‘What do we ordinarily do with this vital verb, and how is ‘know’ different from the contrasting verb ‘think’? Everyday usage provides some clues. Consider the following two sentences:
Jill knows that her door is locked.
Bill thinks that his door is locked.
We immediately register a difference between Jill and Bill – but what is it? One factor that comes to mind has to do with the truth of the embedded claim about the door. If Bill just thinks that his door is locked, perhaps this is because Bill’s door is not really locked. Maybe he didn’t turn the key far enough this morning as he was leaving home. Jill’s door, however, must be locked for the sentence about her to be true: you can’t ordinarily say, “Jill knows that her door is locked, but her door isn’t locked.” Knowledge links a subject to a truth. This feature of ‘knowing that’ is called factivity: we can know only facts, or true propositions. ‘To know that’ is not the only factive construction: others include ‘to realize that’, ‘to see that’, ‘to remember that’, ‘to prove that’. You can realize that your lottery ticket has won only if it really has won. One of the special features of ‘know’ is that it is the most general such verb, standing for the deeper state that remembering, realizing, and the rest all have in common. Seeing that the barn is on fire or proving that there is no greatest prime number are just two of the many ways of achieving knowledge.’
– Nagel. J. (2014) Knowledge Oxford, United Kingdom: Oxford University Press p. 7, 8