Let me go digging and see if I can find where someone found CO2 levels rose and fell on a curve behind temperature change. The reason theorised was that the warmer oceans couldn't hold as much in solution.
Yes, the chart I posted earlier showed historic CO2 levels as measured over the past few hundred thousands years, as determined by ice core samples. A similar chart could plot CO2 and temperature together on the same timeline, and you would see that cyclical variation in temperature leads CO2. You might conclude from this that temperature is a driver of CO2, and you would be absolutely correct, as changes in ocean temperature change the ability of the ocean to hold CO2, so as the oceans warm and cool the concentration of CO2 in the atmosphere rises and lowers.
If we stop here, there are two mistakes we can make. One is to say "well, that solves it, CO2 doesn't cause warm, warm causes CO2". The mistake here is thinking that causes and effects can only happens in happy pairs of one cause married to one effect, but there's no reason why our brains shouldn't be able to grasp that a cause can have an effect that impacts the cause. In other words, warming encourages rising CO2 concentration, and rising CO2 concentration encourages warming. CO2 is a positive feedback. Before people came along, the warming was driving the CO2 and the CO2 magnified the cycles of warming and cooling.
Today, the CO2 concentration is being jacked up by human contributions, and CO2 is encouraging warming.
The second naive mistake we can make is to say "so, there, it's not CO2 causing warming, the warming is natural and the warming is driving CO2, just like usual". This is a particularly bad mistake, because we're putting enough CO2 into the atmosphere to account for double the observed rise, so we're not exactly at a loss to explain how that CO2 got there. Also, per the chart I posted earlier, the current CO2 level is well above any level seen in any sample taken from the past 800k years.
There's no doubt surrounding the ability of CO2 to encourage warming, that's just basic science, observable in the differences between the Earth and the Moon and between Mercury and Venus. Where there is doubt is in how this complex climate system reacts to rising CO2 and in the relative impacts of the many positive and negative feedbacks.
-harry
