1.3 may be a more useful answer than 2.
I responded elsewhere with this:
"One of my biggest revelations in mathematics was in statistics, when, after the class (including me) worked unsuccessfully for a couple of hours to integrate an equation, the instructor (who I'm sure was laughing at us) walked up to the board, converted into a different coordinate system, and integrated the now very easily integrated equation in about thirty seconds."
Imagine you're an alien, for a moment, whose mathematics don't have any of the trigonometric functions - no sine, no cosine, no tangent. Whenever they're called for in their mathematics, they do a fourier transform of an infinite series of aperiodic waves, although they would never understand them -as- aperiodic waves, but as simple equations. This is an equally valid way of representing the trigonometric functions - but there would be a lot of very intractable mathematical problems.
Before you call that ridiculous, we didn't have set theory until the 19th century; it permitted the solution of a lot of mathematical problems we had, until then, been struggling with. Set theory overcame a lot of the problems arithmetic had struggled with. New mathematical models have arisen since then, such as category theory.
It's useful, therefore, to recognize arithmetic as a model, and one we may have a bias for, in consideration that another model might be more useful. More specifically, it's useful, when building AI for example, not to build into it a requisite bias for a particular model, if your goal is to permit it to solve problems which we have thus found far intractable; you may be building into it the very structural problems which have made it intractable for us.
Eliezer's post How To Convince Me That 2 + 2 = 3 has an interesting consideration - if putting two sheep in a field, and putting two more sheep in a field, resulted in three sheep being in the field, would arithmetic hold that two plus two equals three?
I want to introduce another question. What exactly are you counting?
Imagine one sheep in one field, and another sheep in another. Now put them together. Do you now have two sheep?
"Of course!"
Ah, but is that -all- you have?
"What?"
Two sheep are more than twice as complex as a single sheep. It takes more than twice as many bits to describe two sheep than it takes to describe a single sheep, because, in addition to those two sheep, you now also have to describe their relationship to one another.
Or, to phrase it slightly differently, does 1+1=2?
Well, the answer is, it depends on what you're counting.
If you're counting the number of discrete sheep, 1+1=2. However, why is the number of discrete sheep meaningful?
If you're a hunter counting, not herded sheep, but prey - two sheep is, roughly, twice as much meat as one sheep. 1+1=2. If you're a herder, however, two sheep could be a lot more valuable than one - two sheep can turn into three sheep, if one is female and one is male. The value of two sheep can be more than twice the value of a single sheep. And if you're a hypercomputer running Solomonoff Induction to try to describe sheep positional vectors, two sheep will have a different complexity than twice the complexity of a single sheep.
Which is not to say that one plus one does not equal two. It is, however, to say that one plus one may not be meaningful as a concept outside a very limited domain.
Would an alien intelligence have arrived at arithmetic? Depends on what it counts. Is arithmetic correct?
Well, does a set of two sheep contain only two sheep, or does it also contain their interactions? Depends on your problem domain; 1+1 might just equal 2+i.