Comment by griffzhowl
1 day ago
You could say they exist as concepts, that are necessary to use for some reasoning processes, without having any kind of independent existence.
It's similar for the case of programs or algorithms. We can say that a sorting algorithm exists, or a chess-playing program or whatever, which means we know how to implement the logical process in some physical system, but it doesn't mean that they have some kind of existence which is independent of the physical systems. It's just a way of talking about patterns that can be common to many physical systems
My view is that something exists iff there is any statement that is true of it.
I of course don’t mean that mathematical objects (such as the number 2, or some sorting algorithm) have the same kind of existence as my bed. To make the distinction, I would say that my bed “physically exists”.