Okay, English major to the rescue.

A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed.

Let's break it down, shall we? The logic implied by the grammar is a basic syllogism, as follows:

Major premise: A well regulated militia is necessary to the security of a free State.
Minor premise: The only way to maintain a well regulated militia is to give the people the right to keep and bear arms.
Conclusion: Therefore, because a well regulated militia is necessary to the security of a free State, and the only way to maintain a well regulated militia is to give the people the right to keep and bear arms, the right of the people the to keep and bear arms is necessary to the security of a free State.

One may render a syllogism invalid by proving one or more of its premises false. In this case, the premise in question is whether or not the only way to maintain a well regulated militia is to give the people the right to keep and bear arms. One may argue then, that because a well regulated militia exists in the form of the National Guard, there is a method of maintaining a well regulated militia without giving the people the right to keep and bear arms.

But of course, humans are particularly invulnerable to logic, so who cares?