Singular they

Singular they was a set of personal pronouns widely used to refer to a single individual. (AUDIO: The Eternal Summer, Mindbomb, Disassembled, My Dinner with Andrew, How to Make a Killing in Time Travel, World of Damnation, Enemy Lines, Celestial Intervention, Havoc, The Power of River Song, ScrapeJane, Serenity, The Famished Lands, Conversion; TV: The Lie of the Land, The Haunting of Villa Diodati) It included the pronouns "they", "them" and "themselves". (AUDIO: Enemy Lines)

Singular they was, in some cases, the only correct set of pronouns to apply to someone, on account of the referent's gender, (AUDIO: Orr, Superiority Complex, Poker Face, The Web of Time, "Flight of the Blackstar", The Poison of Peladon, etc.) and in others, an expedient and open-ended alternative to constructions such as "he or she", (AUDIO: Appropriation, Subterfuge) encompassing any number of unknowns, (AUDIO: Enemy Lines) avoiding presumptions, (AUDIO: Crush) and allowing for ambiguity. (AUDIO: Mindbomb)

As gender-neutral pronoun
On consulting its styleguide, the sentient Encyclopedia Gallifreya decided that "they"/"them" pronouns were the correct terms to apply to the Doctor, thought of generally, once they had regenerated into a new female form. It had briefly considered changing each "he" to "she" in every entry, to reflect the Doctor's latest identity. Rather than revise all past entries to reflect each of the Doctor's new forms, however, it chose to employ each incarnation's respective pronouns when referring to them specifically, and continued forward with gender-neutral language in all other cases. The encyclopaedia had already been employing they/them pronouns for the Master during the Twelfth Doctor's time. (PROSE: Citation Needed)

Indeed, those who knew the Doctor well, like Jack Harkness, (AUDIO: Piece of Mind, Mighty and Despair) the War Master, (AUDIO: He Who Wins, Masterful), (AUDIO: Masterful) the Lumiat (AUDIO: The Lumiat) Kate Stewart, (GAME: Reverse the Polarity) and River Song, would sometimes employ they/them pronouns to refer to the Doctor generally, (AUDIO: The Power of River Song, Concealed Weapon, He Who Wins) or when unsure of incarnation. (AUDIO: Concealed Weapon) Clive Finch, who had studied evidence surrounding the Doctor's many incarnations all his life, used they/them pronouns to refer to his hero. He described always wanting to meet them. (PROSE: Rose)

When speaking of a hypothetical Time Lord, Braxiatel offered up "he, she or they" to cover all options. (AUDIO: Beyond) Without much further information, the Eighth Doctor used they/them pronouns to refer to the Time Lord most recently known as the Eleven, on finding out that they had regenerated into the Twelve. (AUDIO: Dreadshade)

Beyond the Time Lords, Orr, a psychomorph with no fixed gender, used they/them personal pronouns, (AUDIO: Orr, etc.) as did Mx Neon, a transtemporal museum curator, (AUDIO: The Web of Time) and Calypso Jonze, (AUDIO: "Flight of the Blackstar") a 51st century human bounty hunter who was non-binary. (AUDIO: The Lovecraft Invasion)

The Ashtallans, who had never so much as encountered gender, used they/them pronouns to refer to one another. (AUDIO: The Invention of Death)

Alpha Centauri, an Alpha Centauran, also used singular they pronouns. River Song corrected others when they mistakenly used she/her.

When asked for her own pronouns, River Song explained to Alpha Centauri that whether she used "he, she or they" depended on who she was with. (AUDIO: The Poison of Peladon)

A pronoun with broad applicability
It was frequently the case that singular they was employed to refer to an unidentified person — a specific "someone" — (AUDIO: X and the Daleks, Lost Property, The Lovecraft Invasion, Gallifrey) like an individual or being who had been seen, (AUDIO: Renaissance, Divine Intervention, PROSE: Rose) heard (AUDIO: Sphere of Influence) or even smelled (AUDIO: Mighty and Despair) by the speaker but whose identity remained unknown, or one whose existence was presupposed only by the fruits of their actions, as with the unknown perpetrator of a crime. (AUDIO: Enemy Lines, Subterfuge) It was, for example, useful to refer to "one of the subjects" in particular, from a large sample, and as of yet unidentified, with singular they. (AUDIO: The Unzal Incursion)

As a placeholder for the unidentified person, the use of singular they was sometimes abandoned when new information came in. For example, the Eighth Doctor readily switched from "they" to "he" when a recent visitor to Srangor was described as a "troubled man", finding a more useful placeholder for the mysterious gentleman who'd arrived in a TARDIS. (AUDIO: Tangled Web)

However, they/them pronouns were also used in cases where other, gendered pronouns for whomever was being referenced were already made clear. (AUDIO: Sync) For instance, those who sought to withhold knowledge of the identity of an unknown intruder might employ such language to maintain ambiguity, and as a pretence, to obscure their own involvement until the truth came out. (AUDIO: The Famished Lands)

In this way, they/them pronouns could be used by speakers who wished to keep the other's identity a secret (AUDIO: The True Saviour of the Universe) or intentionally vague. (TV: The Haunting of Villa Diodati) Some speakers made pointed implications with singular they, just shy of explicitly stating who was being referenced. (AUDIO: Emancipation) In some cases, the person was known to the addressee of the sentence, but not to the speaker. (AUDIO: The Lamentation Cipher)

Even when both individuals in a conversation knew well to whom they were referring, as with Annos and Narvin privately discussing "instructions" received by Annos from someone they both understood to be Darkel, (AUDIO: Mindbomb) singular they could be used to intentionally create ambiguity in their statements. (AUDIO: ScrapeJane, Emancipation) After Narvin made clear that he would not have to reveal who this was, Annos noted, of the "person responsible" for the suggestion in question, "their judgment might be clouded by [a recent injury] and the direct threat to their person" therein. (AUDIO: Mindbomb)

They/them was also used to make a general or hypothetical statement involving a posited individual who only served as a placeholder. (COMIC: Hidden Human History, AUDIO: The Famished Lands) For example, when Ian Chesterton explained to Sharlan that "love is when you are close to someone", he continued with singular they pronouns: "when you want to spend all your time with them, when you care about them very much." (AUDIO: The Invention of Death)

Singular they was also useful when attaching rights or actions to any individual in a certain role, or under specific circumstances. For instance, citing the Gallifreyan constitution, Narvin stated that Romana II, while imprisoned for high treason, could not be denied visitation from "her legal counsel and their assistant". In the particular, this applied to K9 Mark I and Leela, K9's "assistant". (AUDIO: Mindbomb)

On Earth
On Earth, singular they was in use, and commonly understood without confusion, at least as far back as the 19th century, both among the English (AUDIO: A Photograph to Remember, Brimstone and Terror, Save Our Souls; TV: The Haunting of Villa Diodati) and, across the Atlantic, among Americans. (AUDIO: The Coney Island Chameleon)

In 1945, when Alicia Dowan challenged Winston Churchill's assumption that an unidentified traitorous double agent must be a "he", Churchill repeated her correction — "he, or she" — before switching to they/them as he continued. (AUDIO: Subterfuge)

Constance Clarke and the Sixth Doctor took very little time, if any, after first meeting Calypso Jonze, to begin using their correct pronouns. They respected Calypso by using they/them in private conversation, not only in their presence. (AUDIO: "Flight of the Blackstar") Mrs Clarke needed prompting at first not to call Calypso "Ms Jones", but by the end of their first adventure committed to remembering it was "just Jonze". (AUDIO: The Lovecraft Invasion) Calypso was happy that she remembered this when they next met. (AUDIO: "Flight of the Blackstar")

In the early 21st century, some of Orr's colleagues at Torchwood Three took time to get used to singular they pronouns, which were new to them. Though they stumbled over Orr's unfamiliar pronouns, they soon got used to this gender-neutral language. (AUDIO: Orr, Superiority Complex) Yvonne Hartman, in part due to her personal relations skills, had no such qualms, and consistently used they/them for Orr before even first meeting them, having read the files. (AUDIO: Poker Face)

Behind the scenes
No pronouns are used on-screen for En Sentac or K-Toscs, but the script for The Halloween Apocalypse used singular they for En Sentac and he/him pronouns for K-Toscs.