Full Idea
For intuitionists, all but the smallest, most well-behaved infinities are rejected.
Gist of Idea
Intuitionists only accept a few safe infinities
Source
Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 1.1.3)
Book Reference
Colyvan,Mark: 'An Introduction to the Philosophy of Mathematics' [CUP 2012], p.7
A Reaction
The intuitionist idea is to only accept what can be clearly constructed or proved.