This is just a quick sketch. It seems to me that the meaning of "knowing" depends a good deal on the context within which we use the word, so I am trying to understand the various ways that we employ the word "know."

• I know something to be true. Example: The earth is round. I take this to be an indisputable fact.
  
• I know about something. Example: I have studied auto mechanics. Give me a problem and I can probably figure it out.
  
• I know somebody. Example: I have met and have spent time with Barak Obama, and now I am familiar with his personality and his character.
  
• I know of something or somebody. Example: I attended a class on world religions, so I know a little bit about Islam, so you don't have to rehearse the basics with me. Or, I know the person you are talking about, though I haven't actually met him/her.
  
• I know the meaning of something. Example: I know the meaning of the word "love." I can explain it to you.