So I am reading Hammer's German Grammar and it says:

Kosten and lehren are normally used with two accusatives:

Der Flug hat meinen Vater 5000 Euro gekostet

The flight cost my father 5000 euros

How are these two accusatives, I only see one accusative here and that is 5000 euros.

Meinen Vater seems like an indirect object to me because it answers the question: To whom did the flight cost 5000 euros?

Sie hat mich Deutsch gelehrt.

She taught me German.

Same thing here. To whom did she teach German? To me, so it should be mir right?

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    German does not have direct or indirect objects. We have acc verbs, acc+acc verbs, dat verbs, gen verbs, acc+gen verbs, intransitive verbs, etc. etc. And yes, you must learn them with the verbs, – Kilian Foth Jan 16 at 16:56

The concept of direct and indirect object doesn't really work in German. If you want to ask for accusative, the question is wen oder was.

Der Flug hat wen 5000 Euro gekostet? Meinen Vater.

Der Flug hat meinen Vater was gekostet? 5000 Euro.

Same for lehren:

Sie hat wen Deutsch gelehrt? Mich.

Sie hat mich was gelehrt? Deutsch.

Usually that doesn't really help, if you're not a native speaker. You just need to learn the right case for the verbs.

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    Actually it is easy to tell that meinen Vater is accusative because of the ending of meinen. In the case of 5000 Euro, it's not that obvious, but you see it if you replace it: Der Flug hat meinen Vater einen großen Betrag gekostet. – RHa Jan 16 at 18:00

The first sentence does not answer “To whom did the flight cost 5000 euros?”, that’s a question in a different language. It answers „Wen hat der Flug 5000 Euro gekostet?“ That kosten and lehren take two accusative objects is exceptional, that’s why the book mentions them. But it is like it is.

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  • That's right, but it is a bit circular, isn't it. Like "it is accusative... because it is accusative". - I don't blame you. Things in languages are often not to be explained logically (although many people keep asking "why") but rather "it's so, because it is". – Christian Geiselmann Jan 17 at 11:31
  • @ChristianGeiselmann, I don't disagree, but my point stands that it is indeed unusual that these verbs take two accusative objects, but they just do, and that's exactly why the grammar book mentions them. Although now that I think about it, at least for lehren the historical reason for it being mich and not mir may be that it is/was a causative. – Carsten S Jan 17 at 13:43

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