Is reference logically intransitive?

In its strict technical sense (i.e. as used by philosophers of language) the verb phrase ‘refers to’ is logically transitive. If ‘London’ refers to London, then something is the referent of ‘London’ and ‘refers to’ is therefore logically transitive in the sense defined here. Thus the following conjunction is inconsistent when ‘refers to’ is taken in its technical sense.

(*) Tom is referring to a winged horse, but there are no winged horses.

Informally and in ordinary use, however, it seems to be logically intransitive. For example, you might get the following question in a multiple choice exam:

(**) Who is Shakespeare referring to when he says “the power of beauty will sooner transform honesty from what is to a bawd than the force of honesty can translate beauty into his likeness”? (see here for a real example)

Clearly the answer will be right or wrong, and thus true or false. Indeed, the a generally accepted answer is that Shakespeare is referring to Hamlet’s mother Gertrude, and so ‘Shakespeare is referring to Gertrude’ is true. But Gertrude being a fictional character, there is no such person as Gertrude. Thus

(***) Shakespeare is referring to Gertrude, but there is no such person as Gertrude

is not inconsistent. thus, in its ordinary sense (for example in GCSE exam questions about Shakespeare and Dickens), the verb phrase ‘refers to’ is logically intransitive.

In the posts that follow I will be exploring the concept of Story relative reference – reference to an individual within a text (or group of texts) such that the individual is identifiable within that text, but not outside it, and I will demonstrate its connection with the subject I began with, namely the intentionality of singular thoughts.