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They can't both know the time. Only one time is the correct time so only one person can know the time. Look at the requirements again for justified true belief.

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What I am saying is that I do not like the OP definition of knowledge.

When someone says, “I know that A is true” They do not mean ‘true belief in the sense the OP uses the word. They are referring to the state of their mind, not making a deep and profound statement about the nature of the universe. Their assertion of knowledge has only indirect relation on the truth of A.

We are not discussing anything magic here, just fitting definition to terms.

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1. S must believe P (It makes no sense to say: "I know it's raining but I don't believe it"

2. P must be true (I think no further explanation is needed here)

3. S must be justified in believe P (Otherwise the clock case would be knowledge, or any wild belief that we have that HAPPENS to be true would also be knowledge)

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For a strong definition of justified, it is impossible for 3 to apply to anyone.

No one can be completely sure his or her belief exactly corresponds to reality. Hence it is necessary to weaken 3 in some fashion.

For instance you might say that it is only possible to know the time by reference to a timepiece that has been given an accreditation of accuracy from some governing body.

But doing things like this makes 3 subjective. The definition of ‘true belief’ is incomplete in the sense that you need a further assumption as to what level of justification is required for true belief.

If you wish to disallow two people to simultaneously have mutually contradictory true beliefs, you need to be very careful how you define ‘justified’. To repeat the alternative to this is to have a definition of ‘true belief’ that can never be applied to a human.

Another point. When I hear ‘true belief’ used in casual conversation, it is usually in the phrase:

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I truly believed A was true.

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They are usually referring to something they beloved was true but currently do not believe is true.

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The question was not, "When does someone think they know that p," which is what you seem to be describing, but rather, "When does someone know that p." It can't just be a state of mind to have knowledge, for otherwise anyone can know anything as long as they really think they do, so to speak. We can't put scientific knowledge for example on a par with this subjective state of mind you are referring to, for otherwise scientific knowledge has no special justificatory status--it's as subjective as me knowing that the moon is made of cheese (which is possible by your account).

We're also not asking what someone means when they say "I know that p," because that's not the same question as what was originally asked, i.e., what conditions have to be satisfied for someone to actually know that p. People may mean all different sorts of things when they say "I know that p," so obviously that wouldn't get at what the conditions are for having genuine knowledge are either. If knowledge really were just being in a certain subjective state of mind, then when a scientist (or anyone else, for that matter) claimed to know that the moon was made of cheese no one would dispute it--after all, he would only be reporting some subjective state of mind. But since we *know* in fact that the moon is not made of cheese when someone claims to know that it is we point out that they are wrong.