I think for many philosophers, the claim “abstract objects are real” doesn’t depend on the use of mathematics to model physical reality. I think considering pure math is more illustrative of this point of view.
Andrew Wiles once described the experience of doing math research as:
“Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. You go into the first room and it’s dark, completely dark. You stumble around, bumping into the furniture. Gradually, you learn where each piece of furniture is. And finally, after six months or so, you find the light switch and turn it on. Suddenly, it’s all illuminated and you can see exactly where you were. Then you enter the next dark room...”
Since this is also what it feels like to study an unfamiliar part of physical reality, it’s intuitive to think that the mathematics you’re studying constitutes some reality that exists independently of human minds. Whether this intuition is actually correct is a rather different question…
I think for many philosophers, the claim “abstract objects are real” doesn’t depend on the use of mathematics to model physical reality. I think considering pure math is more illustrative of this point of view.
Andrew Wiles once described the experience of doing math research as:
“Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. You go into the first room and it’s dark, completely dark. You stumble around, bumping into the furniture. Gradually, you learn where each piece of furniture is. And finally, after six months or so, you find the light switch and turn it on. Suddenly, it’s all illuminated and you can see exactly where you were. Then you enter the next dark room...”
Since this is also what it feels like to study an unfamiliar part of physical reality, it’s intuitive to think that the mathematics you’re studying constitutes some reality that exists independently of human minds. Whether this intuition is actually correct is a rather different question…