Is human nature the subject of philosophy, or of the empirical sciences?

I myself am inclined to think that both philosophy and (certain) empirical sciences--including psychology--investigate human nature, although they investigate it in different ways. For example--and oversimplifying--the genetic differences between human beings and other animals can be investigated by biology; philosophy, however, can investigate whether there is some ultimate, natural end that all human beings seek, a question that does not seem to me to admit of resolution by natural science but squarely to fall within the province of philosophy. (Aristotle, for example, claims that 'all men by nature desire to know': I do not think that this claim admits of empirical confirmation or disconfirmation.)

What's the best definition of Nature and its contrast to the supernatural?

In the early modern period, there was considerable debate about the metaphysical status of miracles. Philosophers as different as Hobbes and Malebranche seem to agree, however, that some event is a miracle if and only if it caused by God's willing that that event take place. On this account, even an event that normally takes place according to natural laws could occur miraculously, if and only if it were a direct effect of God's will. This would be a metaphysical characterization of a miracle. Even granting this definition, of course, there remains a question as to how one could know that some event were a direct effect of God's will. This would be an epistemological question. An alternative definition of miracle, advanced by Leibniz, is that some event is a miracle just in case it cannot be understood by a created mind. According to Leibniz, all natural events can in principle be understood by created minds, provided one has access to the information necessary to understand that event; a...