Full Idea
Two modern approaches to logicism are the quantificational approach of David Bostock, and the abstraction-free approach of Neil Tennant.
Gist of Idea
Logicism might also be revived with a quantificational approach, or an abstraction-free approach
Source
B Hale / C Wright (Logicism in the 21st Century [2007], 1 n2)
Book Reference
'Oxf Handbk of Philosophy of Maths and Logic', ed/tr. Shapiro,Stewart [OUP 2007], p.167
A Reaction
Hale and Wright mention these as alternatives to their own view. I merely catalogue them for further examination. My immediate reaction is that Bostock sounds hopeless and Tennant sounds interesting.