There are close parallels between Frank Jackson's case of black-and-white Mary and David Lewis's case of the two omniscient gods. This essay develops and defends what may be called “the ability hypothesis” about the knowledge that the gods lack, by adapting Lewis's ability hypothesis about the knowledge that Mary acquires. What the gods might lack despite their propositional omniscience is not any distinctive kind of information, but certain abilities of introspection. The motivating idea is that knowledge one acquires by exercising introspective abilities cannot fail to be knowledge about oneself or indexical knowledge. So in order to envisage the gods' epistemic situation coherently, we need to assume that they lack those introspective abilities. But once we recognize that, it turns out that positing a special kind of information is a gratuitous addition. The two gods' ignorance simply consists in their lack of introspective abilities.
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Hongwoo Kwon; Mary and the Two Gods: Trying Out an Ability Hypothesis. The Philosophical Review 1 April 2017; 126 (2): 191–217. doi: https://doi.org/10.1215/00318108-3771998
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