 The motivation behind MC2 is that Athena seemingly has exactly the same location and exactly the same parts as Piece. So ‘Athena’ and ‘Piece’ are plausibly just different names for the same thing. The motivation behind MC3 is that Piece and Athena seem to have different modal properties: Piece is able to survive being flattened and Athena isn’t. MC4 follows from the Principle of the Indiscernibility of Identicals (a.k.a. Leibniz’s Law): ∀x∀y(x=y → ∀P(Px iff Py)). In other words, if x and y are identical, then they had better have all the same properties. After all, if they are identical, then there is only one thing there to have or lack any given  property.[21] 