[__mbm__]

It is interesting to interpret the body of mathematics as you would a collection of fictional tales. However, the philosophy begins to unravel (to me) when it asserts that "8 is larger than 5" is false while "Sydney is larger than San Francisco" is true because the latter statement "has referents".

What is it that makes Sydney and San Francisco real objects with meaningful sizes while 8 and 5 are not real and do not have meaningful sizes? Sydney and San Francisco are defined by political and legal "stories" in the same way that 8 and 5 are defined in mathematical "stories". The theory only seems to be consistent if all out-of-context falsifiable statements are taken to be false.

This theory placates me, since it leaves the truth value of mathematical statements (in the context of the mathematical story) to mathematicians. However, it renders any conclusions meaningless to mathematics, even if it is meaningful for a philosophy dealing with human stories.

[Retra]

I've always considered true and false to be properties of models, which are (necessarily) approximations of some underlying reality. So I'd say "8 is larger than 5 in some sense" and "Sydney is larger than San Francisco in some sense", where we might admit that the senses differ, and maybe 8 > 5 is 'truer' because the senses in which it are true are more general and require fewer experiences to verify.

But at the end of the day, you don't want to just say "everything can be true if you stretch far enough", you want to say that things are true only when we've demonstrated some utility in saying that they're true. So we just defer the issue: if you want to say something is true, you always need to know what difference it makes.

[__mbm__]

> if you want to say something is true, you always need to know what difference it makes.

Absolutely. It seems that fictionalism avoids both the "in some sense" qualifications and worrying about what difference it makes by asserting that statements out of context are simply false. While consistent, I'm similarly not convinced that its useful.

[hyperpape]

You may just be hung up on the examples of Sidney and San Francisco, which are not essential to the point. Suppose I bring you a 5 pound weight a 1 pound weight, and say "this is heavier than that". Then we can substitute those for Sydney and San Francisco in the example.

Put another way, the metaphysical status of cities is not a direct consequence or assumption of the metaphysics of mathematical entities.

[__mbm__]

So... the assertion is that physical things are real and numbers are not? It's alluring to accept this axiom, but when challenging a platonic view of mathematics, I don't think that we should accept that without discussion.

In other words, I'm supposed to entertain that math is a fictional tale with fanciful characters called "numbers" that don't exist outside of the story, but the boundaries of so-called physical objects are so apparent that they shouldn't be questioned?

Most physical boundaries are arbitrary, part of the stories that we tell ourselves, and not meaningful in a deep sense. I'd like to know how mathematics, and numbers in particular, are different.

[As an aside: Is it possible to convincingly argue that "this is larger than that" without using numbers?]

[hyperpape]

> It's alluring to accept this axiom, but when challenging a platonic view of mathematics, I don't think that we should accept that without discussion.

Not sure I follow. It's not an axiom, but the conclusion of a bit of argument, so it's not accepted without discussion.

If you mean my statement, then yes, I'm going to assume that rocks are real (as almost everyone except maybe Idealists) do, but not assume mathematical objects are real, for the sake of the present debate.

[__mbm__]

I may be misunderstanding, but the author asserts that Sydney and San Francisco are real (or rather, they have referents), and I'm confused because, in particular, Sydney and San Francisco are real in essentially the same way that numbers are real. Your weight example is more concrete, but I was trying to make the point that it suffers (at a less apparent level) the same problem.

[hyperpape]

I don't know what you mean by "essentially the same", but there are some significant differences. There are reasons you might doubt that San Francisco exists, the primary two of which are: 1) you believe that only things described by fundamental physics are real, everything else we talk about is either reducible to physics, or some sort of strictly inaccurate approximation to some physical reality. 2) You don't believe (1), but still think that for some reason San Francisco seems too vague of an object.

But that said, if San Francisco does exist, it exists in space and time. It didn't exist until the past 500 years, though the land it inhabits existed before then. It's also between 1 and 13 thousand miles from the Easter coast of China. You can locate it, you can go to it, etc.

None of those things are true of the number 5 (http://plato.stanford.edu/entries/abstract-objects/).

It's perfectly open for someone to deny that either or both of numbers and San Francisco exists, but the considerations seem a little different.

[mannykannot]

I cannot speak for _mbm_, but he may be saying that while the urban area known as San Francisco exists, the City of San Francisco is a legal, and therefore abstract, entity. I take your point that it has referents, namely the urban area.

If there are five of something in the universe, is that a referent for the number 5?