A traditional Realist position is that time and space have existence independent from the human mind. Idealists, however, claim that space and time are mental constructs used to organize perceptions, or are otherwise unreal.
Descartes and Leibniz believed that, without physical objects, "space" would be meaningless because space is the framework upon which we understand how physical objects are related to each other. Sir Isaac Newton, on the other hand, argued for an absolute space ("container space"), which can continue to exist in the absence of matter. With the work of Sir Albert Einstein, the pendulum swung back to relational space in which space is composed of relations between objects, with the implication that it cannot exist in the absence of matter.
Although Parmenides denied the flow of time completely in ancient times, echoed more recently by the British Idealist J.M.E. McTaggart (1866 - 1925), much debate in both philosophy and physics has centered on the direction of time ("time's arrow"), and whether it is reversible or symmetrical. As for whether objects persist over time, then the endurantism / perdurantism dichotomy described above applies.