There is concern that climate change might lead to abrupt and irreversible changes in parts of the Earth system at so-called tipping points. Theoretical considerations suggest that statistical measures can be used to detect early warning signals (EWSs) for reduced resilience, which could be interpreted as an increased proximity to climate tipping points. Here we discuss limitations of commonly used EWSs and their detection and discuss how alternative explanations can lead to resilience loss in the absence of tipping points. We argue for better testing of the existence of tipping points, beyond the application of EWSs, and propose a method to better quantify the probability of approaching tipping points using EWSs.