Philo, hi! Thanks for your comments. The problem is that I do not detect any condition in your "conditional" sentence. Consequently, as a non-native, non-educated no-body, I cannot accept your argument as true.
Well, if you'll forgive the double negative, you're certainly not a 'nobody' in this forum, Svartnik! Indeed, you demonstrate at times a level of analytical ability that frankly surpasses that of some of the native contributors. I can therefore only conclude that, as regards this particular issue, you have something of a 'blind spot', or perhaps have simply been misled by a diabolical entry in a dictionary whose editor ought to have known better (and who I would humbly recommend be taken outside and shot at dawn for letting it through!)
Given your normally sharp eye for grammatical structure and pattern, I must confess to genuine puzzlement at your contention that you "do not detect any condition" in the sentence at issue. To my mind, it is so screamingly obvious that I am almost at a loss where to start explaining it. But, I'll have a try, anyhow:
Take any sentence of the type
[[S1+would V][+if+S2+Ved]]
in which 'if' cannot be supplanted by 'whether' (i.e. where it introduces an adverbial clause), then you have perforce a
conditional sentence, of the type most commonly labelled a
second conditional, wherein the VP of the subordinate denotes, according to verb type, an event or state considered by the speaker to be anything ranging from relatively improbable to downright counterfactual.
Examples:
[1]
I would be angry if my wife bought a diamond ring.
(i.e. in reality she does not buy diamond rings, or, at least, would be most unlikely to buy one.)
[2]
Would you be angry if your wife bought a diamond ring?
[3]
I would mind very much if my wife bought a diamond ring.
[4]
Would you mind if your wife bought a diamond ring?
[5]
Would you mind if I bought a diamond ring?
As I trust you can now see, the sentence at issue,
[6]
Would you mind if I opened the window?
is structurally identical, in every conceivable respect, to [5] above and that, needless to say (perhaps, but I'll say it anyway!),
[6a]
*Would you mind if I open the window?
would be every bit as ungrammatical, and for precisely the same reason, as
[1a]
*I would be angry if my wife buys a diamond ring.
[2a]
*Would you be angry if your wife buys a diamond ring?
[3a]
*I would mind very much if my wife buys a diamond ring.
[4a]
*Would you mind if your wife buys a diamond ring?
[5a]
*Would you mind if I buy a diamond ring?
What, I suspect, may be causing you some confusion here is the
illocutionary function of [6]. We happen, in this case, to be employing a second conditional sentence in order to make a kind of request, disguising that request in a hypothetical form that is more socially acceptable than a direct request for permission: it seeks to maintain a kind of "polite fiction" that the act of my opening the window is so highly improbable that any question as to my collocutor's potential view of/reaction to it amounts to little more than academic speculation. Yes, it is semantically equivalent (or rather, to be precise,
functionally equivalent) to more direct, simple
May I open the window?
but I am sure that I hardly need point out to you of all people that most fundamental of linguistic axioms that mere similarity of meaning neither implies nor confers identity of construction. If we were to be foolish enough to reason along those lines, we would be forced to conclude that, for instance,
*May I to open the window?
must be acceptable, since it means exactly the same as
Would it be OK for me to open the window?
!
I hope that these few notes may serve to make things a little clearer.
