[FOM] Intuitions of Mass and Volume

joeshipman@aol.com joeshipman at aol.com
Fri Feb 17 19:39:06 EST 2006

Friedman criticizes RVM as an axiom because he claims that the 
intuition supporting it is shown to be incoherent by results on the 
necessary non-invariance of countably additive measures.

This criticism is not to the point. The intuition I am talking about is 
a primordial physical intuition of MASS, not of VOLUME.  Even if one 
believed matter to be infinitely divisible, one would not expect matter 
to be absolutely uniformly distributed, so there is no intuitive 
requirement that two subsets of a mass of "stuff" that are related by a 
rigid motion must have the same "mass".

On can then interpret the absence of an invariant countably additive 
measure as indicating that absolute homogeneity and isotropy are 
impossible, that space has a "grain" or a "lumpiness" which affects the 
matter in it. If you believed in infinitely divisible matter because 
you didn't know any atomic physics, but had been lucky enough to 
discover general relativity which depends only on classical continuous 
physics, this would be a reasonable interpretation, which would 
preserve the intuition of infinitely divisible matter that retained the 
property of "mass".

The intuition that every subset of SPACE has an invariant "volume" is 
indeed shown to be incoherent by results that depend on the Axiom of 
Choice, but this is a different, and logically stronger, intuition than 
the intuition that every subset of a material object has a "mass".

-- JS

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