[FOM] Mathematics and precision

[A. Mani]

On Tuesday 06 Mar 2007 20:59, Timothy Y. Chow wrote:
> 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.
> 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
All this sounds like an attempt to reduce the problem to an abstract 
chicken-egg problem. In my opinion, the precision approach can work only in 
the methodological context. The concept of *sufficiently precise* is 
necessarily a methodological and ontological concept. Neither can the 
methodological abstraction make sense without some concrete associations and 
ontology to guarantee that it is sufficiently mathematical and precise. 

This dialectics can be modelled to result in measures of *coherence*, that 
guarantee the mathematical nature of the context. That is my standpoint. Then 
we can argue about the measures : )

Best

A. Mani
Member, Cal. Math. Soc