newtonian mechanics - Logical connection of Newton's Third Law to the first two

The first law and second laws of motion are obviously connected. But it seems to me that the third law is not related to the first two, at least logically.

(In Kleppner's Mechanics the author states that the third law is a necessity to make sense of the second law. It didn't make sense to me, though. I'll post the excerpt if anyone would like to see it.)

EDIT: Excerpt from Introduction to Mechanics by Kleppner & Kolenkow (1973), p. 60:

Suppose that an isolated body starts to accelerate in defiance of Newton's second law. What prevents us from explaining away the difficulty by attributing the acceleration to carelessness in isolating the system? If this option is open to us, Newton's second law becomes meaningless. We need an independent way of telling whether or not there is a physical interaction on a system. Newton's third law provides such a test. If the acceleration of a body is the result of an outside force, then somewhere in the universe there must be an equal and opposite force acting on another body. If we find such a force, the dilemma is resolved; the body was not completely isolated. [...]

Thus Newton's third law is not only a vitally important dynamical tool, but it is also an important logical element in making sense of the first two laws.