The paper by J. S. Bell reconsiders the demonstrations by von Neumann and others that quantum mechanics does not permit a hidden variable interpretation. Bell argues that the essential axioms of these demonstrations are unreasonable and suggests that an interesting axiom would be that mutually distant systems are independent of one another. The paper discusses a simple example of a 2-dimensional system where a hidden variable scheme can be constructed, showing that it can provide precise predictions for measurement results. Bell critiques the additivity assumption in von Neumann's proof, arguing that it is a peculiar property of quantum mechanical states and not a necessary requirement for hypothetical dispersion-free states. He also examines the arguments by Jauch and Piron and Gleason, finding that their demonstrations require additional properties of dispersion-free states that are unreasonable. Bell concludes by suggesting that further "impossibility proofs" could be pursued by replacing arbitrary axioms with conditions of locality or separability of distant systems.The paper by J. S. Bell reconsiders the demonstrations by von Neumann and others that quantum mechanics does not permit a hidden variable interpretation. Bell argues that the essential axioms of these demonstrations are unreasonable and suggests that an interesting axiom would be that mutually distant systems are independent of one another. The paper discusses a simple example of a 2-dimensional system where a hidden variable scheme can be constructed, showing that it can provide precise predictions for measurement results. Bell critiques the additivity assumption in von Neumann's proof, arguing that it is a peculiar property of quantum mechanical states and not a necessary requirement for hypothetical dispersion-free states. He also examines the arguments by Jauch and Piron and Gleason, finding that their demonstrations require additional properties of dispersion-free states that are unreasonable. Bell concludes by suggesting that further "impossibility proofs" could be pursued by replacing arbitrary axioms with conditions of locality or separability of distant systems.