I doubt that: the Founding Fathers were smart enough not to write illogical statements into the Constitution (well, except for that three-fifths clause). The contradiction I feel coming lies more in the irrational reasoning of folks like the Second Amendment Sisters, who think you ought to be able to pack heat anywhere, anytime, or Governor Rounds and far too many of our state legislators, who think you should be able to make and use guns and ammo in South Dakota without any federal regulation.
Did someone say regulation? Let's review the Second Amendment:
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.
First phrase: well regulated Militia. The Founding Fathers framed the proper keeping and bearing of Arms in the context of regulation. The Constitution gives Congress the power to call up, organizing, arm, and discipline that militia. Our right to bear Arms appears to exist, in the Founding Fathers' minds, under the assumption that Congress gets to regulate those Arms.
Compare the phrasing of the Second Amendment with its neighbors. No other Amendment feels the need to explain itself. The First Amendment does not say why we need freedom of religion and speech ("A well exercised and expressed conscience, being necessary to the functioning of a free Democracy and personal integrity..."); it goes right to business, saying "Congress shall make no law...." Same with the other amendments: Washington, Franklin, Hamilton, et al. don't explain why the government can't quarter soldiers in peacetime or search without a warrant or impose excessive bail. The later amendments don't go there, either: the Constitution doesn't tell use why we can't have slaves or why we should have an income tax or why we should not or should have a stiff drink.
The Second Amendment is an anomaly, specifying the context motivating its protection. And that context is not individual self-defense or pheasant hunting or a God-given right to blast old buckets with your AK-47 (that happens here at Lake Herman). The Second Amendment explicitly assumes our guns exist in a framework of regulation to serve the State. If you want to posit other gun rights and oppose gun regulation, you can't rely on the Second Amendment; you have to hope for judicial activism.