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Full Idea
In my personal opinion, predicativism is the best version of conceptualism that we have yet discovered.
Gist of Idea
The best version of conceptualism is predicativism
Source
David Bostock (Philosophy of Mathematics [2009], 8.4)
Book Ref
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.259
A Reaction
Since conceptualism is a major player in the field, this makes predicativism a very important view. I won't vote Predicativist quite yet, but I'm tempted.