In our constitutional republic there are two criteria for determining if an action by government is moral and/or legal. Would U.S. military action against ISIS, which has become the face of evil in the world at the moment, meet that criteria?
The first criteria is the "Laws of Nature and Nature's God." This requires the action committed by government to be moral, which means to be in accordance with natural law. This natural law requires military action to be morally justified given the human toll at stake. Dating all the way back to Augustine's City of God, this is what's more commonly known today as "just war theory."
There are seven components to Just War Theory. Let's take a look at each and see if military action against ISIS applies.
Just Cause
ISIS has already kidnapped and beheaded two Americans in full view of the world. How many Americans do they need to kill for a U.S. military response to be justified? They have also declared war on the United States, and have already demonstrated in Iraq and elsewhere they at least have some military capability to wage one. Not to mention all those they have already crucified, murdered, tortured, and violated. I believe this clearly makes the case this would be a just cause.
Comparative Justice
What's already been done to Americans, and is being threatened to do to even more, means eradicating ISIS clearly crosses this threshold.
Competent Authority
Our Constitution requires a process for the declaration of war, which is something administrations in both parties have ignored for decades. Some may argue that Congressional resolutions supporting military action, like we saw in both Iraqi wars, meets the criteria for declaring war since the Constitution never explicitly states what form that declaration of war must take. Only five times in American history has there been a formal declaration of war, and we’ve certainly been involved in many more military conflicts than that. Our first formal declaration of war came in the War of 1812, and we had already engaged in military action versus the Barbary Coast Pirates (who where the Jihadists of their day) several years before then. So even our Founding Fathers debated this question.
Right Intention
We have clearly demonstrated we have no more will/desire to invest heavily in nation-building in another Muslim land. Therefore, the only motive here isn't war for empire, but the eradication of a would-be caliphate (empire) in its nascent stages. Knowing what you know now from history, would you not have supported FDR eliminating the Nazi threat before it was too late? Therefore, we have a right intention here to eliminate a threat that has already proven it is mobile and extremely hostile.
Probability of Success
This is where it gets dicey. There were plenty of complaints about the tepid rules of engagement over there under George W. Bush, and now those complaints are even more pronounced under the politically-correct rules of engagement from Barack Obama. Will our current commander-in-chief unleash the hounds and allow the military to prosecute its mission to its fullest extent, or will he ask them to fight in a way that pleases the New York Times editorial board? In my opinion, a lack of trust in the current civilian leadership of our military is the biggest (only?) reason not to do this.
Last Resort
Obviously a marauding gang of villainous thugs like ISIS, that is too radical for even Al-Qaeda, is beyond reasoning with.
Proportionality
If ISIS is everything they've shown themselves to be, and our military is given the tools and the rules of engagement necessary to eradicate them, then the potential benefits to the American people out-weigh the cost of military action.
Conclusion
According to Just War Theory there is a strong case to be made for militarily engaging and erasing ISIS, with the one caveat being the lack of confidence in the current commander-in-chief. Of course, that is a crater-sized caveat.
Which brings us to our second criteria -- the will of the people. A majority of Americans currently believe President Obama has been a failure, but nine out of ten Americans also believes ISIS to be a serious threat. Therefore, since this has the makings of a just war, it is now up to President Obama to make his case for waging it to the American people should he choose to fight it.