Most physics textbooks will introduce Newton's 2nd law as $$F = ma$$ or $$F = \frac{dp}{dt}$$ and I've seen educators that interpret this as "the product of mass and acceleration lead to a net force" or "the change in momentum leads to a net force". So they rather claim that more appropriate expressions of the 2nd law would be $$a=\frac{F}{m}$$ and $$\frac{dp}{dt}=F$$ thus implying a better sense of causality; that it's the force that comes first, and this is what leads to motion.
So my question is can the ordering of a physics mathematical model be such that it properly takes causality into account?
Or is there a more proper convention/notation to take causality into account?
