Will the sun rise tomorrow?

Phoebe, the more intellectual of the Terrible Twins, has been reading up on the 18th Century philosopher David Hume, and it has made her very worried.

"What's the matter with you today?" asked Philip, her more down-to-earth sibling, with a
notable lack of sympathy.

"I'm worried that the sun won't rise tomorrow morning and we'll all freeze to death"
wailed Phoebe piteously, tears welling up in her eyes.

"Oh for goodness sake!" snapped the ever-practical Philip. "Listen! The sun has risen
every day for thousands of years, so of course it will rise tomorrow. It's obvious.
Stop worrying and pull yourself together!"

"But how do I know ... the future ... will be the same ... as the past?" stammered Phoebe
between sobs. "Perhaps it's just about to change and we'll all die. Waaaahhhh!!"

Philip stared at her, scarcely able to believe his eyes. "Sisters!" he grumbled. "It's about
time she stopped reading philosophy. It's obviously not good for her!"

* * *

Can you set Phoebe's mind at rest? Can you prove to her that the run will rise tomorrow
morning as usual? Or are we not sure that it will?

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