Explaining Necessary Truths

TL;DR

This paper introduces a computational complexity framework for explaining necessary truths, contrasting deductive explanations with error-based reasons, and validates the theory through GPT-4o simulations of SAT puzzles.

Contribution

It proposes a novel complexity-based model for explaining necessary truths and demonstrates its applicability through simulations of human reasoning on SAT puzzles.

Findings

Explanations for deductive truths co-emerge with search simplifications

Error-based reasons can serve as fictitious contingency-causes

Simulations validate the proposed explanatory framework

Abstract

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.