The Counterexample Game: Iterated Conceptual Analysis and Repair in Language Models

TL;DR

This study explores whether language models can perform iterative philosophical analysis by generating and repairing definitions through counterexamples, revealing limitations and partial alignment with human reasoning.

Contribution

It demonstrates that language models can engage in iterative conceptual analysis, but face diminishing returns and inconsistencies compared to human judgments.

Findings

LM judge accepts twice as many counterexamples as humans do.

Extended iteration leads to more verbose but less accurate definitions.

Some concepts resist stable definitions in the iterative process.

Abstract

Conceptual analysis -- proposing definitions and refining them through counterexamples -- is central to philosophical methodology. We study whether language models can perform this task through iterated analysis and repair chains: one model instance generates counterexamples to a proposed definition, another repairs the definition, and the process repeats. Across 20 concepts and thousands of counterexample-repair cycles, we find that, although many LM-generated counterexamples are judged invalid by both expert humans and an LM judge, the LM judge accepts roughly twice as many as humans do. Nonetheless, per-item validity judgments are moderately consistent across humans and between humans and the LM. We further find that extended iteration produces increasingly verbose definitions without improving accuracy. We also see that some concepts resist stable definitions in general. These findings suggest that while LMs can engage in philosophical reasoning, the counterexample-repair loop hits diminishing returns quickly and could be a fruitful test case for evaluating whether LMs can sustain high-level iterated philosophical reasoning.