Consider the following sentences:

  • How could you know if you have cancer.
  • How can you know if you have cancer.

Note that the sentences are not interrogative, but both of them are to be the title of an article/news.

What is the difference between the above two sentences (in meaning)?

  • 1
    If you want to write a title, simplify it: How to know if you have cancer. That would be my recommendation.
    – J.R.
    Nov 9 '14 at 2:44

I don't know why OP says "the sentences are not interrogative". Obviously they are, regardless of whether the question mark is present or not.

1: How could you know if you have cancer?
2: How can you know if you have cancer?

OP has taken his two examples from titles of articles, in which context there's no possibility of them having different meanings. They'll both be followed by text answering the "title" question by setting out possible ways to self-diagnose that you have cancer.

In other contexts it would be possible to distinguish different implications. For example, interpreting could as the past tense of can in #1 leads to...

1a: How was it possible for you to know you have cancer? (perhaps implying disbelief or surprise)

...or one could see could there as equivalent to would, indicating an "irrealis" context. Using could/would like that "distances" the speaker from his enquiry ("I don't actually think I've got cancer - but if I did, how could/would I find out for sure?")

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