That's a load of shit. 6 + 6 will always equal 12.
There is no way to get 10 out of SIX OBJECTS and ANOTHER SIX OBJECTS.
Think about it, just because we call it six, doesn't mean if it had a different name (i.e it was called Foeoriojgdfg instead) it wouldn't make it six.
One stone plus another stone, in the whole universe, no matter what species/race/w.e will always equal 2.
You won't get 6, you will get B objects. That's just a simple example, but if we apply that to more important axioms ... you get the point.
Look, why do you think we go from 9 to 10? It's cause we have 10 fingers and that results in a decimal system. If some alien race were to have, lets say, 16 fingers, they would be counting hexadecimal. Now this is just a basic example to illustrate what axioms actually do - they create facts for us on which we then build what we call "mathematics".