Combining Philosophers
Ideas for Melvin Fitting, Wilhelm Dilthey and Kurt Gdel
expand these ideas
|
start again
|
choose
another area for these philosophers
display all the ideas for this combination of philosophers
11 ideas
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17885
|
Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner]
|
10614
|
The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel]
|
3198
|
Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey]
|
10072
|
First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P]
|
9590
|
Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman]
|
11069
|
Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna]
|
10118
|
First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman]
|
10122
|
Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman]
|
10611
|
There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P]
|
10867
|
'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg]
|
10039
|
Some arithmetical problems require assumptions which transcend arithmetic [Gödel]
|