More CO2 captures more heat. It's that simple.
It's not that simple at all. Given the current composition of the atmosphere, for instance, to the best of our observations, more CO2 in the troposphere traps more heat in the troposphere, raising its temperature, BUT more CO2 in the stratosphere radiates more heat out of the stratosphere, lowering the temperature of the stratosphere. There may be a point in the system, after which the absorption bands in the troposphere are saturated enough that the cooling effect on the stratosphere of additional CO2 is greater than the warming effect on the troposphere.
Life on earth will continue but it could be that lots of hurricanes, higher temperatures, combined with periods of draught could make life very unconfortable and may result that a total population of 11 billion people cannot be supported anymore...
Or it could be that global warming will lead to fewer hurricanes and less drought. The idea that we can use a computer model to predict the behavior of this system outside the region that we have data for is naive.
And it could also be that we can ONLY support 11 billion people with global warming, as the one thing that global warming certainly leads to is higher evaporation rates, which means more fresh water produced by nature. And fresh water supply is the biggest limiter to human population.