Hi. Can we replace “to let” with “letting”?
He cannot be a good father letting her go out alone in the dark.
Yes, we can, Guinevere. In fact, the sentence sounds even better with ‘letting’, I’d say.
Hi Conchita and Guinevere,
I am really interested in the example and I just wonder if there were any slight difference between ‘to let’ and ‘letting’ to be applied in the sentence.
Could it be possible that: “He cannot be a good father to let her go out alone in the dark.” suggests “He cannot do such a thing, as a good father, to let her go out alone in the dark.” while “He cannot be a good father letting her go out alone in the dark” implies “Letting her go out alone in the dark, he cannot be seen as a good father”.
But I am not sure. May I have any or any other ideas on this?
Thank you!
Haihao
Well, I am not a native English speaker, but, as you asked for others’ ideas, I think I should share mine 
He cannot be a good father to let her go out alone in the dark -> She wants to go but he is not a good father and he does not let her go.
He cannot be a good father letting her go out alone in the dark -> He lets her go but if he were a good father, he wouldn’t let her go.
Hi folks
If my common sense works duly, it is the same case as this. Please see:
Expression: “…come to help celebrate…”
…and much more detailed discussion here:
englishforums.com/English/Ex … c/Post.htm
Tom
Hi Guinevere
I agree with Conchita that both are possible, and I also like ‘letting’ better.
The use of ‘letting’ would suggest more strongly to me that possibly ‘he’ often allows her to go out alone.
The use of ‘to let’ suggests to me that the speaker might be referring to only one specific instance in which ‘he’ allowed her to go out alone.
In both cases, the speaker feels that allowing her to go out alone in the dark is not something a good father would do.
Hi Tom
I’d say this is a bit different from the discussion in the other forum in that it involves the verb ‘let’ rather than ‘come’ or ‘go’ (i.e. ‘to let’ vs ‘letting’). In the other forum, the discussion also involved the past participle and the omission of “who have/had”. In the sentence here, the discussion is about the infinitive vs the present participle.
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Hi Amy
Thank you, first of all. 
I wanted to highlight MM’s point and apparently could not do so successfully. :shock:
ghosts come to …(defines ghosts)
father letting her…(defines father)
I disagree with this, Alex. To me the basic meaning is the same whether ‘to let’ or ‘letting’ is used. 
.
Hi Tom
There is an omission in those phrases:
“ghosts (who/that have/had) come to”
“father (who is/was) letting her”
PS
I edited my first post slightly before I saw the subsequent posts.
Thank you all so very much for your opinions, which are all so beneficial to me.
But I still feel that Alex’s “She wants to go but he is not a good father and he does not let her go.” is another choice or possibility to explain the original sentence: He cannot (be a good father to let her go out alone in the dark) = He cannot become such a person as so called a good father who would allow her to go out alone in the dark.
Maybe I am very wrong but I am really still confused.
Haihao
Yeah, I agree with you (that the infinitive denotes a single action, and the gerund - a sequence of actions). 
I just mixed that sentence up with this one:
He is not good enough to let her go out…
(i.e. She wants to go but he does not let her, because he is not good enough to do it)
(Is that right ? :? )
Hi Haihao
For the meaning that Alex mentioned (in his first post), I might possibly word the sentence this way:
He cannot be a good father and let her (do something she wants to do).
There is also the question of context. “Allow her to go out alone in the dark” is not something that would typically be thought of as better or safer than “not allow her to go out alone in the dark”.
.
Yes, I agree with you on that. But, I’d also suggest that the sentence would probably end differently than the original sentence. For example:
He wasn’t good enough to accompany her in the dark. (i.e. He forced her to go alone.)
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Bear in mind, too, that “can’t” here is used as the negative of ‘must’ and has the sense of “it isn’t probable/likely”. E.g.: It must be the doctor/It can’t be the doctor.
We could rephrase the sentence as: “I’m sure he isn’t a good father, since he lets her go out alone in the dark”.