THE concepts of state-descriptions and ranges seem useful means for the definitions of basic concepts both in deductive logic' (e.g., 'L-truth' and 'L-implication') and in inductive logic2 (e.g., 'degree of confirmation'). A state-description is defined as a conjunction or class of basic sentences (i.e., atomic sentences and negations of such) which for every atomic sentence S contains either S or non-S but not both and no other sentences. A state-description is intended to represent a possible state of affairs of the universe of discourse. In order to assure that this purpose is fulfilled, the atomic sentences of the language-system in question must be logically independent of each other. This is called the requirement of logical independence (Logical Foundations of Probability, ? 18B). Now Dr. Yehoshua Bar-Hillel3 has pointed out a peculiar difficulty which arises in connection with this requirement, when the primitive predicates of the language system designate not only properties but also relations. For example, let 'W' be a primitive predicate such that 'Wxy' means 'x is warmer than y.' Since the relation Warmer is asymmetric, the basic sentences 'Wab' and 'Wba' are incompatible, and hence any state-description containing both would not represent a possible case; and, since Warmer is transitive, 'Wab,' 'Wbc,' and 'Wac' are incompatible and any statedescription containing all three would not represent a possible case. Furthermore, since Warmer is irreflexive, the atomic sentence 'Waa' is selfcontradictory and hence should be banned from any description of a possible case. According to customary conceptions, the relation Warmer possesses the structural properties mentioned in virtue of its very meaning and hence with logical necessity; therefore the cases mentioned are logically