 Carnap assumes a fixed domain of quantification for his quantified system, the functional calculus with identity FC, and consequently for the modal functional calculus with identity MFC, a quantified form of S5. The language of FC contains denumerably many individual constants, the universe of discourse contains denumerably many individuals, each constant is assigned an individual of the domain, and no two constants are assigned the same individual. This makes sentences like \(a = a\) L-true, and sentences like \(a = b\) L-false (1946: 49). Concerning MFC, the Barcan formula and its converse are both L-true, that is, 