Ok, I know Goroff and Sagnotti proved that the two loop contribution to pure gravity is divergent, but I guess I don't understand non - renormalizability. Looking, at the BPHZ method it seems that you could subtract out the divergences at each level. Although, you need an infinite number of counter terms for the entire path integral. It seems to me that at each loop level it would only take a finite number of counter terms to cancel the divergences. What am I missing here?