Are Axioms of Math Subjective?

[apeiron]

Then back to the "maths is subjective" camp. And from the co-founder of category theory no less. Looks like a book worth tracking down...

http://en.wikipedia.org/wiki/From_Action_to_Mathematics_per_Mac_Lane

 

[qsa]

counter argument

http://books.google.com.kw/books?id...ok_result&ct=result&resnum=9&ved=0CCgQ6AEwCA#

 

[JoeDawg]

they were chosen because they generate the theory of Euclidean geometry.

That doesn't really respond to the problem.
Why is Euclidean geometry important?
Its important to us, no doubt, but why.

All our reasons for creating mathematics the way we have, are based on what mathematicians have wanted to do with math. Its true, once you have your axioms, you can start refining your method... adding new axioms and delving into the implications of how your axioms interact, but invariably math has to have a purpose before you can start defining axioms.

The purpose is us living our lives within the constraints of our reality. But essentially that is always going to be subjective, based on our personal and collective perspective on things.

 

[apeiron]

counter argument

http://books.google.com.kw/books?id...ok_result&ct=result&resnum=9&ved=0CCgQ6AEwCA#

How would you sum up what Putnam is trying to say?

I found that chapter very woolly and rambly - not helped by so many pages being missing of course.

It did start out with the argument that if there are many equivalent descriptions in math, then this should bolster believe that there is something deeper and solid that maths has been trying to describe - a bit like the feeling different parts of an elephant example.

But actually, when you look at all the examples Putnam offers, you find they are dualities and antimonies. Or what I call dichotomies or asymmetries.

And dichotomies are about immanence rather than transcendence. It is the division of the one in two directions, towards complementary limits. So again we would be talking about processes of development rather than "objective" existence.