How can we define space and time?

Space and time can be defined in terms of causation. Two events are related temporally (as before and after) if there is a causal signal beginning with the one and ending with the other. And two events are related spatially if there is a third event two which they have non-overlapping causal ties. ‘Space’ and ‘time’ are simply the totality of these causal relations (or possibilities thereof).