This paper confronts the wide political support for the 2C objective of global increase in temperature, reaffirmed in Copenhagen, with the consistent set of hypotheses on which it relies. It explains why neither an almost zero pure time preference nor concerns about catastrophic damages in case of uncontrolled global warming are prerequisites for policy decisions preserving the possibility of meeting a 2C target. It rests on an optimal stochastic control model balancing the costs and benefits of climate policies resolved sequentially in order to account for the arrival of new information (the RESPONSE model). This model describes the optimal abatement pathways for 2,304 worldviews, combining hypotheses about growth rates, baseline emissions, abatement costs, pure time preference, damages, and climate sensitivity. It shows that 26 percent of the worldviews selecting the 2C target are not characterized by one of the extreme assumptions about pure time preference or climate change damages.