If you spend time with officers in the U.S. military, fewer than you might expect have been assigned Clausewitz in their professional military education or read it on their own (even just the first chapter). Many just know the soundbite, "war is an extension of politics with other means."
> if there is no political goal, there will be no war
In Clausewitz, this is more of a normative statement than a rule about war in reality. One of the things he's trying to caution against is the escalatory dynamic that he views as inherent to purely military logic – that war (in a vacuum, so to speak) will always increase in intensity. But in reality, certain factors can and should ameliorate this inexorable escalation – political goals, "friction," and the "fog of war" are examples. War without the control of a political goal will be ceaselessly increasing destruction to the point of purposelessness. This is one reason why we insist on civilian control of the military, because we do not wish for an independent general staff to be prosecuting a war according solely to war's inner logic.
> if there is no political goal, there will be no war
In Clausewitz, this is more of a normative statement than a rule about war in reality. One of the things he's trying to caution against is the escalatory dynamic that he views as inherent to purely military logic – that war (in a vacuum, so to speak) will always increase in intensity. But in reality, certain factors can and should ameliorate this inexorable escalation – political goals, "friction," and the "fog of war" are examples. War without the control of a political goal will be ceaselessly increasing destruction to the point of purposelessness. This is one reason why we insist on civilian control of the military, because we do not wish for an independent general staff to be prosecuting a war according solely to war's inner logic.