Can 1+1 be proven? If so, then is mathematics a science?
In the usual formulation of Peano arithmetic, that is the definition of the number represented by '2'.Is the Peano model based on the assumption that 1+1=2?
No, it is not. That is a theorem (although a very easy one).Is the Peano model based on the assumption that 1+1=2?
I know of Principia Mathematica, but I've not actually studied it. But judging from how I hear it described, I'm quite content to stick with modern styles.When the OP posted his question, I was thinking along the lines of Russell&Whitehead, that you know a lot more about than me, Hurkyl.
Hope my nonsense fraction was acceptably small..