I was reading the Monty Hall problem to discuss it with a friend.
The problem is defined as:
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
And a whole documentation about this problem is available (for instance) here:
Wikipedia: Monty Hall problem
When discussing it with my friend, the sentence "You pick a door, and the host opens another door" caused a conflict between us because my friend (who speaks English and is in the US) told me that this means that the host opens the initial door and another one since, the action consists in "opening another" which means it applies to the initial and another one.
My understanding of this sentence is " what is opened ?" -> another door. How is defined "another door" -> it is a door different than the initial one. So what is opened ? a door different than the first one.
Thus my understanding is that after I chose a door, the host opens a single one, that is different than mine (thus the second or third in the problem situation).
My friend tells me that my reasoning is incorrect because is not how English works (and she tells me she knows this better since I am not a native English speaker). However since, I know this logical problem pretty well, I was quite confident with my understanding and look for a strong grammatical/syntaxic/semantic/linguistic/morphologic/etc… arguments/proof that could provide a definitive understanding of this and that I could share with my friend and definitively convince them.
Best Answer
It is ambiguous.
The offer is of the following form:
What happens to the one you picked is unspecified. It is left to the context to supply the missing information.
Consider a host saying to his guest:
There is a strong expectation that the host will get the drink the guest picked (as well as another drink for himself). It would be odd for the host to return with a single serve of a drink the guest didn’t pick. Another situation with similar semantics is at sales: “You choose any product and I’ll give you another.”
Now consider two friends choosing costumes for a ball.
Now there is a strong expectation that the speaker is not going to wear the friend’s costume as well as her own.
Why does the speaker ‘do’ the verb with the picker’s choice in one case and not in the other? It’s because the context dictates different expectations in each case.
For games such as the one you describe, the context is not defined by broader social customs. If the organisers wanted to, they could change the rules so that they open both boxes - the one the contestant picked, plus another one. That would change the game, but they could still legitimately say, “You pick one and I’ll open another.”
This reliance on unspoken context makes the offer ambiguous when one is not familiar with the context.