument that Popper's own desiderata for evidential support measures, once cleaned of ad hoc elements, are qualitatively indistinguishable from inductivist measures. **John D. Norton's** "The Rise and Fall of Karl Popper's Anti-inductivism" (in Yafeng Shan, ed., *Karl Popper and the Open Future of the Philosophy of Science*, Routledge, 2025) is perhaps the single best recent treatment — Norton credits Popper's "laudable purity of philosophical analysis" and "admirable rigor" before systematically demonstrating that science is ineliminably inductive. His two-volume *Material Theory of Induction* (BSPSOpen/University of Calgary Press, 2021/2024), available open-access, develops the positive alternative. --- ## Works that engage but fall short, and one clear strawman Several works offer genuine but less focused engagement. **Peter Lipton's** *Inference to the Best Explanation* (Routledge, 2nd ed. 2004) acknowledges Popper's challenge and concedes that "enumerative induction has been shown to be strikingly inadequate as an account of inference in science" — partly conceding a point to Popper — but offers IBE as a superior alternative without extensive steelmanning. **Larry Laudan's** "The Demise of the Demarcation Problem" (1983) takes Popper seriously but is somewhat polemical — prompted by outrage at the use of Popper's criterion in the McLean v. Arkansas creationism trial. His *Progress and Its Problems* (1977) is more balanced but treats Popper as one of several targets. **Clark Glymour's** *Theory and Evidence* (Princeton, 1980) works in the same problem-space and addresses Popper's critique of confirmation through his bootstrapping approach, but engagement is more implicit than explicit. **Brian Skyrms's** *Choice and Chance* (Wadsworth, 1966; 4th ed. 2000) presents Popper fairly as part of the landscape but the engagement is expository rather than dialectical. **Philip Kitcher's** *The Advancement of Science* (Oxford, 1993) and **Stathis Psillos's** *Scientific Realism* (Routledge, 1999) treat Popper as a background figure rather than a primary interlocutor. **D.C. Stove's** *Popper and After: Four Modern Irrationalists* (Pergamon, 1982) must be flagged as a clear strawman. Multiple independent assessments converge: Stove criticizes four authors simultaneously in a few paragraphs each, never lays out Popper's position in detail, begins from the assumption that Popper is an "irrationalist" rather than asking whether his arguments succeed, and ignores Popper's alternative framework of corroboration and critical rationalism entirely. As one detailed analysis puts it: "Rather than present and discuss Popper's solution to the problem of induction, Stove simply asserts that the only alternative to induction is irrationalism." His lottery argument has some formal interest, and his diagnosis that "deductivism" is the key shared premise of Popper, Kuhn, Lakatos, and Feyerabend has merit as intellectual genealogy, but the book fails the steelmanning test completely. --- ## Essential edited volumes and special issues For researchers wanting to trace the full dialectic, several collections are indispensable. The **Schilpp volume** *The Philosophy of Karl Popper* (Open Court, 1974) contains 33 essays plus Popper's extensive replies — the definitive collection, with key inductivist contributions from Putnam, Lakatos, Grünbaum, Quine ("On Popper's Negative Methodology"), and Bar-Hillel. The **1975 *Synthese* special issue** "Methodologies: Bayesian and Popperian" (Vol. 30) stages a direct confrontation between the two traditions, with Jeffrey, I.J. Good, and Rosenkrantz contributing. *Criticism and the Growth of Knowledge* (Lakatos & Musgrave, eds., Cambridge, 1970) records the famous 1965 London conference where the Popper-Kuhn debate crystallized. The O'Hear volume *Karl Popper: Philosophy and Problems* (Cambridge, 1995) contains Lipton's reliabilist response and Worrall's essay on theory-change, with its introduction noting: "Few qualified observers believe that Popper has succeeded in solving the problem of induction." The recent *Karl Popper and the Open Future of the Philosophy of Science* (Shan, ed., Routledge, 2025) brings the debate into the 21st century with Norton's comprehensive reassessment. --- ## Conclusion: what the best engagements reveal Five patterns emerge from this survey. First, **the strongest steelmanners had institutional proximity to Popper** — Howson, Urbach, Lakatos, Worrall, and Musgrave were all LSE-connected, giving them firsthand knowledge of his actual positions rather than secondhand caricatures. Second, **Salmon's dilemma remains the central unresolved challenge**: either corroboration smuggles in induction, or Popper's framework provides no basis for rational prediction. No Popperian has satisfactorily answered this since 1967. Third, **the most productive engagement came from those who built on Popper** — Mayo's error statistics and Lakatos's research programmes both start from Popperian insights and extend them, rather than attacking from outside. Fourth, **Carnap's technical argument about mixed-quantifier sentences and Hintikka's non-zero probability systems** represent devastating but under-discussed challenges to the logical foundations of Popper's program. Fifth, **genuinely fair engagement with Popper is rare** — even among the works surveyed here, many treat Popper as one target among several rather than devoting the sustained attention his arguments deserve. The works of Howson, Salmon, Mayo, and Norton come closest to the ideal of presenting Popper's arguments in their strongest possible form before offering an inductivist counter.