This criterion seems to give reasonable results for true existential sentences. Thus, ‘∃x Elephant(x)’ is committed to (“presupposes”) elephants because the open sentence ‘Elephant(x)’ applies to all and only elephants, and there are some. It is likewise committed to any kind that contains all the elephants: to mammals, to animals, to living things. (It has these commitments whether or not these kinds are expressible in the object language.) And it is not committed to any kind that leaves out any elephants, such as male elephant. The kind elephant is the smallest kind to which ‘∃x Elephant(x)’ is committed. So far, so good.