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The world's governments agreed to limit global mean temperature change to below 2 °C compared with pre-industrial levels in the years following the 2009 climate conference in Copenhagen. This 2 °C warming target is perceived by the public as a universally accepted goal, identified by scientists as a safe limit that avoids dangerous climate change. This perception is incorrect: no scientific assessment has clearly justified or defended the 2 °C target as a safe level of warming, and indeed, this is not a problem that science alone can address. We argue that global temperature is the best climate target quantity, but it is unclear what level can be considered safe. The 2 °C target is useful for anchoring discussions, but has been ineffective in triggering the required emission reductions; debates on considering a lower target are strongly at odds with the current real-world level of action. These debates are moot, however, as the decisions that need to be taken now to limit warming to 1.5 or 2 °C are very similar. We need to agree how to start, not where to end mitigation.