IN THE arithmetic of death, the latest fight between Israel and Hamas has been an unequal contest: more than 350 Palestinians killed in Israeli air strikes in the first four days, many of them civilians, against four Israelis killed by Hamas's rockets. But does such one-sided bloodshed make Israel guilty of using “disproportionate force”, as argued by, among others, Amnesty International and Nicolas Sarkozy, the French president, just ending his six-month presidency of the European Union?

Proportionality is intimately bound up with notions of the just war, and has been enshrined in treaties regulating warfare's conduct since the Hague Convention of 1907. But familiar as it is, proportionality is a slippery idea. It has two different meanings in Western theory. On the grounds for going to war, jus ad bellum, the cause must be important enough to justify force; any good that will follow must outweigh the inevitable pain and destruction. In the conduct of war, jus in bello, any action must weigh the military gain against the likely harm to civilians.

Human-rights law has developed mostly in terms of jus in bello. The Geneva Conventions of 1949, dealing mainly with the protection of non-combatants in conflicts between states, were updated in 1977 to include more explicitly wars within states. Israel and the United States have not ratified the later protocols, though they do not really question the principle that armies must avoid “an attack which may be expected to cause incidental loss of civilian life, injury to civilians, damage to civilian objects, or a combination thereof, which would be excessive in relation to the concrete and direct military advantage anticipated”.

The arguments are over the nebulous facts of a particular incident. Did Israel do enough to avoid civilian deaths? Do Palestinian policemen count as combatants? For Israel, the use of overwhelming force is both legitimate and, given its desire to restore its “deterrent effect” towards its enemies, sometimes necessary. Israel says that intent is what matters: it says it tries to avoid civilian deaths, whereas Hamas deliberately seeks to kill Israeli civilians with its rockets, relatively ineffective as they may be. Hamas responds with two arguments: as the disproportionately weaker party, Palestinians must use the crude means at their disposal to free their lands from Israeli occupation; more controversially, it often says there are no Israeli civilians since most Israelis serve in the army.

Proportionality in jus ad bellum and jus in bello are hard to separate: indiscriminate killing will colour the view of whether a war is justified; and even proportionate actions in battle will be denounced if the war is deemed unjust. In the Israeli-Palestinian context, arguments about legality fast turn into ones about history. If the tit-for-tat starting point is Hamas's rocket attacks, then the Israelis have a right to defend themselves; if it is Israel's occupation of Palestine or the dispossession of Palestinians when Israel was born in 1948, then Palestinians can argue for a right to resist. Proportional or not, the killing of innocents will go on until the dispute is settled.