As someone who plays a lot of art songs, I am constantly faced with issues of poetic interpretation. Is there a right or wrong interpretation of a poem? What would it mean for an interpretation to be right or wrong?
One could say that an interpretation is right if it accounts for every detail in the poem, and does so in a way that is the simplest possible accounting of all of those details. If an interpretation either does not account for every detail, or it contradicts a detail, or another interpretation accounts for all the details in a simpler way, then it is a wrong interpretation, or at the very least incomplete.
That's all well and good, but is that really a useful definition? For example, suppose I have an interpretation that accounts for every detail of the poem. How would I actually know that it accounts for every detail? It might just account for every detail I have thought of, and someone else might be able to point out another detail that it does not account for, or worse, a detail that it contradicts.
So, while, theoretically there could be an interpretation that satisfies all those criteria, I don't see any way it could really be said that a given interpretation is the correct one, or that a given interpretation is a wrong one. After all, a so-called wrong interpretation, one which is contradicted by some detail, might actually be vindicated by the discovery of another detail which removes the contradiction.
Let's explore what I think is the actual root of this problem. It seems to me that any definition of "correct interpretation" is ultimately trying to capture the notion that the correct interpretation is the one the poet had in mind. This is an issue not just in poetry, but in all kinds of art, music, writing, etc. I would like to challenge the notion that the poet's interpretation actually has any more validity than that of anyone else.
You might say "it's his/her poem, of course it should be up to him/her what it means!" What do you even mean by "mean"? If the poet wishes to express him/herself directly, he/her could do that, instead of writing a poem. I think there must be a distinction here between "what the poem means" and "what the poet means". The latter would be a feature of the poet's own psychology, but the former is a more complicated matter. A poem is not a conscious being, and does not have its own intentions. It is a collection of words, which can evoke meanings in the minds of its readers. Those meanings can agree or disagree with each other, they can change over time, they can take into account some or all of the details of the poem, they can take into account details the poet was not aware of. They can be the result of a misunderstanding of the poem, or of a greater understanding of the subject matter than the poem itself suggests.
How can you say that any of these interpretations is the "correct" one?