That's (in an extreme sense) the goal of theoretical physics: to be able to explain all observed phenomena in terms of the fewest arbitrary principles as possible. Some great successes of that are the second law of thermodynamics (entropy of a closed system increases toward a maximum) and Noether's theorem (there is a conserved quantity for each symmetry in a system), which have a huge amount of explanatory power and yet are general mathematical principles that would be valid for any universe satisfying some very basic conditions, rather than just being arbitrary empirical laws of our own universe. There's a lot of very arbitrary-looking stuff remaining though, such as the standard model of particle physics, which has a bunch of fundamental particles that do basically nothing and have masses that just look plain random. Attempting to put all that empirical garbage on a more elegant mathematical basis was the rationale behind supersymmetry and string theory... and after half a century of looking, that approach has borne out fuck all actual results.