If cooling due to present-day levels of atmospheric aerosol is suppressing global temperatures, future reductions in aerosols emissions would allow the full greenhouse gas induced warming to be realised. The many uncertainties in aerosol physics and chemistry mean that a large range of present-day aerosol cooling is possible which could imply a large climate sensitivity, extremely large future warming and the increased risk of catastrophic consequences.Despite large uncertainties in aerosol physics and chemistry, observed spatial and temporal patterns of past temperature change allow quantitative assessment of the strength of present-day aerosol cooling. Such observational constraints provide a probabilistic framework in which to assess the likelihood of extremely large warming if a very large suppression of global warming by aerosols were to be removed. The likelihoods of future warming extents are calculated assuming four scenarios of future anthropogenic emissions. While such results are still subject to uncertainty, they indicate that future warming by the end of the 21st century is likely to be between the extremes implied by very strong or very weak present-day aerosol cooling. It is very likely that present-day aerosol cooling is suppressing a major portion of current greenhouse warming.