I'd have to disagree that our notion of causality is vague. Certainly at a classical level, our notion of causality is quite specific. We understand fluid dynamics (Navier Stokes), we understand classical thermodynamics, electromagnetic interactions, etc... In each case, at a classical level, there's a fundamental premise - a philosophy of how these things interact. The interactions are causal, but they are also local. These local/causal interactions don't depend on other interactions some distance away, they are independent of nonlocal interactions. Any causal, local interaction must propogate through space and other mediums at a velocity dependant on the physical interactions.
Finally, the local interactions are 'indistiguishable'. By that I mean that given two identical volumes of space with identical physical states, then a given causal action operating on either of those two identical volumes of space will produce the same change in physical state.
What this says is that each interaction within any classical mechanical system is dependent only on the local interaction and the causal action will produce a reaction dependent only on that particular causal, local interaction. This is "bottom-up" causation.
There have been attempts to dethrone this philosophy, but they really aren't mainstream as near as I can tell. They are attempts such as Alwyn Scott for example, who has proposed that any non-linear physical system is in some way 'emergent' and therefore, subject to 'top-down' causation. I think this non-linear attack on bottom-up causation fails however as all non-linear systems can be broken down into finite regions of space and the non-linear phenomenon can be largely duplicated. An extreme example of this non-linear attack is by Robert Bishop (See "Downward Causation in Fluid Convection") in which he argues that Rayleigh-Benard convection is an example of a nonlinear system that supports downward causation (ie: top-down causation). Yet here we are as physicists and engineers using conventional FEA approches (ie: bottom-up approaches) to calculating the phenomenon of Rayleigh-Benard convection, which we can do quite successfully.
The only reputable 'top-down' approach to causation I'm aware of is at a quantum level. Quantum mechanics is fundamentally holistic in a way that classical mechanics is not.