As with many questions, “knowledge” is a more complicated topic than it seems. It is used different ways at different times by different people and for different reasons and uses.
However, there really are only two kinds of knowledge, aren’t there?
1) Certain knowledge and 2) contingent knowledge
1) If I’m wrong about a simple arithmetic expression like 2+2-4 (base 10) a logical tautology like A=A I must be dreaming or insane.
2) The proposed problem is all about contingent knowledge. A state of affairs is what it is apart from what one believes (belief being what we think we know, whether we do or don’t). We tend to base contingent beliefs based on perceptions or what we believe to be warranted, benigh assumptions. It’s how we operate in everyday life.
Generally, only 1) certain knowledge deserves to be called “knowledge” in is fullest sense.
As for 2), when we use the word “knowledge” we need to realize that how we use it is quite complicated. I know where I left my sunglasses whereas unbeknownst to me, my cat has decided to knock them to the floor and has batted them under my dresser drawer unit.
I can know things quite certainly (for practical purposes) by simply knowing what’s possible and/or practical and what’s not. Example: I’m quite certain there is no sea turtle on my bed, even though I can’t see my bed from where I’m writing. I suppose there’s a theoretical possibility I’m wrong about that, even so, barring proof I’m wrong (which would presumably be due to some elaborate prank carried out by Davis), I do know that to be true in the most commonly-used sense of “to know something.”
To get to your questions:
“Someone is counting books on her bookshelf (from a distance) and counts 15 books. Little did she know one of the objects she thought was a book was a brick. Was she correct that there were 15 books on the shelf?
“As it turns out, there was a book behind that brick…so in reality there were 15 books on the shelf. However, even though there were 15 books on the shelf after all and she concluded there were 15 books (even though she included the brick in his count) … WAS SHE CORRECT?”
She was correct for the wrong reason.
“In answering this question try to explain why you think she was or wasn’t correct taking into account what “knowing” something means, what role subjective and objective information plays in “being correct” and try to consider all the variables in this scenario and the relationship between knowledge and being correct.”
What it is “to know something” as you may have guessed from my preface, is not a question with just one possible answer. It is a word with different uses. Sometimes we use it to express literal certitude. Sometimes it’s a way of expressing a belief with various degrees of confidence.
The way you pose the problem, she was counting books she (thought she) could see. Let’s consider that this is not her bookshelf, so counting what she can see apparently from a distance, she was incorrect in that sense. Why do I say not her bookshelf? Because, who knows? It may be a bookshelf deep enough to have a second row of books behind the row she can see and she is unlikely based on common experience to even consider that possibility. However, in another sense she was correct.
Yes, I know I’ve gone beyond the problem as stated, but it was you who brought up that it might have room for a second row.
So, to ask what it is “to know something” is to pose a question without a single answer. Also, one can be accidentally correct or incorrect because when it comes to day-to-day knowledge, as distinguished from knowledge of formal systems (math, logic), what we say is contingent upon what we perceive, and perception isn’t knowledge.