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Is it grammatically correct to use "can/can't" with "possible"? Can by definition indicates possibility, so in my opinion using can and possible is redundant and poor English. But I recently came across such usage in TV media and hence wondering if my understanding is incorrect.
Ex 1. This can be possible/This can't be possible.
Ex 2. Can it be possible to refine this further?
Ex 3. It can be possible that she never received the letter.
Yes, each contains an (essentially the same) redundancy, but as has been said before on ELU, that doesn't constitute 'poor English' per se.
I find
unacceptable (I could possibly find a context where it would work, but it would take some time.) It is possible that she never received the letter is far more idiomatic and non-redundant.
sounds almost as awkward, but Could it be possible to refine this further? might be used as a hedged (polite) form of Is it possible to refine this further?
These examples show the unpredictability of the English language.
While I find 1a jarring, though perhaps situations with two necessary conditions could rectify this (eg This can be possible: the prior conditions must be met. But even then there are no guarantees.) It still sounds clumsy.
But 1b 'This can't be possible!' is fairly idiomatic as a stressed alternative of 'This is impossible!' (Both are already problematic as contradictions in terms.) And 'How can this be possible?' is also fairly common, showing that we have a negative polarity item here.
Complement of answer
1.
A1 This can be possible
A2. This can't be possible.
As explained in user Edwin Ashworth it seems that given a plain possibility, this construction refers twice to the same possibility (or, as well, that one of two possibilities is missing in the context) thereby the sense of imprecision it communicates in a simple context. However, in the context of a possibility subordinate to another, it seems also that this is a sound construction.
ex.
— Could it be that the wind banged the door shut?
— This can become a possibility only if there was a sufficiently strong wind that day, and if the corridor pulls in strong enough draughts.
— (After two phone calls) This can be possible: it was windy and the caretaker confirms that the wind in the corridor can at times bang the doors shut.
A negative alternative in this dialogue is in fact naturally put into words by means of the negative (A2).
[…]
— This can't be possible; there was no wind that day.
2.
B Can it be possible to refine this further?
The same comment as in "1." can be made for "B", insofar as the felt impropriety. As to assert that complex contexts justify its use, I have no certitude. It seems that in a context where the "final" possibility is subordinate to the basic possibility of being a particular case, some other construction might be used, as the following, for instance.
ex.: possibilities of application of a processus of restauration to various paintings (hypothetical)
— Is it ever possible to refine this further?
— Yes, it is, but in rare cases when the painting is not too old and if you can find an expert willing to take the risk.
I don't see it as poor English or redundant. You can say that the word possible is descriptive in those cases. Remove the word possible from your examples and think how it changes the sentence. While first and third could work, second example doesn't seem right.
