[Piers]

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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.