I don't think there's much of an answer, at least within the constraints of the science-based tag. Aristotelian philosophy (re the physical sciences) just isn't science as we know it today -- it has (a) little/no predictive ability and (b) tries to convince the reader of false things.
Since our universe isn't really based on four primal elements, but actually 118 as of this writing, any explanation would be, ahem, alternative-science -- or, if you like, magic. Are you looking for real science or some sort of Magical theory/structure that would make it work in a story or game?
For example, if I were to mix Oxygen (O2/'air'), Carbon (C/'earth'), Water (H2O) and heat them to some high temperature (heat input/'fire') and let the reaction run to effective equilibrium, classical-element-based chemistry could make wild guesses of what would result, but only wild guesses, based on the apriori knowledge. After the experiment, an Aristotelian could/would probably come up with some halfway-plausible explanation of why the results were what they were -- but only if he didn't die from Carbon Monoxide poisoning first. A real chemist would know to expect CO, unless the mix was very, very rich in Oxygen relative to the H and C.
Similarly, classical-element chemistry (AKA alchemy) taught that gold could be made from things other than gold, by purely alchemical reactions (rather than fusion in a supernova.) But they never found their Philospher's Stone.
That said, I'm interested in magic(s) based on the classical four elements, to the point of world-building something like that myself. Maybe start a chat if others are interested?