[FOM] Mathematics and precision

[Timothy Y. Chow]

On Mon, 5 Mar 2007, Henrik Nordmark wrote:
> It seems as if Mathematics is defined by its methodology and not so much 
> or at all by its underlying ontology whatever that may be.
>
> I guess the same could be said about other disciplines such as Logic or
> Philosophy.

Actually, I still prefer my original formulation, in terms of "degree of 
precision" rather than "methodology vs. ontology."  To favor methodology 
over ontology is to bias the formalist/platonist debate in favor of the 
former, whereas I would say of both methodology and ontology that they are 
mathematical if they are sufficiently precise.

So for example, you will consider V a legitimate mathematical object if 
you think it's sufficiently precise; otherwise, you won't.  It's not that 
there are necessarily no mathematical objects; it's that whether some 
particular subject counts as mathematical depends on whether the subject 
is sufficiently precise.  Ditto with "methodology" in place of "subject."

Anyway, I'm not sure if this idea stands up to more careful scrutiny, or 
whether it degenerates into some existing philosophy of mathematics; I'd 
have to work it out in more detail.  I gather, though, that this does not 
seem to be a viewpoint that has *already* been pursued in detail by 
someone else.

Tim