word usage - "Do you think he can still be alive?", "Can" used for probability, or what?

I came across these sentences in a learner's dictionary (see examples for sense 3a) today:

Do you think he can still be alive? [= do you think it is possible that he is still alive.]

I don't think he can still be alive. [= I think he must be dead.]

Since the second one is negative, it's probably not wrong, as it's pretty much a paraphrase of I think he can't still be alive. and can't can be used with the sense of 0% probability, i.e. can't = I'm certain it's not true.

The Problem

From what I've known and what I've read, could, but not can, is usually used this way to indicate probability either in the present or the future, as in he coud be in the garden.

As for possibility, can can only be used to tell general possibilities/truths (It can be rainy here during September.) or the possibility in a particular situation (We can go to Paris this weekend, since we don't have to work).

What I Think & What I've Tried Doing

I think the first one should read

Do you think he could still be alive?

and probably even the second one should read

I don't think he could still be alive.

However, it seemed strange to me (who is a non-native) when I replaced could with may in the first sentence, which is usually possible when talking about probability.

*Do you think he may still be alive?

I also noticed that

Do you think he is still alive?

seemed more natural.

The Questions

• What is can doing there?


• In what context is can used like this?



• Can could do the job too?

---

Note

• 
  

  I'm talking about using can and could in the present here. (This may lead to varying answers if I don't make this clear, I think)

  
  


• 
  

  Please, please avoid the word "possible" where possible. If you're going to use it, please make it clear what kind of "possible" you mean: generally possible (he can be hard at times), possible in the situation (we can go to Paris this weekend because we don't have to work), possible as in probability (he could be in the car.)

  
  
  

Answer

This sense of can is what linguists call a negative polarity item (NPI). You're already aware that can't can be used to mean "is not possible", and you clearly have little difficulty accepting that can can be used to mean "is possible" when the context effectively negates it ("I don't think that …"). So the tricky part is just recognizing that in English, negative polarity items are also licensed by (i.e., allowed to occur in the context of) questions.

Another negative polarity item is any; as you can see from these examples, they have similar distributions:

• Direct negation:
  
  
  
  • 1 isn't greater than any other positive integers.
  
  
  • 2 can't be greater than 3.
  
  
  
  
  


• Negation in a matrix (containing) clause:
  
  
  
  • I don't think 1 is greater than any other positive integers.
  
  
  • I don't think that 2 can be greater than 3.
  
  
  
  


• A question:
  
  
  
  
  • Is 1 greater than any other positive integers?
  
  
  • Can 2 be greater than 3?
  
  
  
  


• Use after only:
  
  
  
  • Only 1 is greater than any other positive integers. [This is false, of course, but the statement is grammatical.]
  
  
  • Only 2 can be greater than 3. [Ditto.]
  
  
  
  

Note that not all NPIs are licensed by the exact same contexts: some require more thoroughly negative contexts than others. Also, a word can be an NPI in one dialect, or in one register, without being an NPI in a different dialect or register. So this is a rough observation, rather than an firm guarantee of identical behavior. But it's a good first approximation.