Scientific Progress and Convergence to Truth

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Core Idea

Does science accumulate knowledge cumulatively, with each discovery building on prior ones, or does it undergo revolutions where old frameworks are abandoned? Does science converge toward truth or merely become pragmatically more useful? The answer determines whether science is rationally justified or merely instrumentally successful.

Explainer

From your study of Kuhn's paradigm shifts, you learned that science does not accumulate smoothly but undergoes revolutionary periods when one framework displaces another — and that competing paradigms may be incommensurable, making it difficult to directly compare their claims. From your study of Lakatos's research programs, you learned a more nuanced framework: programs are "progressive" if their theoretical revisions generate novel successful predictions, and "degenerating" if they only make post-hoc adjustments. These two accounts set up the central debate about progress: is science getting closer to truth, or just becoming more useful?

The convergent realist position argues that the long-term success of science — particularly the fact that mature theories make successful novel predictions — is best explained by assuming science is converging toward truth. This argument is sometimes called the no-miracles argument: if our best theories were not approximately true, it would be miraculous that they predict phenomena they were not designed to account for. Newtonian mechanics predicted the existence of Neptune from gravitational anomalies; the germ theory of disease predicted the effectiveness of antiseptics before the mechanism was fully understood. If the theory were not tracking something real, these successes would be inexplicable coincidences.

The pessimistic meta-induction is the strongest objection to convergent realism. The history of science is littered with theories that were once the best available, made successful predictions, and were then abandoned: caloric fluid, phlogiston, luminiferous ether, Newtonian absolute space. If all those theories were false despite their apparent success, what reason do we have to think our current best theories are any different? Laudan sharpens the challenge: the track record of scientific revolutions shows that the *central theoretical entities* of past successful theories are routinely abandoned in subsequent revolutions, suggesting that empirical success and truth-tracking come apart.

The structural realist response attempts a middle ground: while the *ontology* of science (the specific entities it posits) changes dramatically across revolutions, the mathematical structure of successful theories is approximately preserved. Fresnel's equations for light diffraction survive the transition from wave to particle theories; Newton's laws survive as a limiting case of general relativity. On this view, what science converges on is not the identity of fundamental entities but the abstract structure of nature's relations. Instrumentalists reject this entirely, holding that science need not be converging toward truth at all — only toward greater empirical adequacy and predictive power. Distinguishing between these positions requires thinking carefully about what "success" means and what would count as evidence of genuine convergence rather than mere pragmatic improvement.

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Prerequisite Chain

Counting to 10Counting to 20Understanding ZeroThe Number ZeroCounting to FiveOne-to-One CorrespondenceCombining Small Groups Within 5Addition Within 10Addition Within 20Two-Digit Addition Without RegroupingTwo-Digit Addition with RegroupingAddition Within 100Repeated Addition as MultiplicationMultiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Two-Digit by One-Digit DivisionDivision with RemaindersRemainders and Quotients in DivisionDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueReading and Writing DecimalsComparing and Ordering DecimalsAdding and Subtracting DecimalsMultiplying DecimalsDividing DecimalsDividing FractionsMixed Number ArithmeticOrder of OperationsInteger Order of OperationsVariable ExpressionsThe Distributive PropertyVariables and Expressions ReviewIntroduction to PolynomialsAdding and Subtracting PolynomialsMultiplying PolynomialsFactorialPermutationsCombinationsCounting Principles: Addition and Multiplication RulesIntroduction to Graph TheoryPropositional Logic FoundationsLogical Inference and Proof RulesProof Strategies in Discrete MathematicsSoundness and Completeness of Propositional LogicSoundness and Completeness of First-Order LogicCompactness Theorem for First-Order LogicBasic Model TheoryLöwenheim-Skolem TheoremsGödel's Incompleteness TheoremsIntroduction to Intuitionistic LogicIntroduction to Modal LogicA Priori and A Posteriori KnowledgeRationalism vs. EmpiricismThe Problem of InductionPopper's FalsificationismLakatos and Research ProgramsScientific Progress and Convergence to Truth

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