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Full Idea
Quine's view of logical consequence is that it is when there is no way of uniformly substituting nonlogical expressions in the premises and consequences so that the premises all remain true but the consequence now becomes false.
Gist of Idea
Logical consequence is marked by being preserved under all nonlogical substitutions
Source
report of Willard Quine (Carnap and Logical Truth [1954], p.103) by Theodore Sider - Logic for Philosophy 1.5
Book Ref
Sider,Theodore: 'Logic for Philosophy' [OUP 2010], p.9
A Reaction
One might just say that the consequence holds if you insert consistent variables for the nonlogical terms, which looks like Aristotle's view of the matter.