In this note we show how Carnap's theory of degree of confirmation (inductive logic) may be constructed upon a very simple and restricted semantical basis. The semantical meta-languages here may either be based upon a relation ofmultiple denotationor may even benon-translational. To these meta-languages a suitable metric for sentences may be appended. Axioms for such meta-languages are suggested, so that an especially simple formalization of Carnap's inductive logic is in effect presented in outline.For Carnap, inductive logic consists, roughly speaking, of a semantics augmented by a metric. More specifically, for a finite object-languagethe semantics consists of a theory of designation for, and to this are added numerical functions on sentences oftaking real numbers as values. (, it will be recalled, contains justNdistinct individual constants as primitive, where ‘N’ is a constant standing for some fixed finite number.contains a denumerable infinity of distinct individual constants as primitive, and will be discussed in a moment.) Were we to formalize this theory we should have, then, a translation of(or justitself), a syntax for, a primitive relation of designation, real numbers, and several different kinds of class and relational variables. The character of the underlying syntax is not clear from Carnap's account, but this can easily be supplied by a suitable adaptation of Tarski's method. For this, variables for classes of and relations between the expressions of the object-language are needed. Also in Carnap's theory of designation, variables over relations between expressions and objects are needed fundamentally. Real numbers may be handled in various ways. To simplify, let us suppose these are introduced by having a special kind of variable to range over them. Then suitable axioms for real numbers may be given, e.g., one of the axiom sets of Tarski.