The conventionality of geometry is merely incomplete

This article proves two no-go results against the conventionality of geometry. I then argue that any remaining conventionality arises from scientific incompleteness. I illustrate by introducing a new kind of conventionality arising in the presence of higher spatial dimensions, where the incompleteness is resolved by introducing new physical theories like Kaluza–Klein theory. Thus, conventional choices of this kind may guide scientific discovery, but if successful, they would dissolve the original conventional freedom.