Are Newton's laws of motion redundant?

[V0ODO0CH1LD]

My question has to do with something Leonard Susskind, a professor of theoretical physics at Stanford University and director of the Stanford Institute for Theoretical Physics, said in one of his lectures. Basically that he didn't know why Newton wrote three laws of motion, when they could all be summarized as $F=ma$.

I can see why you would think that of Newton's first two laws, seeing as they are the same observation: force is proportional to acceleration. But I can't say the same about the third law. Which states that, in a closed system, the center of mass suffers no acceleration.

Isn't the third law a separate/additional observation?

 

[Jano L.]

If he says so, then he is probably mistaken. I think if one law was direct consequence of another, Newton would notice and wrote so.

There are more approaches to formulate "Newton's laws", but the obligatory reading is what Newton wrote (Principia Mathematica):

http://archive.org/details/Newtonspmathema00newtrich

(see p. 83.)

As you can see from his book, each law says something different.

In modern physics the laws got reformulated a little bit, mainly due to new notion of inertial reference frame, but even after that, the Newton's laws are three separate statements.

Some people arrived at conclusions that the first law can be derived from the second, but I think this is only because they sticked to literal meaning of his or someone's else words and lost the original meaning Newton intended to transmit. I think that if more care and understanding were put into reformulation, it would be possible to restate the three laws in such way that would satisfy even a logician.