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Full Idea
Set theorists often point out that the set-theoretical hierarchy contains as many isomorphism types as possible; that is the point of the theory.
Gist of Idea
The set-theoretical hierarchy contains as many isomorphism types as possible
Source
Stewart Shapiro (Philosophy of Mathematics [1997], 4.8)
Book Ref
Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.136
A Reaction
Hence there are a huge number of models for any theory, which are then reduced to the one we want at the level of isomorphism.