Belief
I've laid out several, and they've yet to have been given careful consideration. You've been drowning strawmen in the poison well instead. I've no idea what your intent is. I still like to believe that you're arguing in good faith, and I ought make my words as impeccable as I can.. That's worth saying. So, here goes...
The position you're arguing for/from arrives at either self-contradiction or incoherence. Neither is acceptable. You're all over the place. Earlier you claimed that the clock in S's belief was both... broken and not. Clocks cannot be both at the same time. We're talking about S's belief at time t1. The clock that S looked at
is the clock in S's belief, and it was broken. There is no grey area here. None.
But, you want to invent a completely different clock - whole cloth. As if just because S does not believe the clock is broken, as if just because S does not know that the clock is broken, as if just because S does not know they were trusting what a broken clock said, as if just because S believed that that particular broken clock was working at that particular time....
Somehow - magically - there's now two clocks instead of one(according to you). The new one is not broken, because S believes it's working...
:yikes:
So much for the distinction between truth and belief. I was surprised to see that from you, but Janus, not so much.