We know how much carbon man has put into the atmosphere, and we know the physics of how that leads to global warming. The measured increases in global temperature are corroboration that the physics is right.
There is no proof that we are actually having an impact. Yes we dump large amounts of pollutants, and it certainly looks bad when you stand next to a smoke stack, but studies have shown that CO2 rises AFTER the temperature rises, not the other way around. Also, water vapour has a much greater greenhouse effect than CO2.
The real problem is that we have no way to actually test any of this. If would be nice to have a planet that ages at a 100 fold rate so that we can perform experiments. But we only have this one planet to try to form a theory. Try to use the same methodology in ANY other discipline and you would be laughed at.
The measured increases in global temperature are corroboration that the physics is right.
What about the warm period in the middle ages? When it was hotter than now, and Greenland was actually green? Then it got cooler and the Vikings had to leave or starve. Now its getting warmer again.
Yes, yes, the curve is said to be steeper than normal, but what is normal? Historical data is much to vague to nail that down.
BTW, the rhetoric is so prevalent that intelligent discussion is almost impossible. One side calls the other either deniers or alarmists whenever either side tries to question anything.