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5. Theory of Logic / K. Features of Logics / 4. Completeness

[all the truths of a system are formally deducible]

14 ideas
A system is 'weakly' complete if all wffs are derivable, and 'strongly' if theses are maximised [Hughes/Cresswell]
Soundness and completeness proofs test the theory of meaning, rather than the logic theory [Dummett]
A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton]
Completeness and compactness together give axiomatizability [Tharp]
Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
A theory is 'negation complete' if one of its sentences or its negation can always be proved [Smith,P]
A theory is 'negation complete' if it proves all sentences or their negation [Smith,P]
'Complete' applies both to whole logics, and to theories within them [Smith,P]
We can live well without completeness in logic [Shapiro]
In a complete logic you can avoid axiomatic proofs, by using models to show consequences [Sider]
A 'complete' theory contains either any sentence or its negation [George/Velleman]
If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman]
If a theory is complete, only a more powerful language can strengthen it [Wolf,RS]
Completeness can always be achieved by cunning model-design [Rossberg]