| > You seem to be missing the rather important point that chemical elements are a thing. I fundamentally disagree with this. Elements are a human-created categorization of atoms (granting that atoms are real) by atomic number. > Maybe author/title/year? No. For one, I’m sure you can find distinct books that share these values. Author/title/year is very much like atomic number: extremely useful and sufficient for very many practical purposes. But when dealing with books, sometimes we need more than author/title/year, and when dealing with atoms, sometimes we need more than atomic number. Atomic number is a natural key to the elements, because it's part of the definition of element. This is why natural keys don't exist in nature, but can exist for things we invent: because a key uniquely identifies any member of a set. A key makes every possible distinction. When we categorize things, we select some distinctions (such as the number of protons in an atom's nucleus) and throw away others (such as the number of neutrons.) The enumeration and definition of relevant distinctions is necessary for the existence of a key. We defined the elements, and as a result of how we defined them, they have a key. When we define a book table in a database, it has a key as a consequence of how it is defined. If we don't define the set ourselves, as our invention, it is impossible to anticipate all of the possible distinctions between members, so it is impossible to construct a key. |