@Isa,
Isa wrote:Only if A is you. If A is anyone else, it is subjective: unless now you have the ability to read another person's thoughts.
I don't see how it makes any difference who A is. For any A, if A knows that p, then p is true. And if A is someone other than me, whether he knows that p is true depends on whether p is true. If p is not true, then whether or not he believes that he knows that p is true, he does not know p is true.
Determining whether I know that Quito is the capital of Ecuador depends on whether it is true that Quito is the capital of Ecuador. And that cannot be determined by looking inside my mind. It can be determined only by doing something like looking at a map. And if you claim to know that Quito is the capital of Ecuador, I could not determine whether you know it by looking into your mind even if I could do such a thing, for it is a necessary condition of your knowing that Quito is the capital of Ecuador that Quito be the capital of Ecuador, and I could not determine that by looking into your mind.
What
could be determined by looking into A's mind, whoever A is, is whether A
believes that Quito is the capital of Ecuador, for belief is subjective. And for someone, whoever he might be, to believe that Quito is the capital of Ecuador, it need not be true that Quito is the capital of Ecuador, for it is possible (alas!) to have false beliefs. It is not possible to have false knowledge.
So, it may very well be that you are confusing believing with knowing, and thinking that because believing is a mental state which can be introspected, that knowing is a mental state which can be introspected. I cannot, of course, know that it is that someone else believes except if he tells me. But I can certainly know whether or not someone else knows something wheter or not he tells me because if what he claims to know is not true, he cannot know it. So, if the question is whether A knows that La Paz is the capital of Ecuador, I don't have to ask A anything, since I know that A does not know that La Paz is the capital of Ecuador, since La Paz is not the capital of Ecuador. Of course, if the question is whether A
believes he knows that La Paz is the capital of Ecuador, then I would have to ask him whether he does. For believing one knows is subjective (all believing is subjective), but knowing is not subjective. And clearly, although someone may
believe he knows some proposition is true, it does not follow that he knows that proposition is true. So it may also be that you are confusing A's
believing he knows, with A's (actually) knowing. As Mark Twain said, "It is not what a man doesn't know that gets him into trouble, it is what a man knows that is false that get him into trouble". And what Twain is clearly saying is that it is not what a man doesn't know that gets him into trouble, but what a man
believes he knows, but does not know because what he
believes he know is false that gets him into trouble.
So, to summarize: whether a person believes, or whether a person believes he knows, is subjective. But whether a person knows, is objective.
P.S. I notice that Bogie asks, Why would you believe you know something without knowning it?" I would think that the answer is all too obvious: because you have made a mistake. In the middle ages lots of people believed they knew that the Earth was flat. They made a mistake.