Evidence and Elimination: A Bayesian Interpretation of Falsification in Scientific Practice

TL;DR

This paper reinterprets falsification as a Bayesian model elimination process, providing a quantitative framework that clarifies theory testing, auxiliary hypotheses, and ad hoc modifications through classical celestial mechanics examples.

Contribution

It develops a unified Bayesian account of falsification, integrating Popper's eliminative view with model comparison, and addresses longstanding philosophical issues in scientific theory testing.

Findings

Bayesian model comparison aligns with Popper's falsification criteria.

Auxiliary hypotheses can increase or decrease a theory's credibility.

The approach explains the success of general relativity over Newtonian gravity in Mercury's precession.

Abstract

The classical conception of falsification presents scientific theories as entities that are decisively refuted when their predictions fail. This picture has long been challenged by both philosophical analysis and scientific practice, yet the relationship between Popper's eliminative view of theory testing and Bayesian model comparison remains insufficiently articulated. This paper develops a unified account in which falsification is reinterpreted as a Bayesian process of model elimination. A theory is not rejected because it contradicts an observation in a logical sense; it is eliminated because it assigns vanishing integrated probability to the data in comparison with an alternative model. This reinterpretation resolves the difficulties raised by the Duhem-Quine thesis, clarifies the status of auxiliary hypotheses, and explains why ad hoc modifications reduce rather than increase theoretical credibility. The analysis is illustrated through two classical episodes in celestial mechanics, the discovery of Neptune and the anomalous precession of Mercury. In the Neptune case, an auxiliary hypothesis internal to Newtonian gravity dramatically increases the marginal likelihood of the theory, preserving it from apparent refutation. In the Mercury case, no permissible auxiliary modification can rescue the Newtonian model, while general relativity assigns high probability to the anomaly without adjustable parameters. The resulting posterior collapse provides a quantitative realisation of Popper's eliminative criterion. Bayesian model comparison therefore supplies the mathematical structure that Popper's philosophy lacked and offers a coherent account of scientific theory change as a process of successive eliminations within a space of competing models.