On the logical formalization of theory change and scientific anomalies

Abstract

An investigation of what might be called the logical formalization of the process of theory change due to anomalies is presented. By anomaly we mean an observed fact falling into the explanatory scope of a theory that does not agree with the theory prevision. A classical approach to restore the explicative power of a theory faced with an anomaly is to propose new, tentative auxiliary hypotheses which, along with part of the old set of auxiliary hypotheses, are able to solve the anomaly. After laying down some conclusions about the structure of such process, we propose a multi-modal and nonmonotonic logical framework able to represent some key aspects of this important facet of the dynamics of scientific theories. Due to the necessity of accommodating incompatible tentative hypotheses, this framework incorporates a weak form of paraconsistency. As a case study, we analyze the anomalous behavior of the planet Uranus which threatened the Newtonian celestial mechanics for more than half a century and gave rise to the discovery of Neptune.