The most famous concept of possibility and necessity in Antiquity is the Aristotelian one. However, there was a totally different understanding in ancient Greek philosophy: in the Megarian school, possibility was seen as only a modal moment within the real. The present paper suggests a re-reading of this concept in order to explore its implications, its possibilities and challenges. Here, ‘Megarian thinking’ is understood in the larger sense of a philosophical ‘facticism’. Thus, Parmenides of Elea and Aristippus of Cyrene can be seen as ‘Megarian thinkers’ and the onto-theological and ethical relevance of this kind of thinking becomes obvious.