Quest for a Unified Logic of Science in Statistics

Establish a unified logic of science for statistical inference that resolves the currently unsolved status of this problem and provides a coherent foundation for scientific reasoning under uncertainty.

Background

The paper frames the development of a unified logic of science as a central, longstanding challenge in statistics and scientific methodology. The authors position this topic within a 260-year historical arc, reviewing major frameworks—including Bayesian inference, Fisher’s fiducial approach, Dempster–Shafer theory, and inferential models—to assess their potential to serve as a general logic of science.

They note that despite significant progress, a fully satisfactory solution remains elusive, echoing broader concerns in the field (e.g., the unresolved use of Bayes’ theorem without prior information). The paper explores this problem through the proposed Transformational Belief framework and evaluates candidate approaches, emphasizing the need for frequency-calibrated, probabilistic reasoning as part of a unified logic of science.