The Western Approach:
"The Elements" were introduced to western civilization by the greeks. It all happened during the period historians and modern day philosophers tend to call "From Mythos to Logos", a period in greek history where philosophers went from explaining everything as divine to seeking more down to earth explanations.
One of the important questions that were posed, was "What is everything composed of?" (We know it's nodegel of course, but that is beside the point). Many people belived water was the primary substance of cosmos, other belived earth was the deal. One crazed philosopher by the name of Democrites even thought the world constisted of itsy, bitsy unbreakable bits he called atoms. Democrites was proved wrong by the impeccable logic of Aristotles.
Aristotles belived that the Universe was more complicated. How could it possibly be made up of only one thing? He decided that (allmost) all of his predecessors were right. Sure, the world was made up of water, but also earth, air, fire, and ether.
The philosopher created a worldview consisting of spheres. The innermost sphere was earth. Outside of earth was water, then air, and then fire. Around all of this was the perfectly spherical and unmovable ether. This was proven beyond doubt by the known fact that everything seeks to it's natural state.
Aristotele's experiment: Earth is in the middle, so "earth"-things will allways travel downwards. Throw a rock in the air and see how it stops, turns around, and returns to Earth where it belongs. Water thrown up in the air does the same, but it does not penetrate Earth, so Water belongs therefore outside (above) Earth, but inside (beneath) Air.
Fire was harder, but since flames reach upwards no matter where you burn it, and since a flame is only a manifestation of fire and you'll get burned if you hold your hand even several inches above it, it seems perfectly reasonable to assume that fire travels upwards. Thus fire belongs above air.
Above all of this resides the celestial matter, ether. Ether is perfectly spherical and has a host of other properties that alchemists have tried to figure out for a long time.