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Full Idea
One who believes in the independent existence of mathematical objects is likely to accept the law of excluded middle, impredicative definitions, the axiom of choice, extensionality, and arbitrary sets and functions.
Gist of Idea
If mathematical objects are accepted, then a number of standard principles will follow
Source
Stewart Shapiro (Philosophy of Mathematics [1997], 1)
Book Ref
Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.25
A Reaction
The underlying thought is that since the objects pre-exist, all of the above simply describe the relations between them, rather than having to actually bring the objects into existence. Personally I would seek a middle ground.