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It is an apparent truism that, for any things x and y, if x and y are identical, then x and y have the same properties. For if x and y are identical they are one and the same thing, and so it seems whatever properties the one has the other must have as well. In this paper we will explore views that deny this apparent truism. We begin with familiar examples like the following: Hesperus/Phosphorus: Hesperus is Phosphorus. But while the ancients knew that Hesperus was visible at night, the ancients did not know that Phosphorus was visible at night. This example presents a putative false instance of the following schematic principle: Substitution a ¼ b ! ðu $ u½b=aÞ. 1 We will call false instances of Substitution cases of opacity. Given the existence of cases of opacity, it follows, given classical quantificational logic, that there are false instances of: Quantified Substitution 8x8yðx ¼ y ! ðu $ u½y=xÞÞ.

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Robert Aumann presents his Agreement Theorem as the key conditional: "if two people have the same priors and their posteriors for an event A are common knowledge, then these posteri-

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