Carnap and The Antinomy of the Name-Relation

Carnap discusses what amounts to what Quine calls opacity in Meaning and Necessity, pp. 133-144.

He discusses Frege, Quine, Church, Russell, Entensional Language, and Extension and Intension as possible solutions.

My symbol_0r, symbol_1r, and symbol_2r relations correspond to what Carnap calls the name-relation.

Frege’s solution.

Frege’s pair of concepts are nominatum and sense. The two conincide in extensional contexts but not intensional (Carnap, p.124)

The problem with Frege’s solution (Carnap, p. 129.) is that it leads to an infinite number of entities and an infinite number of expressions as names for them.

Quine’s solution

Quine says there is no nominatum in intensional contexts.

The problem with Quine’s solution is that logicians who are interested in contructing or in semantically analyzing systems of modal logic will hardly be inclined to adopt this method. All nonextensional contexts are grouped together with contexts in quotation marks.

Church’s solution

Church proposes, for semantical discussions, “to adopt some notational device to distinguish the oblique use of a name from its ordinary use.”

The difficulty with this view is the complexity it results in, Carnap says. He says there would be an infinite number of types (of names I suppose) on this view, but I do not see why. In my (Dennis J. Darland’s) analysis of belief I am careful to distinguish names and names of names etc. though I mostly continue to use quotation marks. And the belief_r relation, which relates the believer to symbols (names) of objects, rather than objects themselves, resolves the problem.

Russell’s Solution

Russell’s solution is his theory of definite descriptions. But it seems to me that, although many names could be eliminated by definite descriptions, not all could. For example, you would need names for the predicates used in the definite descriptions.

Extensional Language

Another proposal is to ban all except extensional language, but Carnap says it is not clear that this is adequate for science.

Carnap – Extension and Intension.

Carnap proposes getting rid of the name-relation altogether.