|Scope, range, logic, philosophy: range is a property of quantifiers or operators to be able to be applied to a larger or smaller range. For example, the necessity operator N may be at different points of a logical formula. Depending on the positioning, the resulting statement has a considerably changed meaning. E.g. great range "It is necessary that there is an object that ..." or small range "There is an object that is necessarily ....". See also quantifiers, operators, general invariability, stronger/weaker, necessity, Barcan Formula.|
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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