Are there 2 laws of motion or only 1? It seems clear that Newton's first law is a special case of his second. Although perhaps people might argue that it emphasizes the centrality of inertial frames.
But is the third law also just a special case of the second? Could a physical system exist which obeyed the first two laws but not the third? Or does the third again simply emphasize an aspect of the second that is useful didactically?
Responding to a comment about why the third is a subset of the second, take an example of an object sitting on a table. The object has gravity pulling down but it is not accelerating so the net force must be 0 (from N2). Similar logic can be applied to other situations (I think). At least, that's what this question is trying to clarify.
 A: Historically, people thought that a projectile needed a continuing force to keep it moving through the air.  Newton's first law cleared this misconception up by stating that due to an object's inertia, that object will preserve its state of motion until an outside force acts on it.
Newton's second law provides an equation that can be used to calculate how much force is required to change an object's state of motion by a given amount.
Historically and still today, there is a huge misconception that when a big object collides with a small object, the big object imparts a big force on the small object, and the small object imparts a small force on the big object.  Such a situation seems intuitively obvious, but it is wrong.  Newton clarified this situation by stating that the forces between objects are equal in magnitude and opposite in direction, even when field forces are involved (and in fact, all fundamental forces are field forces).
Newton's law 1 and law 3 are NOT restatements of the second law.  Laws 1 and 3 necessarily need to be formally stated to eliminate the misconceptions that most people take to be intuitively obvious, but are wrong. 
