[FOM] A new definition of Cardinality.

[Vaughan Pratt]

Monroe Eskew wrote:
> It is worth pointing out that your definition still has a disadvantage
> if you don't assume choice.  Without choice, not all cardinalities are
> comparable.  If they were then all cardinalities in your sense would
> be comparable to a cardinality that contains a Von Neumann ordinal,
> but from this you could derive choice.  (It is nice to have a linear
> order on set sizes.)

How is this a disadvantage?  Those uncomfortable with choice are surely 
going to be uncomfortable with the idea that every set has an injection 
either to or from the set of reals.

Vaughan Pratt