7.19 wollen
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In the subjunctive II, sollen expresses a possible obligation ( ‘should’, ‘ought to’): Das hätten Sie mir gestern sagen sollen. You ought to have told me that yesterday. Warum sollte sie nicht ins Kino gehen? Why shouldn’t she go to the cinema? Das sollte ihm inzwischen klar geworden sein. He ought to have realized that by now.
7.19 wollen wollen most often expresses a desire ( ‘want/wish to’): Sie will ihn um Geld bitten. Sie wollte ihn um Geld bitten. Hättest du wirklich kommen wollen?
She wants to ask him for money. She wanted to ask him for money. Would you really have wanted to come?
In this sense it can be used without a following infinitive, as a main verb: Sie will Geld. Was wollen Sie von mir?
She wants money. What do you want from me?
wollen can express intention. In this sense it is close in meaning to the English future construction with ‘be going to’: Wie wollen Sie ihm das klarmachen? Ich will sie erst morgen anrufen. Ich wollte Sie danach fragen.
How are you going to explain that to him? I don’t intend to phone her till tomorrow. I was going to ask you about that.
With an inanimate subject, wollen corresponds to English ‘need’ (or, when negative, ‘refuse’): Eine solche Arbeit will Zeit haben. Das will geübt sein. Das Fenster wollte nicht zugehen.
A piece of work like that needs time. That needs to be practised. The window refused to shut.
wollen can be used in the sense of ‘claim’, typically in the present tense with a perfect infinitive: Sie wollen dich in Hamburg gesehen haben. Er will krank gewesen sein.
They say they saw you in Hamburg. He claims to have been ill.