I've asked a couple of professors, how can you say F=ma is empirically true unless you define what F and m are. Each basically said they didn't have a perfectly good answer to that question. The most obvious answers (in my opinion) lead to circular definitions. Well, I was thinking about this and I can up with the following (perhaps sloppy) way of making sense of things. We define the mass of any uniformly composed rock to be one kilogram. Then we say that the mass of any similar rock that is twice as large has twice the mass (or one half the size has half the mass). We now say that the mass of two bodies are equal if they balance an equal-arm balance near the earth. By empirical observations we note that mass is time-invariant and transitive (i.e. if m1 = m2 and m1=m3, then m2 = m3). Now we know what it means to say the mass of a particular system is x kilograms. Let us now define the center-of-mass of a body of uniform composition to be at its geometrical center. The center-of-mass of any other body is then the limit of breaking up this body into smaller pieces of approximately uniform composition and summing up their mass-weighted geometrical centers. Now when we talk about the acceleration of a body, we are really talking about the acceleration of its center-of-mass. Finally, we define the net force on a body to be equal to the product of its mass and acceleration (perhaps it is more appropriately defined in terms of momentum). Now we can state Newton's Law (an empirical observation) in this form [edit: actually, i'm not so sure this is a 'form' of his law]: The net force acting on a body (the central body) when surrounded by other bodies (the surrounding bodies) is equal to the sum of the net forces that would act on the body if the each surrounding body were considered in turn as an isolated system with the central body. I know some of the definitions (such as the one involving an equal-arm balance) aren't entirely precise, but at least its something, which is always better than nothing.