 The distinction between accidental and essential properties is, at least on the most basic version of each account, both exclusive and exhaustive. (On some more refined versions of these accounts, the distinction remains exclusive, but not exhaustive. Exhaustiveness is lost when certain properties—like the property of being such that there are infinitely many primes—are not counted as properties to which the essential/accidental distinction applies. See the discussion of Della Rocca (1996a) in §3.) In addition, it seems that the root of each of the characterizations goes back at least to the work of Aristotle. (For the modal characterization, see Topics 102b5ff; for the definitional, see Metaphysics 1031a12; and for the explanatory, see Posterior Analytics 74b5ff. For more on the notion of essence in Aristotle’s work, see the entry on  Aristotle’s Metaphysics.)  It is not clear whether these three characterizations should properly be thought of as competing characterizations of a single notion or instead as ways of trying to capture three related, but different, and equally legitimate, notions. (A similar point has been made by Livingstone-Banks (2017) and Cowling(2013).) Since the modal characterization has been so common, and since the distinction between essential and accidental properties, which is the topic of this entry, is almost always understood modally, it will dominate the remainder of this entry.