 Some philosophers, most prominently Kit Fine (1994), have found these results disturbing. Fine thinks that the notion of an essential property of a thing should be bound up with the notion of the thing’s nature or what it is to be that thing, but, Fine thinks, being such that there are infinitely many primes intuitively has nothing to do with what it is to be Socrates. And although it seems that having the number 2 as its sole member is part of what it is to be the unit set \(\{2\}\), it does not seem that being this unit set’s sole member is part of what it is to be the number 2. It is Fine’s view that these sorts of properties are counterexamples to the modal  characterization.[2][3]  To replace the modal characterization, Fine offers a definitional characterization of essential properties, according to which the essential properties of an object are those of its properties that are part of the object’s “definition”. What exactly is a “definition” of an object? This is a difficult question. At first sight, it seems to be a category mistake: it is words and perhaps concepts—but not objects—that have definitions. Even so, it must be admitted that some objects—such as the number 2 and the unit set \(\{2\}\)—do seem to be definable: it is plausible to think that the number 2 is defined as being the successor of the number 1; and it is plausible to think that the unit set \(\{2\}\) is defined as being the set whose sole member is the number 2. But other objects—such as Socrates—do not seem to admit so readily of definition. So even if the notion is understood well enough for some objects (never mind that not everyone would allow that the number 2, for example, is an object), a major challenge for the advocate of the definitional characterization is to provide a respectable general understanding of the notion of a definition for an object.