A Categorical Solution to the Grue Paradox

Abstract

We offer a systematic analysis and solution to the grue paradox, based on the categorytheoretic formulation of statistical models. By formulating implicit assumptions in inductive inferences, categorical analysis shows that there are actually two distinct grue paradoxes, the hypothetical and the descriptive, which can be tackled separately and with mathematical rigour. In both cases, problematic grue inferences are shown to violate the naturality condition to which any rational inductive inference must conform. This breaks the symmetry between the green-and grue-based inferences in a way not liable to the infamous mirroring argument using the translation from the green–blue to the grue–bleen languages, and thereby solves Goodman’s new riddle of induction understood as a challenge to make explicit our rationality norm of inductive reasoning.