I’m not super up-to-date on fictionalism, but I think I have a reasonable response to this.
When we are talking about fictional worlds, we understand that we have entered a new form of reasoning. In cases of fictional worlds, all parties usually understand that we are not talking about the standard predicate, “exists”, we are talking about some other predicate, “fictionally-exists”. You can detect this because if you ask people “do those three Jedi really exist?”, they will probably say no.
However, with math, it’s less clear that we are talking fictionally or talking only about propositions within an axiomatic system. We could swap out the “exists” predicate with something like “mathematically-exists” (within some specific axiom system), but it’s less clear what the motivation is compared to fictional cases. People talk as if 2+2 does really equal 4, not just that its useful to pretend that it’s true.
The main difference between mathematics and most other works of fiction is that mathematics is based on what you can derive when you follow certain sets of rules. The sets of rules are in principle just as arbitrary as any artistic creation, but some are very much more interesting in their own right or useful in the real world than others.
As I see it, the sense in which 2+2 “really” equals 4 is that we agree on a foundational set of definitions and rules taught at a very young age in today’s cultures, following those rules leads to that result, and that such rules have been incredibly useful for thousands of years in nearly every known culture.
There are “mathematical truths” that don’t share this history and aren’t talked about in the same way.
I’m not super up-to-date on fictionalism, but I think I have a reasonable response to this.
When we are talking about fictional worlds, we understand that we have entered a new form of reasoning. In cases of fictional worlds, all parties usually understand that we are not talking about the standard predicate, “exists”, we are talking about some other predicate, “fictionally-exists”. You can detect this because if you ask people “do those three Jedi really exist?”, they will probably say no.
However, with math, it’s less clear that we are talking fictionally or talking only about propositions within an axiomatic system. We could swap out the “exists” predicate with something like “mathematically-exists” (within some specific axiom system), but it’s less clear what the motivation is compared to fictional cases. People talk as if 2+2 does really equal 4, not just that its useful to pretend that it’s true.
The main difference between mathematics and most other works of fiction is that mathematics is based on what you can derive when you follow certain sets of rules. The sets of rules are in principle just as arbitrary as any artistic creation, but some are very much more interesting in their own right or useful in the real world than others.
As I see it, the sense in which 2+2 “really” equals 4 is that we agree on a foundational set of definitions and rules taught at a very young age in today’s cultures, following those rules leads to that result, and that such rules have been incredibly useful for thousands of years in nearly every known culture.
There are “mathematical truths” that don’t share this history and aren’t talked about in the same way.
The motivation to me seems exactly the same as with fiction: we’re talking about things other than physical objects or whatever.
Talking about mathematics, qua fictions, cant possibly have less motivation than talking about fictions qua fictions.
People also tend to regard their own tribal myths as really true, as well.