Objection: Natural variability is the null hypothesis; there must be compelling evidence of an anthropogenic CO2 warming effect before we take it seriously.
Answer: The null hypothesis is a statistical test, and might be a reasonable approach if we were looking only for statistical correlation between increasing CO2 and increasing temperature. But we’re not — there are known mechanisms involved whose effects can be predicted and measured. These effects are the result of simple laws of physics, even if their interactions are quite complex.
But putting aside inappropriate application of the null hypothesis, we are indeed well outside the realm of natural global variability, as seen over the last 2,000 years and even over the last 12,000 years. We can go back several hundreds of thousands of years and we still see that the temperature swings of the glacial/interglacial cycles were an order of magnitude slower than the warming rate we are now experiencing.
In fact, outside of catastrophic geological events like the Paleocene Eocene Thermal Maximum there are no known precedents for warming this fast on a global scale. I’d say the case for “it’s all natural” is the one that needs explaining.
Oh, and by the way, we do in fact have compelling evidence.