Would you mind if I opened the window?

May I ask why should the past tense "opened" be used in the above sentence?

Can't I use "open" instead? Why?

I'll be glad if you could tell me the reason, thank you very much!
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Your sentence is type 2 conditional sentence. Hence the if-clause is in the past tense and the main verb is in the 'conditional' tense. However, the past tense in this is not a real past tense, it is a subjunctive. Therefore, this refers to present or future time. If you use 'open', the verb in the main clause is in the future simple eg. 'Will you mind if I open the window?'
The past tense is used for more than just indicating past time. It's used in an if-clause that goes with a would-clause. This is the general rule.

That said, the formulas Would you mind if I ...? Would it bother you if I ... ? and similar expressions are special cases where, informally, the present tense often follows.
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It's just the grammatically correct way of asking, "May I open the window?" or "Do I have your permission to open the window?"
Thank you very much! I understand now.
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Can you stop writing everything in capital letters? Emotion: smile

I'm assuming you mean within the context of "Would you mind ...?"

... if I smoked ... is more polite. It seems to indicate that you are considering the possibility of smoking, but could be dissuaded if there is an objection.

... if I smoke ... seems to indicate that you are more intent on smoking. It gives the slight impression that you don't expect any objections to the idea.

It's a real conditional question, this is why we use the past form of the verb in this senctence.
AnonymousIt's a real conditional question, this is why we use the past form of the verb in this senctence.
Can someone confirm if this is correct?
I thought that "if I smoked/smoke" was a clause complement to the verb "mind" in "Would you mind if I smoke/smoked?".
Am I wrong and is this really a conditional??
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