To your main point: are irrational numbers, say, "out there"? If so, where?
I believe this to be a bad counterpoint, because you could ask the same thing about natural numbers as well. I've personally never seen a natural number. Sure, I have seen and worked with lots of representations of natural numbers, but the numbers themselves are - as far as I understand it - not physical objects. There is no qualitative difference between natural numbers and any other mathematical objects in that respect. They are all on the same "plane of existence".
At least that's a valid world view or ontology. I know that not everybody thinks like that, but besides clarifying what the parent poster probably meant I think it's not a very meaningful discussion.
I believe this to be a bad counterpoint, because you could ask the same thing about natural numbers as well. I've personally never seen a natural number. Sure, I have seen and worked with lots of representations of natural numbers, but the numbers themselves are - as far as I understand it - not physical objects. There is no qualitative difference between natural numbers and any other mathematical objects in that respect. They are all on the same "plane of existence".
At least that's a valid world view or ontology. I know that not everybody thinks like that, but besides clarifying what the parent poster probably meant I think it's not a very meaningful discussion.