[FOM] Could spacetime be discrete?

[Mark Steiner]

I'd like to point out that both George Berkeley (Principles of Philosophy)
and David Hume (A Treatise of Human Nature) argued that space (and I think
also time) is discrete.

Another possibility in between discrete spacetime and continuous spacetime
would be rational spacetime, i.e. there no no irrational intervals
(supposedly "the" Greek position).  Someone today might argue that we could
trade in differential equations for difference equations without losing any
power of prediction.

I have the following question however: our present (continuous) mathematical
formalisms do not only describe nature, but allow the development of new
theories out of the old by various kinds of mathematical generalization,
deformation, analogy,  etc.  Would mathematics retain its power as an engine
of discovery if we traded it in for discrete or rational alternatives? Have
the experts on reverse mathematics given thought to this very important
aspect of mathematics?