This paper reviews debates related to the social cost of carbon (SCC) and the challenge of pricing uncertain damages that will occur only in the future. They often revolve around the pure time preference rate, which reflects how much one favors present over future well-being. The SCC measures the marginal cost of the impact on economic growth caused by the emission of a quantity of greenhouse gases equivalent to an additional ton of carbon dioxide (tCO2eq). There is significant variance among (...) estimates of the SCC; one of the reasons for it is a disagreement on how to bring future damages to present values, especially over the so-called "delta parameter" – the pure time preference rate – of the corresponding discount function. On the one hand, the descriptive approach, associated with William Nordhaus, proposes to use the time preference empirically observed among individuals, which would result in a significant limitation of the present value attributed to the distant future. On the other hand, the normative approach, associated with Nicholas Stern, proposes to treat everyone impartially, in every generation, and so implies transferring more resources to future generations. In the limit, assuming exponential population growth, it would lead to a philosophical stance akin to the so-called "longtermism" (as defended by William MacAskill in What we owe the future). In addition, the analysis points out obstacles to using the SCC to price carbon for climate policies. These include aspects related to economic methodology (such as ecological economics critiques of welfarist accounts of intergenerational allocations) as well as political philosophy. Thus, challenges related to uncertainty about socioeconomic development trajectories, intergenerational justice, and public reason become key. Finally, we present the target-consistent pricing approach, where one calculates a carbon price compatible with specific mitigation targets – an alternative to SCC methodologies. This approach is advocated as a way to avoid the uncertainty and the disagreements associated with the SCC, emphasizing the importance of meeting goals set by binding political decisions – such as the Paris Agreement. (shrink)