Keep in mind the purpose of insulation is to impede the transport of energy in the form of heat, between conditioned and unconditioned space. The barrier around the conditioned space in a house is referred to as the thermal envelope, which occurs in the walls, ceilings, and floors of most rooms in your house. One notable exception to this is in the ceiling of first floor rooms and the floors of second floor rooms, due to the fact that the space in between the first and second floor should already be within the thermal envelope established around the perimeter of the house. There may be some sound deadening benefit from insulation installed between the floors (depending greatly on the material utilized) but there is not much benefit from a thermal perspective.
However, that does not mean you should completely ignore the cavity between the floors of your house. Multi-storied houses are much more difficult to seal against air transport, which is a huge component of any comprehensive approach to properly insulating a house. “R” values of insulation only relate to resistance to heat transfer through conduction. Massive amounts of heat can be transmitted through convection, or air movement. Therefore, any avenue by which air can be transmitted from unconditioned (outside) to conditioned (inside) space can result in changes in temperature and vapor pressure. Understanding that the air in your attic is essentially outside air, any opening that allows that air into the cavity between your floors will adversely affect the performance of your home. So, if you can roam (carefully) around in your attic and see into the cavity between your floors then you have a condition that should be addressed.
This same concept applies to any size hole from the attic into the conditioned space of your home. Consider all the holes drilled through the top plates of your walls for electrical wires and plumbing pipes. While they may be small, cumulatively they can represent a substantial breach of the thermal envelope in a typical house. Sealing all such holes can be time-consuming and labor intensive (and unpleasant given the heat and insulation), but the benefits can pay off in the form of lower utility costs and higher comfort levels.