Can the theory that everything that exists exists in time and space, which is materialism as I understand it, explain how things have motion as well? Motion is not itself a thing that can be located within time and space it is only the word that we apply to the effect of something changing position in a continuous manner. But if the only things which exists exists in time and space what is there to move the things that is in motion? Certainly not something else which is in time and space since that demands as well an explanation for it's movement.

This is a deep question or set of questions! The history of the philosophy of motion is fascinating as is the general philosophy of space and time. There are historically significant arguments to the effect that to account for motion in the cosmos, one needs to posit an unmoved mover --God (as developed in the work of Thomas Aquinas in the 13th century). If you are interested in this line of reasoning, you may wish to take a look at more recent articulations of the cosmological argument: you can find these in the Stanford Encyclopedia of Philosophy under 'Cosmological Arguments' and in the entry 'Philosophy of Religion' --entries are free and available online (as this website makes clear). These entries will speak to your sense that something more is needed to account for space-time as currently conceived.

There may be two things to keep in mind as you reflect on the philosophy of motion. First, while motion is not a thing in the sense that it is not a concrete individual object (a rock) it is not is not (necessarily) immaterial (or incompatible with materialism). Motion seems, rather, closely tied in with time; without time, there would be no motion. Also, while some do define materialism as the view that everything that exists is in time and space, this is not universally accepted. Significant philosophers (from the 17th century Cambridge Platonists to G.E. Moore in the 20th century) thought that certain things are non-physical (sensations, and for the Cambridge Platonists the soul) was spatial but not material.

You are on to a vital, historically fascinating issue. Richard Sorabji has published a number of important books that address the rich and creative ways in which motion have been conceived of since Zeno. A close look at his work will prove (I wager) to be very rewarding! You may still have questions un-answered but not un-addressed, and Sorabji is brilliant at bringing to light ancient sources that often go overlooked these days.

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