Climate change threatens irreversible and dangerous impacts, possibly leading to extinction. The most relevant trade-off then may not be between present and future consumption but between present consumption and the mere existence of future generations. To investigate this trade-off, we build an integrated assessment model that explicitly accounts for the risk of extinction of future generations. Using the class of number-dampened utilitarian social welfare functions, we compare different climate policies that change the probability of catastrophic outcomes yielding an early extinction. We analyse the role of inequality aversion and population ethics. Low inequality aversion and a preference for large populations favour the most ambitious climate policy, although there are cases where the effect of inequality aversion on the preferred policy is reversed. This is due to the fact that a higher inequality aversion both decreases the welfare loss of reducing consumption of the current generation and also decreases the welfare gain of reducing the future risk of extinction.