more from this thinker
|
more from this text
Single Idea 13538
[filed under theme 5. Theory of Logic / K. Features of Logics / 4. Completeness
]
Full Idea
It is valuable to know that a theory is complete, because then we know it cannot be strengthened without passing to a more powerful language.
Gist of Idea
If a theory is complete, only a more powerful language can strengthen it
Source
Robert S. Wolf (A Tour through Mathematical Logic [2005], 5.5)
Book Ref
Wolf,Robert S.: 'A Tour Through Mathematical Logic' [Carus Maths Monographs 2005], p.191
The
14 ideas
with the same theme
[all the truths of a system are formally deducible]:
9544
|
A system is 'weakly' complete if all wffs are derivable, and 'strongly' if theses are maximised
[Hughes/Cresswell]
|
19065
|
Soundness and completeness proofs test the theory of meaning, rather than the logic theory
[Dummett]
|
9720
|
A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity
[Enderton]
|
10763
|
Completeness and compactness together give axiomatizability
[Tharp]
|
10834
|
Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences
[Boolos]
|
10069
|
A theory is 'negation complete' if one of its sentences or its negation can always be proved
[Smith,P]
|
10598
|
A theory is 'negation complete' if it proves all sentences or their negation
[Smith,P]
|
10597
|
'Complete' applies both to whole logics, and to theories within them
[Smith,P]
|
13628
|
We can live well without completeness in logic
[Shapiro]
|
13698
|
In a complete logic you can avoid axiomatic proofs, by using models to show consequences
[Sider]
|
10127
|
A 'complete' theory contains either any sentence or its negation
[George/Velleman]
|
10161
|
If a sentence holds in every model of a theory, then it is logically derivable from the theory
[Feferman/Feferman]
|
13538
|
If a theory is complete, only a more powerful language can strengthen it
[Wolf,RS]
|
10761
|
Completeness can always be achieved by cunning model-design
[Rossberg]
|