This is just one of dozens of responses to common climate change denial arguments, which can all be found at How to Talk to a Climate Sceptic.
Objection:
Correlation is not proof of causation. There is simply no proof that CO2 is the cause of the current warming.
Answer:
There is no "proof" in science, that is a property of mathematics. In science, one must look at the balance of evidence and formulate theories that can explain this evidence. Where possible scientists make predictions and design experiments to confirm, modify or contradict their theories and must modify these theories as new information comes in.
In the case of the theory of Anthropogenic Global Warming, what we do have is a theory (first conceived over 100 years ago) that is based on well established laws of physics, it is consistent with mountains of observation and data, both contemporary and historical, and it is supported by very sophisticated and refined Global Climate Models that can successfully reproduce the climate’s behaviour over the last century.
Given the lack of any extra planet Earths and a few really large time machines, it is simply impossible to do any better than this.
Aside: It is usually interesting to ask just what observations or evidence your skeptic would consider "proof" that Global Warming is indeed caused by the rising CO2 levels. Don’t be surprised if it an impossible request!
This is just one of dozens of responses to common climate change denial arguments, which can all be found at How to Talk to a Climate Sceptic.
“There is no Proof that CO2 is Causing Global Warming” was first published here, where you can still find the original comment thread. This updated version is also posted on the Grist website, where additional comments can be found, though the author, Coby Beck, does not monitor or respond there.