Falling Tree Syndrome

The answer to this question lies within the question itself.

The tree fell in the forest. I would assume that if I myself tripped and fell, and no one heard me fall, the fact remains that I did trip and fall.

Hence, yes, the tree did indeed fall.

But, having said that, there is a school of thought that says if you put a cat inside a box, and close the box lid, then the cat can be in one of two states; alive or dead.

It follows then that an unobserved tree within an unobserved forest can be in one of many states; standing, fallen, alive, dead, healthy or diseased. Please, don't request I elucidate on this as I have a headache.

Or have I?