Taking the impact of the current COVID-19 pandemic as an example, I investigate some aspects of care of the self and care for the world. Care of the self is considered with regard to the self-knowledge that can be gained by the neurophysiological study of fear, with particular reference to the role of the amygdala and the hormone oxytocin. Care for the world is studied, with reference to the thought of Hans Jonas and the Gaia hypothesis, in the form of a highly speculative suggestion that the COVID-19 pandemic may, in some sense, be envisaged as the result of humankind’s lack of proper care for the biosphere. Some parallels are drawn with Pierre Hadot’s interpretation of ancient philosophy.