During the Paris Conference in 2015, nations of the world strengthened the United Nations Framework Convention on Climate Change by agreeing to holding "the increase in the global average temperature to well below 2°C above pre-industrial levels and pursuing efforts to limit the temperature increase to 1.5°C"1. However, "pre-industrial" was not defined. Here we investigate the implications of different choices of the pre-industrial baseline on the likelihood of exceeding these two temperature thresholds. We find that for the strongest mitigation scenario RCP2.6 and a medium scenario RCP4.5 the probability of exceeding the thresholds and timing of exceedance is highly dependent on the pre-industrial baseline, for example the probability of crossing 1.5°C by the end of the century under RCP2.6, varies from 61% to 88% depending on how the baseline is defined. In contrast, in the scenario with no mitigation, RCP8.5, both thresholds will almost certainly be exceeded by the middle of the century with the definition of the pre-industrial baseline of less importance. Allowable carbon emissions for threshold stabilisation are similarly highly dependent on the pre-industrial baseline. For stabilisation at 2°C, allowable emissions decrease by as much as 40% when earlier than 19th century climates are considered as a baseline.