I didn't think that your view would be changed. Quite honestly I'm not sure I understand the philosophy behind this. But the fact that there is only one model

I didn't think that your view would be changed. Quite honestly I'm not sure I understand the philosophy behind this. But the fact that there is only one model to the second order axioms of arithmetic (Peano's axioms with induction included) is a bit surprising to me. We can't come up with a computable system for finding all mathematical truth but there appears to be a hardwired number system in the universe. It's not computable but it is unique. The natural numbers lead naturally (no pun intended) to the integers in a unique way. The integers uniquely lead to the rationals and the completion of the rationals is a unique object called the real numbers. The unique algebraic closure of the reals is the complex numbers. There is uniqueness at each step. This coupled with the utility of using mathematics to describe natural processes is...strange to me and some others. I don't know what this has to do with your points because I didn't understand them. Not because you didn't write clearly but because I don't know enough philosophy. I'm a mathematician and know very little about philosophy. Thanks for your input.