We live in a world that is full of "theoretical concepts", many of which are highly abstract. Things like logical deduction (e.g. the Principle of the Excluded Middle: something is either

*A*or not

*A*), pure mathematical theory (e.g. the Pythagorean Theorem, a

^{2}+ b

^{2}= c

^{2}), and physical law (e.g. Newton's Law, F = ma) definitely appear to govern the way the world works.

The question is: Do these theoretical concepts exist

*independent*of the world, or are they somehow

*contained*or

*encoded*in our reality?

If there was a separate universe, it could easily have different fundamental constants and different physical laws. Might it also have different laws of mathematics? For example, could pi = 4.3212? Or perhaps could pi be proportional to the diameter of the circle? Or are the laws of mathematics external to our local existence and perhaps always true?

I ask this because it seems in many of the religious-oriented (anti- or pro-) threads on this forum many of the posts indicate that the posters seem to have a clear answer to the above question, and indeed, think that the answer is obvious. (It seems like most people think that theoretical concepts are independent of our reality.)

I'm not sure that the issue is so cut-and-dried, and am interested in hearing people's thoughts on the matter.