Tatsuya Yoshii

We offer a category-theoretic representation of the process theory of causality. The new formalism allows process theorists to (i) explicate their explanatory strategies (etiological and constitutive explanations) using the compositional features of string diagrams; (ii) probabilistically evaluate causal effects through the categorical notion of functor; (iii) address the problem of explanatory irrelevance via diagram surgery; and (iv) provide a theoretical explanation for the difference between conjunctive and interactive forks. We also claim that the fundamental building blocks of the process theory—namely processes, interactions, and events—can be modeled using three types of morphisms. Overall, categorical modeling demonstrates that the philosophical theory of process causality possesses scientific rigor and expressive power comparable to those of its event-based counterparts, such as causal Bayes nets.

We offer a systematic analysis and solution to the grue paradox, based on the category-theoretic 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.