-It's true that the Platonic universe contains all mathematical structures, 
including trivial or uninteresting ones,

-Not only trivial and uninteresting, but also contrary to the ones that are 
interesting.
Brent
 
Putnam (in his "What is mathematical truth?") wrote: "The question of realism, 
as Kreisel long ago put it, is the question of the objectivity of mathematics 
and not the question of the existence of mathematical objects".
 

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