Zhuangzi and the Butterfly

Can we tell if the world is real?

Philip and Phoebe, the terrible twins, rarely agree about anything.
The other day Phoebe found this story in a book of Chinese philosophy:

Once upon a time a Chinese philosopher called Zhuangzi, tired out from
all his thinking, sat down in his garden in the warm sun and started to
doze. Soon he was fast asleep and dreaming. he dreamed he was a beautiful
butterfly, visiting flowers in the sunlit garden and sucking their nectar.

Eventually the butterfly grew tired from all its flying, so it settled
down on a nice green leaf in the warm sun and started to doze. Soon it
was fast asleep and dreaming. It dreamed it was a human philosopher called
Zhuangzi, sitting in his garden.

Zhuangzi woke up feeling really confused. He didn't know who he was! Was
he really Zhuangzi who had dreamed of being a butterfly, or was he really
a butterfly dreaming about being Zhuangzi?

"Silly man!" said Philip. "I never get confused about whether I'm dreaming or not.
Dreams are quite different to real life."

"No they aren't," retorted Phoebe. "I often can't tell I'm dreaming until I wake up.
Anyway, how can you be sure you aren't dreaming at the moment? Maybe you'll
wake up in a minute and you'll still be tucked up in bed!"

"Sisters!" muttered Philip, wandering off to play with his computer.

* * *

Who is right, Philip or Phoebe? Is there any way you can be absolutely sure
you are not dreaming at the moment?

When you've thought about this problem, click here.