Full Idea
Three simple objections to conceptualism in mathematics are that we do not ascribe mathematical properties to our ideas, that our ideas are presumably finite, and we don't think mathematics lacks truthvalue before we thought of it.
Gist of Idea
Conceptualism fails to grasp mathematical properties, infinity, and objective truth values
Source
David Bostock (Philosophy of Mathematics [2009], 8.4)
Book Reference
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.253
A Reaction
[compressed; Bostock refers back to his Ch 2] Plus Idea 18134. On the whole I sympathise with conceptualism, so I will not allow myself to be impressed by any of these objections. (So, what's actually wrong with them.....?).
Related Idea
Idea 18134 Predicativism makes theories of huge cardinals impossible [Bostock]