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Full Idea
Sentential logic has been proved consistent and complete; its consistency means that no contradictions can be derived, and its completeness assures us that every one of the logical truths can be proved.
Gist of Idea
Sentential logic is consistent (no contradictions) and complete (entirely provable)
Source
Alex Orenstein (W.V. Quine [2002], Ch.5)
Book Ref
Orenstein,Alex: 'W.V. Quine' [Princeton 2002], p.98
A Reaction
The situation for quantificational logic is not quite so clear (Orenstein p.98). I do not presume that being consistent and complete makes it necessarily better as a tool in the real world.