Also, could you give an example of a philosophical problem that science has solved.

Considering that science developed out of a style of philosophical thought called 'natural philosophy', every question science has addressed has been a philosophical one.

The real problem is that when actual progress is made on a 'philosophical' question, we associate it with the branch of science that made the progress. Turing and Godel were mathematicians, Schroedinger was a physicist (and one of his most impressive insights was in the intersection of biology and information theory), Fermi a physicist, etc.

The only things that remain in the category of philosophy are those that are utterly useless and fail to expand our understanding of any aspect of the world. It's a simple selection effect - the gold is sifted out while the dross remains.

Turing alone resolved more questions that were traditionally considered to be within with bounds of 'philosophy' as you refer to it than anyone I can think of offhand.