[FOM] Question on the number line

Robert Black Mongre at gmx.de
Thu Nov 17 05:27:51 EST 2005

A number of people have suggested that the standard picture of the 
real line only applies to a mathematical abstraction and not to real 
physical space. But whereas a real physical *stick* is indeed not 
continuous (being composed of atoms, molecules or whatever), and can 
be broken into two parts both of which have ends, according to our 
current best physical theory physical *space* is locally homeomorphic 
to R^3 (or spacetime to R^4). Of course that's a theoretical claim 
which could be wrong and which (like all the claims of basic physics) 
can't be directly tested by experiment. But if we're going to be 
realistic about physical theory (which many of us want to be) the 
claim that real physical space isn't really like this would have to 
be backed up by an account of what it really is like, and an 
explanation of how things like quantum mechanics and general 
relativity should be reformulated to fit in with the new topology, 
and I doubt if anyone is claiming that they can do this (or that some 
scholastic or Aristotelian argument forces us to do it).


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