Morality and Subjectivity

Its a fundemental result that any set of mathematics is unprovable. To do any maths you must have unprovable axioms.In maths there are unprovable statements.The early mathematcians tried to deduce from first principles - read Eucllids elements for a beautiful example of starting with a few assumptions and ending up with a large body of work.But the assumptions are not fixed. Euclid assumed that parallel lines will not corss. Remove that assumption and you get a new kind of geometry, non-euclidian geometry.To include this assumption or axiomin your set is somewhat arbitrary, and must depend on what you want your maths to be able to do.A well known set of axioms for all of math contains 7 axioms. These are chosen somewhat randomly. Joining 2 axioms might result in one statement that could replace these, so you would end up with 6 axioms, with one being a composite of 2. Or you might be able divide one axiom in two and still end up with the same maths.And the axioms are chosen so that we end up with the math we know!

I was referring to Goedel. As English is a second language I was perhaps a little unclear. I simply meant that math as it is is unprovable. You cannot prove math by using only statements from within math - but we are going way off topic, so I'll cease now