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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.

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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?]

> 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.

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.

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.

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?

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