Newton's "Laws" of motion

After a long time, I'm posting something that's a little different from weightlifting. For the last 4 years, I've been thinking that Newton's laws of motion should rather be Newton's theorems of motion.. Let me explain why...

I'm not sure if the concept of momentum existed in the time of Newton, but differential calculus was being developed in those days. Now, linear momentum is mv. According to all textbooks I've ever read (I don't care about the exact definition, this post is about how we use it), the first law states that a body tends to remain in a state of rest or uniform motion until acted upon by a force. Define force as the rate of change of momentum (as it is usually defined) and you have the first law here.... zero force implies a constant velocity vector and a constant velocity implies zero force.

The second law, that force is rate of change of momentum, or force is mass times acceleration, follows from the definition of force. For the first and second laws, all you need to do is to define a physical quantity called force and your job is done. Obviously, you cannot talk about force without defining it. Hence I find no point in calling these two laws laws... The second law should be called the definition of force, and the first law is a mere theorem.

The third law though, is supposed to be called so. Unless you go into that classical physics and all (I've read about this in PH101 or PH102, that the homogenity of space or something is responsible for this conservation of linear momentum), you need something to say that linear momentum is conserved... Even classical physics assumes homogenity of something and all, since there's an assumption, it doesn't follow from an existing thing and has to be considered an independent law.

Conclusion: Define force as rate of change of linear momentum and that's it, forget the first and second laws. The third law is really the most important law.
By the way, I don't mean any disrespect to anyone, just something I've been thinking. What still puzzles me is, how can we be taught about force and all the laws without defining it properly.. once it's defined, it's very obvious, isn't it?

That was my opinion on the laws. I'd love to have a discussion on these here....