# Explanatory model that accounts for universality

Hempel's DN (Deductive-Nomological) model is a kind of explanatory model, that accounts for explanation of certain type of questions. Basically If I look for explanation for the laws of motion of a certain system (or merely it's state at a given time), than given the laws of physics that concern the phenomena and the initial conditions, it is possible to derive the state of the system at a certain time. And this accounts for why the system is in a certain state at that given time.

This kind of explanatory model isn't helpfull for different type of questions, for example concerning universality regarding certain aspects of some systems. An easy example is the indpendence of the period of a pendulum by the mass attached to it. This can be proved by dimensional analysys (even solving a differential equation for small oscillations, but here is taken just as example). I can even think of explaining this fact with a causal mecanical description based on the solution of a complicated differential equation for the atoms of the pendulum ( in this way the D-N schema would fit as an explanation). But this kind of explanation works only for that particular pendulum so it doesn't explain the universal behaviour. This is just an example, others are the universality of critical exponents near phase transitions, for completely different type of systems.

In physics and mathematics these problems are answered by the use of certain methods, like dimensional analasys (for the case of pendulum) or the renormalization group (for the way more interesting derivation of universality classes and its critical exponents). My question is if there exist in philosophy an explanatory model for universality, that would abstracts from the different methods used in science, like the ones mentioned above, to keep only the essential details that express what is essnetial to this methods and what is essential to have an explanation of universal behaviour in general. I hope the question is clear, thanks a lot for the help.

Edit: I am adding some papers (by Franklin and Batterman) that discuss the explanatory status of universality by renormalization group, (I have just given a quick read, but I intend going on when I can, and than maybe post a self answer). Anyway I am adding the link as they could be relevant to someone interested in the question.