This is based on a Facebook post I had seen: would you say a door is “on” or “off” when it’s closed?
I’d say a door is on or off depending on whether it’s mounted on hinges.
I thought this thread was going to be about Airman_Doors.
Ditto. A door that is “on” or “off” is mounted on hinges or not. Unless it’s a removable hatch, but I wouldn’t consider that to be a door.
Doors that are mounted on hinges are “open,” “shut/closed,” or partially open or partially shut (aka “ajar”).
If the door is ajar, you can pull it to. Then it will be closed.
Now a light switch: when the switch is closed, the light will be on. Open the switch, and the light turns off.
I’d say it is on when closed.
It’s like asking about a 0 or 1 on a computer chip.
That’s when a door is not a door. 
I’d evaluate the door by function. The purpose of a door is to provide a way to walk through a wall. Therefore the door is on when it’s open and off when it’s closed.
Or equivalently, the “off” state is similar to if the device didn’t exist. If there weren’t a door, you’d have a wall, and so a closed door (which is like a wall) is off.
I take the opposite view. The purpose of a door is to allow a room to be closed off and made private. When the door is open, there might as well not be a door (i.e. just an open archway). When the door is closed, it is performing its function. Therefore a closed door is “on,” in the sense that it has been activated and is doing its door-y task.
A door is off when it’s closed. An open door is active - it’s sometimes moving, it’s in any number of positions and states of “open”. Closed is simply zero.
Another data point - in my house with 3 young boys, a closed door is inert. An open door is essentially a weapon and tool with which to attack or harm a sibling.
If a door is on, then it’s an automatic door and will open when you step on the right place, or interfere with a beam of light, or whatever they do on the Enterprise to make it go whoosh. So if a door can be opened then it’s on, if it can’t then it’s off.
If it’s not an automatic door then as @Jackmannii said, on means it’s mounted on hinges or otherwise attached to a wall. There is no accepted meaning for a door being ‘on’ or ‘off’ in the language I speak. Remember that ‘door’ may refer to any opening, physical or figurative, and not just the thing that may or may not block that opening.
The door is neither on, nor off, until it is observed. Until then both possiblities exist. Especially if you have kids.
Or to put it colloquially, the door may be both on and off, or even more confusingly, half on and half off.
Given that there isn’t even consensus in this thread as to whether a closed door would be considered “off” or “on,” I think that the terms “on” and “off” are meaningless (or at least, highly ambiguous) for door operation, save for the state of an automatic door (i.e., is it functional or not), as already noted.
No, I wouldn’t.
Well, yes, that’s the point of the question, I think. I wouldn’t use the word “meaningless,” I’d say the correspondence of the binary open/closed to the binary on/off is undefined because there is, as you say, no consensus. So it’s interesting to ask the question and look into one’s own brain to see how one interprets the “door system,” so to speak, and then compare how other people’s brains respond to the same prompt.
I agree that it’s unanswerable, but I have enjoyed thinking about it and reading other explanations.
Yes exactly. It’s a thought experiment and prompt for discussion not a question with an empirical answer. FWIW my gut says an open door is “on” and closed is “off” because an open door makes changes in the system easier and a closed one makes them harder.
Then why did the thread title include the word “important” ?
To quote Spock: A Joke is a story with a humourous climax.
The way I see it, there are two separate elements here - the doorway and the door. The purpose of the doorway is to allow passage; the purpose of the door is to block passage. So if the door is open, then the doorway is “on” and the door is “off”; conversely, if the door is closed, then the doorway is “off” and the door is “on”.