Certainly you must understand that historic, naturally-caused climate change doesn't preclude anthropogenic climate change any more than historic, naturally-caused forest fires preclude arson. Things can, and do, happen for different reasons.

The reference to the "half a degree" rise is given the impossible context of all GHG emissions stopping now. That increase is simply the lagged response of the climate equilibrating to GHGs already having been emitted. A "business as usual" emissions scenario will likely result in an increase of near 4ºC (7ºF).