A system made of several things can host properties which the things themselves do not have. For instance, consider two points on a plane. These points will have a *distance* between them. This distance is not itself a property, but exists in the relation between the points. Emergent properties can arise not only between things in the system, but between other emergent properties. The number and subtlety of these properties can be very much greater than the number of things.
This helps to explain why, for instance, the number of ways of packing boxes into a truck increases exponentially with the number of boxes. It helps to explain why the fallacy of division is a fallacy. Intelligence *emerges* from the connections between neurons. It is not nessesary to propose a "soul" to account for the fact that brains can be intelligent, even though the individual neurons of which they are made are not.