The story goes as follows (translated from German):

"Once I dreamed that there was an island called "the island of dreams". The inhabitants of the island dreamed very vivid and lucid. Indeed the imaginations which occurred during sleep are as clear and present as perceived during waking. Even more their dreamlife follows from night to night the same continuity as their waking perception during the day. Consequently some inhabitants have difficulties to distinguish whether they are awake or asleep.

Now every inhabitant belongs to one of two groups: Day-type and night-type. The inhabitants of day-type are characterized by their thinking during the day being true and during the night being false. For the night-type it is the opposite: Their thoughts during sleep are true and those during waking are false."

Questions:

1. Once an inhabitant though/believed that he belonged to the day-type. Kann be tested whether this is true? Was be awake or asleep at the time of the thought?

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