The Principles of Mathematics (1903)

§ 53

It may be asked whether everything that, in the logical sense we are concerned with, is a verb, expresses a relation or not. It seems plain that, if we were right in holding that Socrates is human is a proposition having only one term, the is in the proposition cannot express a relation in the ordinary sense. In fact, subject-predicate propositions are distinguished by just this non-relational character. Nevertheless, a relation between Socrates and humanity is certainly implied, and it is very difficultto conceive the proposition as expressing no relation at all. We may perhaps say that it is a relation, although it is distinguished from other relations in that it does not permit itself to be regarded as an assertion concerning either of its terms indifferently, but only as an assertion concerning the referent. A similar remark may apply to the proposition A is, which holds of every term without exception. The is here is quite different from the is in Socrates is human; it may be regarded as complex, and as really predicating Being of A. In this way, the true logical verb in a proposition may be always regarded as asserting a relation. But it is so hard to know exactly what is meant by relation that the whole question is in danger of becoming purely verbal.(§ 53 ¶ 1)