You’re right, it doesn’t matter that we have human brains. It matters that we evolved in a world where 2+2=3, regardless of humans. But if it did, then it would mean something deep within the structure of the world was different in some way I find hard to imagine, and then I’d have a different kind of mind that evolved in such a different world. And while that specific scenario, 2+2=3, is very hard for me to imagine, it is very *easy for me to imagine scenarios where it could be meaningful to say that 2+2=1 (modular arithmetic, mod 3 in this case) or 1+1=1 (entities that lack discrete structure but instead just merge when combined, like counting clouds before and after they collide) or 2+2>>4 (two pairs of particles with complex interactions that result in a multitude of Everett branches).
My current understanding is that mathematical truths come from the internal relations of the rules of formal systems. Some of those systems are useful because their structure corresponds to aspects of the world, and those are the systems we bother to deeply investigate, give names to, and so on. One of the long-standing open questions in physics is where the laws of physics come from. Einstein: “What really interests me is whether God could have created the world any differently.” I don’t have all that much insight into that beyond the fact that some models of physics try to derive the apparent laws of reality from deeper structures, like the geometry of spacetime, but that just pushes the question back a step.
You’re right, it doesn’t matter that we have human brains. It matters that we evolved in a world where 2+2=3, regardless of humans. But if it did, then it would mean something deep within the structure of the world was different in some way I find hard to imagine, and then I’d have a different kind of mind that evolved in such a different world. And while that specific scenario, 2+2=3, is very hard for me to imagine, it is very *easy for me to imagine scenarios where it could be meaningful to say that 2+2=1 (modular arithmetic, mod 3 in this case) or 1+1=1 (entities that lack discrete structure but instead just merge when combined, like counting clouds before and after they collide) or 2+2>>4 (two pairs of particles with complex interactions that result in a multitude of Everett branches).
My current understanding is that mathematical truths come from the internal relations of the rules of formal systems. Some of those systems are useful because their structure corresponds to aspects of the world, and those are the systems we bother to deeply investigate, give names to, and so on. One of the long-standing open questions in physics is where the laws of physics come from. Einstein: “What really interests me is whether God could have created the world any differently.” I don’t have all that much insight into that beyond the fact that some models of physics try to derive the apparent laws of reality from deeper structures, like the geometry of spacetime, but that just pushes the question back a step.