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

Fuente: arXiv
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Autores principales: Drucker, Daniel, Mahowald, Kyle
Formato: Preprint
Publicado: 2026
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author Drucker, Daniel
Mahowald, Kyle
author_facet Drucker, Daniel
Mahowald, Kyle
contents 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.
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id arxiv_https___arxiv_org_abs_2605_03936
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle The Counterexample Game: Iterated Conceptual Analysis and Repair in Language Models
Drucker, Daniel
Mahowald, Kyle
Computation and Language
Artificial Intelligence
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.
title The Counterexample Game: Iterated Conceptual Analysis and Repair in Language Models
topic Computation and Language
Artificial Intelligence
url https://arxiv.org/abs/2605.03936