In Federalist No. 40, Madison examines whether the Constitutional Convention was authorized to make so thorough a revision of our government as they did. This is not an idle thought: as many historians have noted since, the Convention was assembled to remedy the defects of the Articles of Confederation, not to completely rewrite them.*
You can tell what Madison thinks of this idea early in the essay, where he calls it a "recommendatory act." Applying some canons of construction to this act, Madison decides that the act's goals (a more effective government and the continued use of the Articles) are inconsistent. That is to say, he believes that there was no way the Convention could have created an effective government merely by revising the deeply flawed structure then in place; to be effective, the form of government must be completely revised.
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So which should they ignore? Making the government effective is a distinct goal; the method of doing so (by amendment to the Articles) is secondary. After all, the Convention could have written an "amendment" that replaced every word in the Articles. This would have been within the letter of the law, but certainly not within its spirit. Instead of enacting such a charade, the Convention started afresh, and accomplished what, to Madison's mind, was the goal -- the creation of a more perfect union.
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That said, perhaps the Convention had the right to rewrite the thing, but did they have the right to change the form of government? That is, could the change the government from a confederation to a federation? Madison answers: yes. The states sent delegates (well, twelve of them did) and the people approved the Constitution they wrote in conventions. What could be a purer exercise of the will of the people? By the time Madison wrote, on January 18, 1788, the Constitution had been approved by the people of five states, with a sixth, Massachusetts, to follow in a few weeks.
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For anti-Federalists to say that they Convention did not act appropriately after several states had endorsed their action was looking increasingly petulant. As Madison says, this opinion "has no foundation to support it; that if they had exceeded their powers, they were not only warranted, but required, as the confidential servants of their country, by the circumstances in which they were placed, to exercise the liberty which they assume; and that finally, if they had violated both their powers and their obligations, in proposing a Constitution, this ought nevertheless to be embraced, if it be calculated to accomplish the views and happiness of the people of America."
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Constitution-making is always a messy process, as no government readily provides for its own replacement. What is important in forming a government is not crossing the "t"s and dotting the "i"s, but making sure that the people's voice is given effect and that their liberties are adequately preserved.

