The Parshiot of Sefer Devarim contain entire chapters on military theory. One of them is in our parsha (Devarim 20:19): When you lay siege to a city many days to fight against it and conquer it…build a siege against the city which fights against you, until it falls." From this verse, the sage Shammai made a special interpretation regarding wars on Shabbat (Talmud Shabbat 19a): "The Rabbis said: "A siege shouldn't be laid against cities of gentiles less than three days before Shabbat. But if (the Jewish army already) started, they shouldn't stop. And regarding this, Shammai said: 'until it falls' – even on Shabbat."
Why do we require Shammai's interpretation of "until it falls"? Presumably, we go to war in order to save lives, and we already know that pikuach nefesh (saving lives from danger) overrides Shabbat and all the other mitzvot of the Torah (except idol worship, adultery and murder). So why do we need an additional interpretation? Some halachic authorities have said that this interpretation of "until it falls" is an extension of the law of pikuach nefesh in war situations. Other rabbis hold that this is a unique halachic definition, which stems from the strategic nature of war. It appears that this disagreement stems from the underlying understanding of Israel's wars at the strategic level. We need to ask whether there is a difference, at the strategic level, between war in the context of a state under sovereign rule (in those days a king and today an elected government) as compared to a situation of danger to an individual or a community. Indeed the strategic nature of war conducted by a state isn't only "saving lives" of one citizen or all of the citizens. Its purpose is to be a tool in the hand of the state to achieve a range of strategic ends, and national goals that could not be achieved by peaceful means or by diplomacy. Sometimes the strategic goal of war is indeed saving lives of the citizen and the public, but even this is only part of the safeguarding the state's "sovereignty." Since in a sovereign state the citizens can live normal lives without fear, then it follows that any threat to its citizens that disrupts their lives is an attack on its sovereignty. Additionally, a sovereign state has goals which explicitly are not "saving lives"; to the contrary, in the process of waging war in order to attain them, the state endangers the lives of its soldiers. (On condition that the danger is reasonable and calculated, according to the value of the goal.) We see this in the Torah regarding "the mitzvah of inheriting the land" (Ramban, positive command 4), which involves a war to conquer the land and its settlement, despite the danger to the lives of soldiers, and despite the possibility that we could suffice with less land. And there is also "milchemet reshut" (discretionary war) whose purpose is, among other things, achieving economic goals, and creating a long-term deterrent, despite the danger to the soldiers. In our beit midrash we say that in most war situations, the circumstance is not "pikuach nefesh" but "messirut nefesh (self-sacrifice)!"
The opinion that "until it falls" is only an extension of pikuach nefesh doesn't differentiate between the war of a state and danger to an individual or a community, and sees the state as a "large community." And according to the opinion that sees war as a unique halachic sphere, the war of a sovereign state whose purpose is to safeguard its national interests is a different field entirely.
This disagreement has broad and significant implications in the national and political spheres, and it is a cornerstone of the Torah-based outlook on the State of Israel (as demonstrated by the dispute between the Haredi world and the religious-Zionist world) and the understanding of the abstract strategic concept of the enforcement of sovereignty as the embodiment of the ownership and possession of the nation and its state. There are additional halachic implications, the first of which involves Shabbat and holidays – what is allowed and what is forbidden during wartime. That is: is a military action regarded salvation from danger, or must we discern the "goal" of the required operation, and whether it is necessary at this moment in order to achieve the goal. (See "Sefer Harel" where this is elaborated upon, and it is emphasized that Shabbat isn't "nullified.") Especially since in many security operations, there is no "dangerously ill person before you" which is the only justification to break the Shabbat in a "pikuach nefesh" scenario. In other words, the purpose of many missions is to pre-empt threats before they actually endanger someone.
HaRav Shlomo Goren ztz"l (the first Chief Rabbi of the IDF and afterwards the Chief Rabbi of Israel) adhered to the second approach in his halachic rulings, with the establishment of the IDF and in General Orders for Shabbat – that the term pikuach nefesh isn't mentioned in them, but rather operational "necessity". The Chief Rabbis of Israel, HaRav Hertzog and HaRav Unterman also followed this approach.
The second halachic area where this dispute has implications regards the endangerment of life, when the individual must endanger himself in order to accomplish a mission and in order to save another's life. When the definition is strictly that of that of saving the life - of an individual or even many people - there is a big question as to whether one has to risk his life in order to save others, and the halachic ruling is that one isn't obliged to. Especially when the mission is to achieve strategic goals which are not saving lives in a direct way. And there are also implications regarding settling the land in a place where danger exists, and the issue of "returning territories." Therefore we must continue to study this issue thoroughly and in depth.