Anthony asks what happens if we attach the sentence "Someone called Shakespeare wrote Macbeth" to a text containing a fragment such as
(*) There was [also] a man called ‘Shakespeare’ who lived in Stratford. Shakespeare was a shareholder of the Globe company
I argued in my previous post that indefinite terms act as ‘referential isolators’. They prevent back-reference to any term in an earlier sentence. What Anthony seems to be getting at here is that ‘wrote Macbeth’ seems to be a description that applies to the Shakespeare who was a shareholder of the Globe, and so we might infer an identity, and hence a reference, that is ruled out by the ‘isolator’ theory.
I don’t agree. Consider
(**) Someone called ‘Shakespeare’ wrote Macbeth. There was [also] a man called ‘Shakespeare’ who lived in Stratford. Shakespeare was a shareholder of the Globe company.
I say that the identity between the Stratford man and the Globe man follows from the truth of the second and third sentence, because we cannot understand the ‘Shakespeare’ of the third sentence without understanding that it refers back to the indefinite ‘a man called Shakespeare’. Hence the identity statement ‘The Stratford man was the shareholder of the Globe company’ is true in virtue of the meaning of the terms.
By contrast, the identity of the author of Macbeth and the Globe shareholder cannot be inferred as a logical consequence of the truth of discourse (**) above. It makes the identity highly probable, admittedly, but probability, even if almost absolutely certain, is not the same as logical certainty. This is because of the referential isolator of the second sentence. By contrast, if we change this to
(***) Someone called ‘Shakespeare’ wrote Macbeth. Shakespeare lived in Stratford. Shakespeare was a shareholder of the Globe company.
i.e. if we turn the isolator into a back-referring term, the statement ‘the author of Macbeth was the Globe shareholder' is now true in virtue of the meaning of the terms.
This resolves Wittgenstein's complaint about identity, Tractatus 5.5303 - "Roughly speaking, to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing at all. To say that "X is identical with itself" is trivial, because 'itself' refers back to the subject of the sentence. Because of the grammar, we cannot place an isolator between 'itself' and 'X'. When there is an isolator, as with (**) above, the identity ceases to be trivial. The identity sign therefore is an essential constituent of our language.