Full Idea
Frege's idea is that the logical notion of predication is enough to generate appropriate objects. Every predicate defines a class, which is in turn an object to which predicates apply; and the notion of a class can be used to generate arithmetic.
Gist of Idea
Frege said logical predication implies classes, which are arithmetical objects
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Morris - Guidebook to Wittgenstein's Tractatus 2H
Book Reference
Morris,Michael: 'Guidebook to Wittgenstein's Tractatus' [Routledge 2008], p.109
A Reaction
At last, a lovely clear account of what Frege was doing - and why Russell's paradox was Frege's disaster. Logicism must take the ingredients of logic, and generate arithmetical 'objects' from them alone. But do we need 'objects'?