Mathematical Explanations
This work addresses a foundational problem in philosophy and AI for researchers interested in explanation and knowledge representation, but it appears incremental as it builds on existing notions of explanation and possible worlds.
The paper tackles the problem of defining explanations for mathematical statements and determining when one explanation is superior, by addressing the issue that mathematical facts cannot be part of standard explanations because they are true in all causal models and known by agents, and solves this using impossible possible worlds.
A definition of what counts as an explanation of mathematical statement, and when one explanation is better than another, is given. Since all mathematical facts must be true in all causal models, and hence known by an agent, mathematical facts cannot be part of an explanation (under the standard notion of explanation). This problem is solved using impossible possible worlds.