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Full Idea
The 'completeness' of first order-logic does not mean that every sentence or its negation is provable in first-order logic. We have instead the weaker result that every valid sentence is provable.
Gist of Idea
First-order logic is weakly complete (valid sentences are provable); we can't prove every sentence or its negation
Source
Robert S. Wolf (A Tour through Mathematical Logic [2005], 5.3)
Book Ref
Wolf,Robert S.: 'A Tour Through Mathematical Logic' [Carus Maths Monographs 2005], p.174
A Reaction
Peter Smith calls the stronger version 'negation completeness'.