The main goal of this symposium is to discuss different conceptions of continuity, from Aristotle to the first set-theoretical developments, both in physics and mathematics, in order to highlight some aspects of what we take to be the philosophical and scientific ‘depth' of the notion of continuity. In particular, the reflexion on continuity will give us the occasion to make two main philosophical points: on the one hand, the mathematisation of the notion of continuity, which made it possible to develop some central empirical concepts in the physics of motion, allows us to argue for the thesis that mathematical language can play a central role in the conceptual elaboration of empirical sciences. On the other hand, the existence of different mathematical notions of continuity offers us direct evidence of the existence of cases of incommensurability in mathematics: in this connection, we will discuss how we may accept the possibility of the change of meaning of a given mathematical term (e.g. ‘continuum'), or the possibility of a change in the extension of the corresponding concept.