The purpose of the military is to achieve Victory...
Various folk have defined military victory as "Killing the enemy and breaking all his things!" Certainly, in earlier times it was kill (or enslave) the enemy and steal all his things. It was true at the time Troy fell. It was true at the time Germany surrendered at Versailles .
Has that changed? If so, the first question in any discussion of military philosophy must be, "What is Victory"?


WWII - the Finns fought on the side of the Germans, and were the only nation to do so that didn't end up under some form of occupation - given that their most likely occupier would have been the Soviet Union, they may well be able to justifiably argue that in the end, the were victorious.
Just as in the October War, both sides could claim a semblance of victory, though a muddled one, certainly. Sadat because in the end, he showed an Arab army could fight much better than expected, and he got much of what he wanted in the political maneuverings after the war, and the Israelis because they held on to their most strategic position - the Golan, smashed the Syrian Army in so doing, and still proved they could take a punch and come back with a devastating counter-punch.
We tend to define victory as an all-or-nothing, because among other things, historians, politicians and generals predecessors frame it that way, when the truth of the matter is rather more flexible.
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"Our will" is a politically-defined term, and as such is beyond the scope of the military. It changes in every different circumstance and may change radically during a war when circumstances change. (see: France vs. Germany in 1870, 1871, 1914, 1916, 1918, 1940, etc)
A limited war has limited objectives, and as such victory looks different than it does during an unlimited war.
Absent very vague definitions of this nature, there is no overarching principle which can define victory. Definitions of this type are created by concrete context. Abstractions are merely masturbation. (Comment this)
The truth is, the military does not win victories or define the word. They win and lose battles of various sizes and importance. In the end, it is the political process that determines the end of the war and its definition. Of note are the many wars that have ended, not because one or the other military force was depleted, destroyed or otherwise put in a position where they were unable to fight any more, but because the political structures of the opposing forces have come to an agreement on expectations or demands, whether they gained or lost.
In essence, the military is a tool of the state or organization. I believe that Clausewitz was correct in this estimation and gave it prominence in his introduction and first chapter.
We are largely programmed by history which puts much emphasis on "last battles" and such moments as Cornwall surrendering his sword, Gen. Lee surrendering at the courthouse (great paintings depicting both), surrender on the USS Missouri, etc and our opinions are informed by these moments and many more.
Thus, I believe, is the general populace's misunderstanding of the Global War on Terror, Iraq and, to some extent, Afghanistan. They expect a USS MIssouri moment when it will look more like the receding waters of the Missouri after a flood: muddy, ugly, damaged, landscape changed, but going out much quieter and with little media attention compared to the initial raging flood and destruction. (Comment this)