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Full Idea
There is a 'primitivist' account, according to which logical consequence is a primitive notion.
Gist of Idea
Maybe logical consequence is a primitive notion
Source
Theodore Sider (Logic for Philosophy [2010], 1.5)
Book Ref
Sider,Theodore: 'Logic for Philosophy' [OUP 2010], p.9
A Reaction
While sympathetic to substitutional views (Idea 13674), the suggestion here pushes me towards thinking that truth must be at the root of it. The trouble, though, is that a falsehood can be a good logical consequence of other falsehoods.