Another case, which Doug alludes to but does not go into in depth, applies in particular to actions-and-events™; there may be no fixed arity relations that can handle all the possible modifications to an action - Sebastian walking; Sebastian walking at 2am; Sebastian walking at 2am in Bologna, etc. ( Davidson - Action & Events)
Of course, this doesn't mean that there are no fixed arity relations whose arity > 2, and that eliminating naturally higher arity relations just because one can is always a good idea...
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