I like PE's definition from answers.com. It contains a few elements not contained in the other one.
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Civil war exists when two or more opposing parties within a country resort to arms to settle a conflict or when a substantial portion of the population takes up arms against the legitimate government of a country. Within international law distinctions are drawn between minor conflicts like riots, where order is restored promptly, and full-scale insurrections finding opposing parties in political as well as military control over different areas. When an internal conflict reaches sufficient proportions that the interests of other countries are affected, outside states may recognize a state of insurgency. A recognition of insurgency, whether formal or de facto, indicates that the recognizing state regards the insurgents as proper contestants for legitimate power. Although the precise status of insurgents under international law is not well-defined, recognized insurgents traditionally gain the protection afforded soldiers under international rules of law pertaining to war. A state may also decide to recognize the contending group as a belligerent, a status that invokes more well-defined rights and responsibilities. Once recognized as a belligerent party, that party obtains the rights of a belligerent party in a public war, or war between opposing states. The belligerents stand on a par with the parent state in the conduct and settlement of the conflict. In addition, states recognizing the insurgents as belligerents must assume the duties of neutrality toward the conflict. See also U.S. Civil War; war.
Let's highlight a few:
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Within international law distinctions are drawn between minor conflicts like riots, where order is restored promptly, and full-scale insurrections finding opposing parties in political as well as military control over different areas.
Are the insurgents in political or military control of any part of Iraq? They were in Falluja and Sadr City, but not anymore, at least not openly.
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A recognition of insurgency, whether formal or de facto, indicates that the recognizing state regards the insurgents as proper contestants for legitimate power.
Does anyone recognize the insurgents as being a "proper contestant for legitimate power"? Does anyone think they have the moral or political agenda that can allow them to rule Iraq long-term?
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Although the precise status of insurgents under international law is not well-defined, recognized insurgents traditionally gain the protection afforded soldiers under international rules of law pertaining to war.
The United States, a party to this "civil war", has not recognized that this enemy deserves the protections afforded to soldiers under international law. This is a separate debate but the insurgents do not meet the minimum standards needed to be considered an army.
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Once recognized as a belligerent party, that party obtains the rights of a belligerent party in a public war, or war between opposing states. The belligerents stand on a par with the parent state in the conduct and settlement of the conflict. In addition, states recognizing the insurgents as belligerents must assume the duties of neutrality toward the conflict.
Again, no one has recognized the insurgents as a party which deserves the rights inherent to a state. I don't know of anyone who thinks of the insurgents in the same terms as the legally elected government of Iraq.
To be fair, Answers.com has a broader list of civil war and its list include at least a dozen conflicts currently going on in the world, including Iraq. Answers.com also has an article which is named
Iraqi Insurgency That article has a nice breakdown of the faction involved, their goals and methods employed.
I will state again that the terms "insurgency" and "civil war" are really facets of the same thing. It is the connotation that changes. An insurgency is by an illegitimate force which would be incapable of ruling and which has no claim to legitimacy. A civil war is between two more or less morally equivalent foes. I believe that what's going on in Iraq is closer to my definition of an insurgency rather than a civil war.