The Stopped Clock

You are walking through the town square and look up at the large heritage clock tower to check the time. The clock's hands clearly read 2:00 PM. You form the immediate belief that it is 2:00 PM. It is, in fact, exactly 2:00 PM at that very moment. However, unbeknownst to you, the clock's internal mechanics suffered a catastrophic failure and stopped working exactly twelve hours ago.