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Self-identification/Mach: E.g. "What a run-down a schoolmaster comes here." It was he himself, who saw himself in the mirror.
Self-identification/Self/Chisholm: "he himself" only shifts the problem - differences: "There exists an x such that x thinks that x is wise, and he is x" - "There exists an x such that x thinks that x is wise and x is x"? - No clear formulation: the property of taking oneself to be wise - ChisholmVs: impossible proposition.
Chisholm: "... that he is x" always implies that x is x, but not vice versa that x is he!.
Die erste Person Frankfurt 1992
Roderick M. Chisholm
Erkenntnistheorie Graz 2004