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Identity pain/neural state/Lewis: contingent. But I do not say that we have two states.
On the other hand: it is also a contingent truth that Bruce is our cat, but it is wrong to say that Bruce and our cat are contingently identical ((s) as if two creatures had found each other who were previously separated, or separately conceivable.) The contingent element here is that the non-rigid concept of being-our-cat applies to Bruce and not to any other cat.
Definition identity/Lewis: the relation in which everything is to itself and nothing else.
Die Identität von Körper und Geist Frankfurt 1989
Konventionen Berlin 1975
Philosophical Papers Bd I New York Oxford 1983
Philosophical Papers Bd II New York Oxford 1986
Cl. I. Lewis
Mind and the World Order: Outline of a Theory of Knowledge (Dover Books on Western Philosophy) 1991