Can somebody explain to me why we allow philosophers to make explicitly positive claims about the mind and psychology without empirical evidence, when were they to do the same thing with regards to, say physics (claiming perhaps that "the sun has a will to orbit the earth"), we'd rightly reject them for lack of proof?
Well, first, there might be some things about human psychology that we can figure out a priori. Notice I said "might". I don't think it's obvious that we should rule out the possibility, at the very least.
More generally, it's just not true that all scientific work (including physics) is done completely by means of empirical research. See Wikipedia's entry on "Thought experiment" for some good cases[1].
I'm not arguing for or against this particular bit of Nietzsche, but I think HN sometimes overvalues empirical or statistical study above all else.
There are different disciplines within the field of philosophy. The scientifically-minded philosopher might be interested in Metaphysics & Epistomology, or roughly, "what we know and how we know it". A standard approach in these fields is to address the Skeptic; someone who logically disagrees with the fundamental assumptions of the philosopher. This is where you get someone like Descartes writing "I think therefore I am" as a starting point for further arguments.
Other disciplines are less concerned with Truth (big "T") so much as they're focused on practical lessons on how to live life.
No answer you get to this will possibly contain empirical evidence or any scientific rigor, and yet you asked it hoping for information. Philosophy isn't science. It's not much more than unusually thoughtful literature. But that's still useful sometimes.
