FOM: real numbers and the real world

[Neil Tennant]

Robert Black wrote:

> Field does think that the reals (not
> set theoretical cardinals, which to my knowledge have no applications in
> physics) can be isomorphically embedded in the physical world. That's
> straightforward, since he's a realist about physical space (or spacetime)
> and its points and regions. 

Suppose one is a realist about physical space, or spacetime. Does it
follow that one thinks it is continuous? Or might our thinking it
continuous be a symptom of our own idealism? Couldn't space (or spacetime)
turn out, on empirical grounds, to be grainy?

Neil Tennant