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Scope/Lewis: If a quantifier is beyond the reach of the modal operator (MO), we have to limit its object area to the actual world - If modal operators occur within modal operators, we have to start working from the outside to the inside.
Scope/De re/de dicto/Lewis: a) narrow scope: (only in actual world): here the modal operator is applied to the already closed sentence. - E.g. every possible world contains one single A so that the sentence ya is true in every possible world - de dicto - this is referentially opaque. - The translation of the apparent Leibnizian identity is invalid. - b) broad scope: here the modal operator is applied to an open sentence to form a new modal sentence f, and the attribute that is expressed by Nf is preceded by the real thing -That is de re - and is referentially transparent. - The translation of the apparent Leibnizian identity is valid here.
Medium scope/Lewis: for each description there are three scopes. Also a medium one: E.g. NM(h = z) - broad scope: de re, transparent: says that the attribute expressed by f is essential and is denoted by z.
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