1 + 1 = 2 without adding?

[Frederf]

Well if it behaves in the same way as addition then it is addition, just by another name. I could define a new symbol called the flarg and then define it the same way as addition. And at that point, it IS addition.

See, that's where I'm not so sure. Perhaps there's some back door way to get around what is fundamentally addition and still achieve the same result. If successful I imagine it's difficult to prove because our definitions of words aren't as rigorous as the mathematics that those words describe.