Gaza Rockets, Eubulides, and the Sorites Paradox

How many grains constitute “a heap”? And how many rockets are "a few" beyond which there are "many"?

Daniel Pinner,

Daniel Pinner
Daniel Pinner
INN:DP

Some 2,500 years ago, the Greek philosopher Eubulides, a disciple of the Socratic philosopher Euclid of Megara (not to be confused with the mathematician Euclid of Alexandria, the father of geometry), posited a paradox.

He poured grains of wheat onto a table, and his students agreed that these grains constituted a heap (in Greek sorites, hence the name of the paradox). He removed one grain, and his students agreed that this was still a heap. He removed another grain – still a heap of grains. He continued removing these grains, one at a time, until at some point his students claimed that was remained was no longer a heap, rather just a few scattered grains.

He counted the grains, and found that, say, 13 grains remained (a random number, chosen just for the purpose of demonstrating the sorites paradox). In this case, he challenged his students, you have defined “a heap” as consisting of 14 grains or more, whereas 13 or fewer are just a few scattered grains.

But this number, or any other number they may have chosen, is obviously purely arbitrary: there is no specific number at which individual grains become “a heap”.

Counting upwards instead of downwards, Eubulides put down a single grain of wheat. Obviously, his students agreed, that is not “a heap”. Two grains – still not. Three grains, four, five, six – again, at some point his students defined these grains as “a heap”.

And again, the cut-off point, the number at which scattered grains become “a heap”, is entirely arbitrary.

And so, Eubulides challenged his students – does “a heap” exist at all?

Just over two weeks ago, on Monday 8th June, Israel opened the Kerem Shalom and Erez crossings to Gaza, which Defence Minister Moshe Ya’alon had ordered to be closed on the previous Saturday night, following a rocket attack a few hours earlier.

That followed an attack the previous Wednesday, in which two rockets were fired from Gaza to the Sdot Negev region, which in turn followed an attack the previous day in which a Grad rocket fired from Gaza exploded near Gan Yavneh.

Explaining the rationale for opening the Kerem Shalom and Erez crossings, Major General Sami Turjeman, OC Southern Command, said on Sunday night (7th June) that it is impossible to go to another war in Gaza just because of a few rockets that one rebellious organisation fired.

The sorites paradox inspires us to ask: If it is impossible to go to another war in Gaza “just because a few rockets” (in this case, four rockets in the space of 12 days), then is it possible to go to war because of, say, nine rockets in one week? Or four rockets in three days? Or three rockets every two days, with a break for weekends?

How many grains exactly are needed to constitute “a heap”? How many rockets are “a few”, beyond which they are “many”? And how many rockets exactly in what length of time exactly constitute a legitimate casus belli?

Every legal system, by its very nature, has to establish limits which will inevitably be somewhat arbitrary: minimum voting age, age of consent, maximum speed limit, duty-free import limit, maximum gestational age at which a foetus can be aborted – examples abound.


What, then, should Israel define as the acceptable limit of missiles fired into our cities?
Does anyone claim that, for example, a 17-years-and-364-days-old citizen is not sufficiently mature to decide who should govern the country, whereas an 18-year old citizen is? Does that one day really make a difference? Or that 50 km/h is a safe driving speed, whereas 51 km/h is unsafe?

Of course not. However, having established a law and decided on an admittedly arbitrary limit, society then recognises that limit as binding.

What, then, should Israel define as the acceptable limit of missiles fired into our cities? More appositely, what limit do Major General Turjeman and the Israeli Government define as the acceptable limit, below which it is impossible to go to another war and above which war becomes justified?

Or should the acceptable limit be defined in terms of citizens killed and injured, instead of number of missiles fired? Say, for up to 3 killed and 5 injured in two weeks it is impossible to go to war, but anything beyond that is a reason for war?

Yesterday (Tuesday) night, another rocket fired from Gaza landed and exploded in the Hof Ashkelon region. Did that rocket make the difference between the acceptable “few rockets” and an unacceptable “many rockets”?

How many grains constitute “a heap”? And how many rockets constitute “a barrage”?

Clearly, any limit at all is as arbitrary as Eubulides’ definition of “a heap”. And so, since any limit is arbitrary, no limit is necessary. Thus, Major General Turjeman to the contrary, it is eminently possible to go to another war in Gaza just because of “a few rockets that one rebellious organisation fired”.








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