Multiple interpretations can also be useful purely as a pedagogical tool though. Using a range of metaphors to tell stories around some formal concept can make

Multiple interpretations can also be useful purely as a pedagogical tool though. Using a range of metaphors to tell stories around some formal concept can make it easier to communicate and understand. That's not to say you should assume every mathematician who communicates their ideas as though the objects 'exist' in some objective sense is a platonist, or that any scientist who talks implicitly about truth when communicating about their work, is committed to a strong philosophical stance on the matter. It can be just a habit one gets into when trying to communicate. No doubt some philosophical remarks could be made about this too, not that I'm qualified...