When translating "he thinks I bought three books, but I didn't buy anything", do we add a completion 了 for "bought"?

Question

When learning about when to use 了, we're typically given simple examples with clear-cut answers, such as the following:

我买了三本书。
I bought three books.
_{Expressing completion with "le"}

We are taught that the reason we add the 了 is for completion: 买 is complete in the above example. Then we get thrown into the real world, where we might want to say something like:

他以为我买了三本书，但是我什么都没买。
He thinks I bought three books, but I didn't buy anything.

We have a grammar vs. context battle: the (local) grammar implies we should add the 了 (as above in 我买了三本书), while the context destroys the logic used above (买 is not complete), which gives a contradiction.

Question: When translating "he thinks I bought three books, but I didn't buy anything", do we add a completion 了 for "bought"?

Answer 1

which gives a contradiction.

There is no contradiction. Everything described in "他以为 (he thought)" is hypothetical.

Similarly, everything described in [He said: "...." ] doesn't need to be in the same universe with the rest of the text.

• Nothing wrong with '他以为我买了三本书，但是我什么都没买。' (The fact -- 'you bought three books' is in his mind only)

• '我看着我买了三本书，但是我什么都没买。' would be contradicting (The two facts cannot be both true)

• '他叫我买了三本书，但是我什么都没买。' would also be contradicting. It has to be '他叫我买三本书，但是我什么都没买。' ('told you to buy' cannot be changed to 'told you to have bought')