～ないでいる verb ending

Question

This is dialogue from a book I have, where a doctor is talking about a patient:

気分が極端に変りやすくなっていて、自分で自分をコントロールできない。神を呪うかと思うと、神に祈る。呪う自分と祈る自分と、絶えず入れ替っていて、どっちが本当の自分か判断できないでいる。

My question is about the way the final verb is conjugated. I am familiar with the ている form for verbs that are not negated, like 「できている」, and I've also seen cases where でいる seems to be used similar to the copula である, for example 「好きでいる」.

In this sentence, is できないでいる just simply できない in the ている form (using できないで rather than できなくて)? Is there any connection with things such as 好きでいる, or is that different?

Answer 1

This usage of いる is unrelated to its usual function as a grammar element.

〜ている

食事を食べている
"I am eating my meal" (progressive)
"I eat meals" (habitual)
?? "I eat my meal and I am here (/I exist)" (conjunction)

Reading #3 is never used because no one would ever need to say that. I included it only to show that the て-form does normally perform a conjunction function, it's just very marginal here.

〜ていない

食事を食べていない
"I am not eating my meal" (progressive)
"I do not eat meals" (habitual)
?? "I eat my meal and I am not here (/I don't exist)" (conjunction)

Again, reading #3 is a terrible way to read this sentence and is essentially wrong.

〜なくている

食事を食べなくている
?? "I do not eat my meal and I am here (/I exist)" (conjunction)

This form is never used because there's never a need to say this.

〜ないでいる

食事を食べないでいる
"I am here (/I exist) without eating my meal." (state adjunct)
"I am here (/I exist) by not eating my meal." (instrumental adjunct)

Reading #1 is Lit. "I am here, in the state of not eating my meal." (It's reminiscent of the stative function 〜ている often performs, but it's slightly different — here, いる is actually still a full-fledged verb and you can't drop the "exist" meaning.)

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In the case of your sentence, context suggests that it's a state adjunct, not an instrumental adjunct; another way to write this form is できずにいる.

Answer 2

A concise answer as per OP's request.

xxx でいる = "to stay xxx", "to stay in the xxx situation", etc.

The xxx part can be a whole mini-sentence as in OP's example, a noun, a 形容動詞 (as I dislike the word "na-adjective"), etc. 　

どっちが本当の自分か判断できないでいる = I have remained unable to judge which one is the real me.

Finally, this form has very little to do with "Verb + ている".