expressing uncertainty on a definitive statement containing "can"

Question

In math or computer science there are a lot of definitive statements that can be formulated with "can" / "cannot".

Examples:

• "If the last digit of a natural number is 0 then it cannot be prime."
• "A natural number can only be even or odd."
• "If I divide an even number by 2, the result can (still) be even."

I am looking for ways to give such a statement some uncertainty to express the following: If I did not make any mistakes, then it definitely must be that way (because it follows from some irrevocable laws / logic / axioms...). But I am not sure that I did not make any mistakes, so please, dear reader / listener, check it yourself and correct me if I am wrong!

Are there compact ways to give the "can (only) / cannot be" a touch of uncertainty in the above sense?

In my native language - German - I could just add a "should (be)" and reorder some words to get that effect.

I think - please correct me if I am wrong - that this is usually possible in English, too, but with normal (non-auxiliary) verbs. E.g.:

• person A: "Is she painting the wall now?"
• person B, certain: "Yes, she is painting the wall now."
• person B, uncertain: "(I'm not sure, but) she should be painting the wall now."

But in my ears, using a combination of "can" and "should" sounds wrong. So what options do I have?

Answer 1

You can indicate uncertainty by backshifting: shall -> should and can -> could.

person A: "Is she painting the wall now?"
person B, certain: "Yes, she is painting the wall now."
person B, uncertain: "I'm not sure, but she could be painting the wall now."

Note that you can't use could not to imply uncertainty, for example you can use this idiomatic expression of somebody who definitely has no organizational skills:

He couldn't organize a piss-up in a brewery.

To express negative capability and uncertainty, you would have to use probably:

person B, uncertain: "I'm not sure, but she probably isn't painting the wall now."