A machine-checked proof has finally shown that a $40$ year old philosophical debate about Spinoza metaphysics cannot be settled with logic alone.
Philosophers have long argued over whether Spinoza's propositions could be simplified using the Principle of Sufficient Reason. This study used the Lean 4 theorem prover to build a formal model of the argument and found it was logically incomplete. It provides the first concrete evidence that human prose was insufficient to resolve this metaphysical dispute. This is a rare case where computer science is used to close a chapter in the history of philosophy. It shows that formal logic tools can act as a truth engine for the most abstract human ideas.
Bennett's Conjecture in Lean 4: Counter-Models for the PSR-Reducibility of Spinoza's Propositions V and XIV
arXiv · 2605.02331
In A Study of Spinoza's Ethics (1984, §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 De