> in the sense that "mathematical entities are abstract, have no spatiotemporal or causal properties, and are eternal and unchanging" oh THAT sense, why didn't

> in the sense that "mathematical entities are abstract, have no spatiotemporal or causal properties, and are eternal and unchanging" oh THAT sense, why didn't you just say so? but seriously what does that sense have to do with a picture of a circle? how would one use the picture of a circle to distinguish from an ellipse? edit: nobody ever checked if i knew diddly squat about "real actual academic platonism v formalism" before peforming mathematical exposition in front of numerous classrooms in at least two countries, and surely i'm not going to hold back while arguing on the internet!