And nowadays, the training people want empirical proof.

Is there empirical proof to corroborate that theory?

I had just had very convincing empirical proof that Arethusa was a single, person with two bodies at her control.

All we have is empirical proof that it works.

Things were posited with no empirical proof, then accepted as true with no further discussion.

However, empirical proof and the universal acceptance of the existence of atoms didn't occur until the early 20th century.

Christopher has empirical proof of the psychology of hair color.

However, given such a long timeline, it is not possible to find empirical proof.

The captain felt no sense of satisfaction that she at last saw the empirical proof that he had been right.

They're satisfied that they know what happened, now; they've got empirical proof.