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In the Middle Ages, Saint Augustine of Hippo asked the fundamental question about the nature of time. A traditional realist position in ontology is that time and space have existence apart from the human mind. Idealists, including Kant claim that space and time are mental constructs used to organise perceptions, or are otherwise unreal.
Suppose that one is sitting at a table, with an apple in front of him or her; the apple exists in space and in time, but what does this statement indicate? Could it be said, for example, that space is like an invisible three-dimensional grid in which the apple is positioned? Suppose the apple, and all physical objects in the universe, were removed from existence entirely. Would space as an "invisible grid" still exist? René Descartes and Leibniz believed it would not, arguing 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. Newton, on the other hand, argued for an absolute "container" space. The pendulum swung back to relational space with Einstein and Ernst Mach.
While the absolute/relative debate, and the realism debate are equally applicable to time and space, time presents some special problems of its own. The flow of time has been denied in ancient times by Parmenides and more recently by J. M. E. McTaggart in his paper The Unreality of Time.
The direction of time, also known as "time's arrow", is also a puzzle, although physics is now driving the debate rather than philosophy. It appears that fundamental laws are time-reversible and the arrow of time must be an "emergent" phenomenon, perhaps explained by a statistical understanding of thermodynamic entropy.
Common-sense tells us that objects persist across time, that there is some sense in which you are the same person you were yesterday, in which the oak is the same as the acorn, in which you perhaps even can step into the same river twice. Philosophers have developed two rival theories for how this happens, called "endurantism" and "perdurantism". Broadly speaking, endurantists hold that a whole object exists at each moment of its history, and the same object exists at each moment. Perdurantists believe that objects are four-dimensional entities made up of a series of temporal parts like the frames of a movie.