Full Idea
Frege's tying the objectivity of arithmetic to the objectivity of logic makes sense of the fact that can find out about arithmetic by thinking alone.
Gist of Idea
Logicism makes sense of our ability to know arithmetic just by thought
Source
Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 06.1.1)
Book Reference
Hofweber,Thomas: 'Ontology and the Ambitions of Metaphysics' [OUP 2018], p.154
A Reaction
This assumes that logic is entirely a priori. We might compare the geometry of land surfaces with 'pure' geometry. If numbers are independent objects, it is unclear how we could have any a priori knowledge of them.