[Just as an example, P can be "My name is Rachel" and Q can be "I know my name is Rachel." Use your own name if the use of "I" bothers you. I am using P and Q generally in what follows.] P, Q, X are statements. C, K, O, are systems. Use different variables if it helps. Q: I know P. P is a true statement in consistent, formal system C. Can I prove Q is a true statement in C? (I am assuming this excludes Q from being an axiom of C.) If I construct C and prove P is true in C, I know P. That is, by proving P is true in C, I am proving Q is true. Q is a true statement in formal system K. K is then consistent, right? (K is only tied to one C, there is one K for each C.) What is the relationship between C and K? If I a) prove X is a true statement in a consistent, formal system or b) directly observe X, I know X is true. Let all X be axioms of formal system O. What is the relationship between C, K, and O? If Q is an axiom of O, how can Q be a theorem of C? Or, how can Q not be an axiom of C? BTW I'm not assuming O is consistent. In fact I think O is inconsistent. I think my question has something to do with self-reference, but I'm not sure how. Sorry, it's difficult for me to ask this intelligently. Perhaps this would be better suited to the Logic forum, but since I am talking about knowledge, I put it here. Edit: I used C for Consistent, K for Known, O for Observed, in case it helps you keep them straight.