Kripke argued that it is not possible for there to be unicorns. For "unicorn" is a natural kind term. But there are many possible natural kinds of single-horned equines that match our unicorn stories, and there is no possible natural kind that has significantly more right to count as the kind unicorn. So none of them count, and no possible world contains unicorns.
But there is another approach, through vagueness and supervaluationism. Let's say that the term "unicorn" is vague. It can be precisified as a full description of any one of the possible natural kinds of single-horned equines that match our unicorn stories.
Now consider the sentence that Kripke is unwilling to assert but which seems intuitively correct:
- Possibly there is a unicorn.
- Definitely, possibly there is a unicorn.
- For every precification U of "unicorn", possibly there is a U.