Limits of human reason, math, physical science

[Jim_Baur]

Where would one look to find a good book(s) on the limits of human reason?

Also, I would try to follow any discussion on the limits of human reason.

I would like to know whether math exists outside of the human mind or is it a creation of human reason?

Also, what is the nature of physical nature laws?

Thanks!

 

[Anselm33]

Where would one look to find a good book(s) on the limits of human reason?

Also, I would try to follow any discussion on the limits of human reason.

I would like to know whether math exists outside of the human mind or is it a creation of human reason?

Also, what is the nature of physical nature laws?

Fr. Stanley Jaki (philosophy professor at Notre Dame) has written several good books; one I’m reading now, a collection of his essays on the limits of science, “The Limits of a Limitless Science” is excellent. Roger Penrose (from the other side of the fence, a distinguished mathematical physicist) has written several books, which emphasize particularly the limits of algorithms (Godel’s Theorem): “The Emperor’s New Mind”, “Shadows of the Mind”, " The Road to Reality". Penrose is a neo-Platonist and says mathematics exists in the “world of ideals” and is discovered by the human mind. Alfred Driessen and Antoine Suarez have collected essays on “Mathematical Undecidability, Quantum Nonlocality and the Question of the Existence of God”–articles about what Godel’s Theorem and quantum non-locality say about the existence of God–very expensive book (over $100) but possibly available at a local university library…
There is also a book by a philosopher, Bas van Fraassen, who claims there are no such things as “Laws of Nature”, rather there are theoretical (mathematical) rules for models scientists use to try to understand the world around them, but these rules/models do not necessarily reflect reality: “Laws and Symmetry”.

hope one or the other of these will be helpful to your quest for understanding.

 

[Just_Lurking]

I would like to know whether math exists outside of the human mind or is it a creation of human reason?

The Standford Encyclopedia of Philosophy has a nice article that addresses this (see here). I’m not a big fan of philosophy, but this article managed to make sense to me as a mathematician. One thing it did was to address the various consequences of the philosophy of mathematics, instead of leaving everything in philosophical terms. For example, there are various different versions of the axioms of set theory–Does a belief in Platonism mean that all but possibly one of these versions must be “wrong”?