Jad:You just blew my mind. So that's where we find the pythagorean theorm, in reality, but not in nature. So nature, in this model, is a subset of reality? You make it sound (with the "share some common entities") like this in not the case. What is in nature that is not in reality? How do the two relate to existence? If you don't want to type it all out, please point me to your resource (in the meantime, I will google "nature reality existence", but my hopes are not high).
Nature might be a subset of reality -- or it might not -- depending on which worldview. I will explain as best as my scientific mind can. There are two basic entities which we can measure: (1) nature, and (2) human perception. Truth in each can be determined by various means, and I do not know the epistemological details. But I know there are four possible conditions:
A) Both nature and human perception are real
B) Nature is real, but human perception is not real
C) Human perception is real, but nature is not (this is the humanistic worldview)
D) Both nature and human perception are not real.
Position D, of course, is relativism. It can withstand little scrutiny (truth vanishes, so does our means of asserting the truth of position D). Position C is the perspective held by most philosophers in academia. Their view is that nature, in its changing forms, is basically an illusion. Human perception, on the other hand, is forever. Position A is sometimes said to be "theistic", because it requires some intelligence to sychronize the two facets of reality. And position B seems to connect more closely with science and objectivism. There are some good authors of each of these positions, if you would like to read them. None of this "limits" what reality can contain, it could contain things beyond these two components -- like mathematical truths for example, which can be confirmed by deduction and independent derivations.