In the numberphile video you linked to, I was disappointed that when the speaker was asked about how a nominalist can think about kinds of numbers that are difficult to describe in physical terms, he went to the example of pi rather than i. It seems to me that how to think about complex numbers is a much trickier problem for mathematical nominalists than how to think about pi is, and I’m curious if anyone here has any thoughts on that matter.
I would guess that most nominalists would stand their ground with only a little pragmatic redefinition. There are things in the world (like waves) we can model using complex numbers. Therefore, they might say, complex numbers are objects that we abstract out of waves in merely a slightly more complicated way than we abstract numbers out of sets of objects.
In the numberphile video you linked to, I was disappointed that when the speaker was asked about how a nominalist can think about kinds of numbers that are difficult to describe in physical terms, he went to the example of pi rather than i. It seems to me that how to think about complex numbers is a much trickier problem for mathematical nominalists than how to think about pi is, and I’m curious if anyone here has any thoughts on that matter.
I would guess that most nominalists would stand their ground with only a little pragmatic redefinition. There are things in the world (like waves) we can model using complex numbers. Therefore, they might say, complex numbers are objects that we abstract out of waves in merely a slightly more complicated way than we abstract numbers out of sets of objects.