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The size and impacts of anthropogenically induced climate change (AICC) strongly depend on the climate sensitivity, ΔT2x. If ΔT2x is less than the lower bound given by the Intergovernmental Panel on Climate Change (IPCC), 1.5°C, then AICC may not be a serious problem for humanity. If ΔT2x is greater than the upper bound given by the IPCC, 4.5°C, then AICC may be one of the most severe problems of the 21st century. Here we use a simple climate/ocean model, the observed near-surface temperature record, and a bootstrap technique to objectively estimate the probability density function for ΔT2x. We find that as a result of natural variability and uncertainty in the climatic radiative forcing, the 90% confidence interval for ΔT2x is 1.0°C to 9.3°C. Consequently, there is a 54% likelihood that ΔT2x lies outside the IPCC range.