As a teacher of high school mathematics and a former student of philosophy, I try to merge the two to engage my students in meaningful conversations about the significance of some mathematical properties. Recently, however, I could not adequately defend the statement "a=a" as being necessary for our study of geometry when one student challenged "When is a never NOT equal to a?" What would you tell them?
(One student did offer the defense that "Well, if we said a=2 and a=5 then a=a would be false, causing problems.")