“Descriptive interpretation”的意思、由来-开放百科全书

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Descriptive interpretation

释义

Examples
Sources

According to Rudolf Carnap, in logic, an interpretation is a descriptive interpretation (also called a factual interpretation) if at least one of the undefined symbols of its formal system becomes, in the interpretation, a descriptive sign (i.e., the name of single objects, or observable properties).^[1] In his Introduction to Semantics (Harvard Uni. Press, 1942) he makes a distinction between formal interpretations which are logical interpretations (also called mathematical interpretation or logico-mathematical interpretation) and descriptive interpretations: a formal interpretation is a descriptive interpretation if it is not a logical interpretation.^[1]

Attempts to axiomatize the empirical sciences, Carnap said, use a descriptive interpretation to model reality.:^[1] the aim of these attempts is to construct a formal system for which reality is the only interpretation.^[2] - the world is an interpretation (or model) of these sciences, only insofar as these sciences are true.^[2]

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.^[3]

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

a: Socrates
b: Plato
c: Aristotle

Predicates:

Fα: α is sleeping
Gαβ: α hates β
Hαβγ: α made β hit γ

Sentential variables:

p "It is raining."

Under this interpretation the sentences discussed above would represent the following English statements:

p: "It is raining."
F(a): "Socrates is sleeping."
H(b,a,c): "Plato made Socrates hit Aristotle."
{{all}}x(F(x)): "Everybody is sleeping."
{{exist}}z(G(a,z)): "Socrates hates somebody."
{{exist}}x{{all}}y{{exist}}z(H(x,y,z)): "Somebody made everybody hit somebody."
{{all}}x{{exist}}z(F(x){{and}}G(a,z)): Everybody is sleeping and Socrates hates somebody.
{{exist}}x{{all}}y{{exist}}z (G(a,z){{or-}}H(x,y,z)): Either Socrates hates somebody or somebody made everybody hit somebody.

Sources

1. ^¹²Carnap, Rudolf, Introduction to Symbolic Logic and its Applications
2. ^¹The Concept and the Role of the Model in Mathematics and Natural and Social Sciences
3. ^{{cite book | last = Mates | first = Benson | title = Elementary Logic, Second Edition | publisher = Oxford University Press | year = 1972 | location = New York | pages = 56 | isbn = 0-19-501491-X }}

3 : Semantics|Formal languages|Interpretation (philosophy)

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