Belief...a choice?

This statement would be true to me as well but then I have to ask myself - "why do I believe that 2 + 2 = 4?" This leads to googling proofs for why '1 + 1 = 2' and that leads to headaches from trying to recall my higher math skills that have been left dormant too long.The easy explanation of why 2 + 2 = 4, is that in a base 10 number system we have labeled a certain number of objects that have a value of 2 and a certain number of objects that have a value of 4. We see when we put a pair of objects labeled 2 together they are identical to the objects labeled 4. In our current numbering concept, it is true that 2 + 2 = 4. However, what if our concept and labeling were different and 5 was the label given to the same number of objects that we currently call 4?We'd certainly be talking about the same number of objects no matter what we labeled them, no? But in the concept where the numbers look like:

quote:

---

1 2 3 5 4 6 7 8 9

---

2 + 2 = 5 is true and I would "believe" it.Ok, now I've gotten myself confused... Anyway, back on topic. I only choose to believe that 2 + 2 = 4 because that is how our current concept of base 10 addition has labeled the sum of 2 + 2. I can certainly be shown two sets of two objects and see that they make four objects but why can't I call the sum 'FRED'? Do we have math truths just because we have defined them that way?thanx
PM1K