>>38
I'm not confused, you're just wrong.
"Why does 1 + 1 = 2"
Tell me then, how would you answer this?
I'm assuming you agree with me that the question would be better worded,
"Why is the statement "1 + 1 = 2" true".
And obviously you could say, that depends on the axiomatic system you are working in.
However, he's almost certainly, without knowing, asking about the standard construction of the natural numbers, let's take peano's as it's an obvious choice.
Now, within that system, we can assign truth values to a statement. The fact that the statement "1 + 1 = 2" is true, follows pretty simply from the axioms.
Godel's incompleteness theorem does not come into it. Peano's axioms have in fact been proved to be consistent by referring to a different mathematical system, but that's irrelevant here.
While there are statements that can be expressed in our system here that are undecidable, the statement "1+1=2" is not one of them.
I don't see where you are expecting philosophical questions to enter into this. "Why those axioms" is hardly a philosophical question. Just because it may or may not be outside the realms of mathematics, which is debatable, does not place it inside the realms of philosophy, and even if it were, it would still be irrelevant to the matter at hand. (HORRIBLE sentence structure there, I apologise)