More on the singular their.
Making the linguistic & logical case for it (from the same source):
The Language Instinct
Steven Pinker
(1994)
Chapter 12: The Language Mavens
Sometimes an alleged grammatical "error" is logical not only in the sense of "rational" but in the sense of respecting distinctions made by the formal logician. Consider this alleged barbarism, brought up by nearly every language maven:
Everyone returned to their seats.
Anyone who thinks a Yonex racquet has improved their game, raise your hand.
If anyone calls, tell them I can't come to the phone.
Someone dropped by but they didn't say what they wanted.
No one should have to sell their home to pay for medical care.
He's one of those guys who's always patting themself on the back. [an actual quote from Holden Caulfield in J. D. Salinger's Catcher in the Rye]
They explain: everyone means every one, a singular subject, which may not serve as the antecedent of a plural pronoun like them later in the sentence. "Everyone returned to his seat," they insist. "If anyone calls, tell him I can't come to the phone."
If you were the target of these lessons, at this point you might be getting a bit uncomfortable. Everyone returned to his seat makes it sound like Bruce Springsteen was discovered during intermission to be in the audience, and everyone rushed back and converged on his seat to await an autograph. If there is a good chance that a caller may be female, it is odd to ask one's roommate to tell him anything (even if you are not among the people who are concerned about"sexist language"). Such feelings of disquiet -- a red flag to any serious linguist -- are well founded in this case. The next time you get corrected for this sin, ask Mr. Smartypants how you should fix the following:
Mary saw everyone before John noticed them.
Now watch him squirm as he mulls over the downright unintelligible "improvement," Mary saw everyone before John noticed him.
The logical point that you, Holden Caulfield, and everyone but the language mavens intuitively grasp is that everyone and they are not an "antecedent" and a "pronoun" referring to the same person in the world, which would force them to agree in number. They are a "quantifier" and a "bound variable," a different logical relationship. Everyone returned to their seats means "For all X, X returned to X's seat." The "X" does not refer to any particular person or group of people; it is simply a placeholder that keeps track of the roles that
players play across different relationships. In this case, the X that comes back to a seat is the same X that owns the seat that X comes back to. The their there does not, in fact, have plural number, because it refers neither to one thing nor to many things; it does not refer at all. The same goes for the hypothetical caller: there may be one, there may be none, or the phone might ring off the hook with would-be suitors; all that matters is that every time there is a caller, if there is a caller, that caller, and not someone else, should be put off.
On logical grounds, then, variables are not the same thing as the more familiar "referential" pronouns that trigger number agreement (he meaning some particular guy, they meaning some particular bunch of guys). Some languages are considerate and offer their speakers different words for referential pronouns and for variables. But English is stingy: a referential pronoun must be drafted into service to lend its name when a speaker needs to use a variable. Since these are not real referential pronouns but only homonyms of them, there is no reason that the vernacular decision to borrow they, their, them for the task is any worse than the prescriptivists' recommendation of he, him, his. Indeed, they has the advantage of embracing both sexes and feeling right in a wider variety of sentences.
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