Godel showed that self-referential problems like this are impossible to resolve. He proved that the existence of these types of problems mean that math can never completely describe reality as outlined in his incompleteness theorems -> https://en.wikipedia.org/wiki/Gödel’s_incompleteness_theorems

This is one of the drivers of post-modernist thinking. Douglas Hofstadter talks a lot about this and the nature of consciousness in his famous book Gödel, Escher, Bach -> https://en.wikipedia.org/wiki/Gödel%2C_Escher%2C_Bach