[speedfreek]

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So you see no inconsistency if someone says, "I know p is true, but I don't believe p."

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No, I said belief is not required, which is quite different from I do not believe. I see no inconsistency if someone says "I know p is true, so belief in p is not required."

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Also, if there is no belief involved when I "know that p" for some proposition p, then what is the difference between knowledge and certainty?

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There is no difference. Knowledge is certainty. If I know something, I am certain of it. It is only when I don't know something, and am therefore not that certain of that knowledge, that I have to resort to asking myself if I believe something or not.

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Q: Do you believe the Sun will come up tomorrow?
A: Yes, I believe the Sun will come up tomorrow, although I can't really know that.

Next day after the Sun has come up.

Q: Do you believe the Sun Came up this morning?
A: I know the Sun came up this morning. I believe it now even more than I did last night.

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My version of this would be

Q: Do you believe the Sun will come up tomorrow?
A: Well, I would like to say I know it will come up tomorrow but I suppose I cannot, so I will have to say I believe the Sun will come up.

Q: Do you believe the Sun Came up this morning?
A: I know it did. There is no question. It is a certainty.
Q: Yes, but do you believe the Sun came up?
A: I do not question it, therefore belief is not required. It's a fact.
Q: Come on, you don't know that for sure, maybe the Sun didn't really come up, and this is a film set and that's not sunlight you are really seeing...
A: Do you want to see stars?!

If someone asks me to name something I believe in, I will often say "Love." [img]/images/graemlins/smirk.gif[/img]