on whether a string of bananas may refer to itself.

The following sentence may express a truth when you use it:

This string of symbols per se does not refer to itself.

But if you proceed to mention the previous sentence and affirm that at it is true, the previous sentence is no longer being used but rather is being referred to, in which case you are, in effect, declaring that a string of symbols is true. But how can a string of symbols not only express a truth, but also be true? I understand, for example, how an arrangement of bananas may express a truth, but what does it mean to say that the arrangement of bananas would thereby itself be true?

That * is bananas.