(October 18, 2016 at 1:22 pm)Jörmungandr Wrote:(October 18, 2016 at 10:46 am)Neo-Scholastic Wrote: Can you conceive of a possible world in which pi is not the ratio of a circle's circumference to its diameter?
Yes, this world. There are no perfect circles in this world so pi is an idealization created by minds. It doesn't exist anywhere but in mind.
It all goes back to the problem of universals, doesn't it? The fact that various knowing subjects can abstract a common feature (circularity) from a wide variety of unique sensible bodies and form the exact same concept of a circle, to me, indicates that circularity has some kind of objectivity, though not necessarily alienable from sensible bodies.