Full Idea
If logic is neutral on the number of objects there are, then logicists can't construe numbers as objects, for arithmetic is certainly not neutral on the number of numbers there are. They must be treated in some other way, perhaps as numerical quantifiers.
Gist of Idea
Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality
Source
David Bostock (Philosophy of Mathematics [2009], 5.5)
Book Reference
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.159