Any attempt to estimate climate sensitivity using observations requires a set of models or model-versions that simultaneously predict both climate sensitivity and some observable quantity(-ies) given a range of values of unknown climate system properties, represented by choices of parameters, subsystems or even entire models. The choices researchers make with respect to these unknown properties play a crucial role in conditioning their climate forecasts. We show that any probabilistic estimate of climate sensitivity, and hence of the risk that a given greenhouse gas stabilisation level might result in a dangerous equilibrium warming, is critically dependent on subjective prior assumptions of the investigators, not simply on constraints provided by actual climate observations. This apparent arbitrariness can be resolved by focussing on the intended purpose of the forecast: while uncertainty in long-term equilibrium warming remains high, an objectively determined 10--90% (5--95%) range of uncertainty in climate sensitivity that is relevant to forecasts of 21st century transient warming under nearly all current emission scenarios is 1.4--4.1¿C with a median of 2.4¿C, in good agreement with the traditional range.