Descriptive interpretation


According to Rudolf Carnap, in logic, an interpretation is a descriptive interpretation if at least one of the undefined symbols of its formal system becomes, in the interpretation, a descriptive sign. In his Introduction to Semantics he makes a distinction between formal interpretations which are logical interpretations and descriptive interpretations: a formal interpretation is a descriptive interpretation if it is not a logical interpretation.
Attempts to axiomatize the empirical sciences, Carnap said, use a descriptive interpretation to model reality.: the aim of these attempts is to construct a formal system for which reality is the only interpretation. - the world is an interpretation of these sciences, only insofar as these sciences are true.
Any non-empty set may be chosen as the domain of a descriptive interpretation, and all n-ary relations among the elements of the domain are candidates for assignment to any predicate of degree n.

Examples

A sentence is either true or false under an interpretation which assigns values to the logical variables. We might for example make the following assignments:
Individual constants
Predicates:
Sentential variables:
Under this interpretation the sentences discussed above would represent the following English statements: