I'm firmly in the first camp. Capitalizing "The" implies that it's a part of the title and should be said at all times, which would be awkward when addressing the Doctor in conversation. To give an alternate example, Batman is sometimes referred to as "the Batman", but it's only capitalized when it's the start of a sentence.
This one is kind of tough. The Doctor usually introduces themselves as the Doctor. "Hello, I am the Doctor." The name also describes a title and a job. In most common usage a title is capitalized if it is before a name but not after it. You wouldn't capitalize "the" unless you were counting it as a title before Doctor as a name.
Maybe take a peek at how official sources use it? Likely a mix based on situational use.
Edited by TuefelHundenIV on Dec 5th 2018 at 9:58:43 AM
Who watches the watchmen?What are actual grammatical rules on this, because I'm reasonably sure "the" is almost never capitalized in this sort of situation unless it's part of an actual title (like a work starting with The) or in a comedic sense when Spell My Name with a "The" comes into play
Edited by sgamer82 on Dec 20th 2018 at 6:34:08 AM
You pretty much have the common rule right there. I would argue the usage in the case of this character would be in what sort of context it is used.
Who watches the watchmen?
Apparently, there are two camps. The first holds that it should only be "The Doctor" (both words capitalized) at the beginning of a sentence, and in all other instances it should be "the Doctor".
The second is of the opinion "The Doctor", even though it is a title, is for all intents and purposes the character's name, and as such, both words should always be capitalized.
I was just wondering if a consensus can be reached.
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