{"paper":{"title":"Bennett's Conjecture in Lean 4: Counter-Models for the PSR-Reducibility of Spinoza's Propositions V and XIV","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A four-element counter-model in Lean 4 satisfies Spinoza's axioms plus substantive PSR yet falsifies the full content of Proposition V.","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Yuki Nakamura","submitted_at":"2026-05-04T08:32:13Z","abstract_excerpt":"In A Study of Spinoza's Ethics (1984, {\\S}17), Jonathan Bennett argues that the demonstration of Proposition V of Spinoza's Ethica contains identifiable invalid moves and that, even granted those moves, \"cannot yield more than the conclusion that two substances could not have all their attributes in common\" -- while Spinoza concludes that they cannot share any. Bennett doubts that any valid reconstruction is available from Spinoza's stated resources without importing further commitments. Michael Della Rocca (Spinoza, 2008, ch. 2) responds that the proposition can be derived if the Principle of"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"A four-element counter-model satisfying both axiom sets while falsifying Proposition V's content establishes the irreducibility against this specific augmentation.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The Lean encoding of Bennett's reading of Spinoza's stated axioms as a typeclass and Della Rocca's substantive PSR as an extension class faithfully captures the original philosophical commitments without introducing extraneous strength or weakness.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Lean 4 counter-models confirm Spinoza's Proposition V cannot be derived from his axioms plus Della Rocca's substantive PSR, supporting Bennett's conjecture on the all-attributes ceiling.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A four-element counter-model in Lean 4 satisfies Spinoza's axioms plus substantive PSR yet falsifies the full content of Proposition V.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8a1d1dabac8c13406e071154087c940cd424c1c041e39b7efefe43a8358ceb73"},"source":{"id":"2605.02331","kind":"arxiv","version":2},"verdict":{"id":"dae40288-e9f9-46de-9a5e-6c6cb4e8a870","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T18:40:52.846811Z","strongest_claim":"A four-element counter-model satisfying both axiom sets while falsifying Proposition V's content establishes the irreducibility against this specific augmentation.","one_line_summary":"Lean 4 counter-models confirm Spinoza's Proposition V cannot be derived from his axioms plus Della Rocca's substantive PSR, supporting Bennett's conjecture on the all-attributes ceiling.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The Lean encoding of Bennett's reading of Spinoza's stated axioms as a typeclass and Della Rocca's substantive PSR as an extension class faithfully captures the original philosophical commitments without introducing extraneous strength or weakness.","pith_extraction_headline":"A four-element counter-model in Lean 4 satisfies Spinoza's axioms plus substantive PSR yet falsifies the full content of Proposition V."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.02331/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T16:28:56.653479Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"a3d2c8524b86a45b3067aad234186ca58f93832738d7441fc8511bf513055980"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":3,"snapshot_sha256":"20ced83986ebaa28318260b4f4387b2f136e926d39148d86748509b56c1b1aee"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}