Explaining Necessary Truths
This work addresses a gap in understanding explanations for necessary truths, which is an incremental advance in cognitive science and AI, potentially benefiting researchers in logic and human reasoning.
The paper tackles the problem of explaining logically necessary truths, such as mathematical facts, by proposing a computational complexity framework where explanations emerge from simplifying steps during search, and when these are absent, error-based reasons serve as explanatory causes. It validates the theory by simulating human subjects with GPT-4o on SAT puzzles, showing how predictions can be tested in future studies.
Knowing the truth is rarely enough -- we also seek out reasons why the fact is true. While much is known about how we explain contingent truths, we understand less about how we explain facts, such as those in mathematics, that are true as a matter of logical necessity. We present a framework, based in computational complexity, where explanations for deductive truths co-emerge with discoveries of simplifying steps during the search process. When such structures are missing, we revert, in turn, to error-based reasons, where a (corrected) mistake can serve as fictitious, but explanatory, contingency-cause: not making the mistake serves as a reason why the truth takes the form it does. We simulate human subjects, using GPT-4o, presented with SAT puzzles of varying complexity and reasonableness, validating our theory and showing how its predictions can be tested in future human studies.