Not that this necessarily answers your question, but the amendment as it was originally proposed by James Madison on June 8, 1789 was a little longer than the current text. The first version was as follows:

The right of the people to keep and bear arms shall not be infringed; a well armed and well regulated militia being the best security of a free country but no person religiously scrupulous of bearing arms shall be compelled to render military service in person.

This clause was meant to be inserted into Article I, Section 9 of the Constitution, which places limits on the powers of Congress. Over the course of the summer of 1789, the phrase was gradually whittled down as it was examined by a special committee, and also proposed as a standalone amendment.

Note that in Madison's original version, a portion of what would become the First Amendment also has a justification: the freedom of the press was not to be violated because it was "one of the great bulwarks of liberty."

Garry Wills, in this article on the Second Amendment, points out that the copyright clause of the Constitution (Article I, Section 8, Clause 8) includes a similar justification: "to promote the progress of science and useful arts by securing for limited times to authors and inventors…"

Note also that the Articles of Confederation include a clause (Article VI, Section 4) that has similar wording to the Second Amendment: "... every State shall always keep up a well-regulated and disciplined militia, sufficiently armed and accoutered, and shall provide and constantly have ready for use, in public stores, a due number of filed pieces and tents, and a proper quantity of arms, ammunition and camp equipage."

What do you mean a justification?

This question has been asked before if you're unaware and its has some interesting responses.