For 10 points, name this theory claiming mathematical objects exist, so named because its description of them is similar to its namesake's theory of forms.
The "full-blooded" form of this theory doesn't privilege any single universe, instead advocating plenitude. One argument against this theory advocates structuralism, and claims there can be no objects with only structural properties. Another argument against this theory is that the non-causal objects it posits cannot account for the reliability of its subject. Frege argued for this theory by claiming that for statements to be true, the singular terms appearing in them must exist, similar to the Putnam-Quine indispensability thesis argument for this theory. Formalism, which directly opposes this theory, claims its subject proceeds purely by syntactic transformations, as exemplified by Hilbert's treatment of geometry. For 10 points, name this theory claiming mathematical objects exist, so named because its description of them is similar to its namesake's theory of forms.
The "full-blooded" form of this theory doesn't privilege any single universe, instead advocating plenitude.
Platonism [or mathematical realism]