Full Idea
The thesis that principles of arithmetic are derivable from the laws of logic runs against a now common view that logic itself has no ontology. There are no particular logical objects. From this perspective logicism is a non-starter.
Gist of Idea
Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own
Source
Stewart Shapiro (Thinking About Mathematics [2000], 5.1)
Book Reference
Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.113
A Reaction
This criticism strikes me as utterly devastating. There are two routes to go: prove that logic does have an ontology of objects (what would they be?), or - better - deny that arithmetic contains any 'objects'. Or give up logicism.