Gödel's second incompleteness theorem
GPTKB entity
Statements (52)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:theorem
|
| gptkbp:bfsLayer |
4
|
| gptkbp:bfsParent |
gptkb:Kurt_Gödel
|
| gptkbp:allows |
formal proofs
|
| gptkbp:applies_to |
the foundations of mathematics
the philosophy of language consistent formal systems |
| gptkbp:challenges |
Hilbert's program
|
| gptkbp:consequences |
gptkb:Gödel's_completeness_theorem
|
| gptkbp:depicts |
the limits of axiomatic systems
|
| gptkbp:has_impact_on |
computability theory
the nature of mathematical knowledge |
| gptkbp:historical_debate |
incompleteness of formal systems
|
| https://www.w3.org/2000/01/rdf-schema#label |
Gödel's second incompleteness theorem
|
| gptkbp:illustrated_by |
gptkb:Gödel_numbering
|
| gptkbp:is_a_framework_for |
gptkb:philosopher
|
| gptkbp:is_analyzed_in |
the context of mathematical realism
|
| gptkbp:is_associated_with |
truth and provability
|
| gptkbp:is_cited_in |
discussions of mathematical truth
|
| gptkbp:is_connected_to |
the concept of undecidability
|
| gptkbp:is_critical_for |
the study of axiomatic systems
discussions of mathematical foundations |
| gptkbp:is_discussed_in |
self-reference
many philosophers academic papers on logic |
| gptkbp:is_explored_in |
graduate-level mathematics courses
|
| gptkbp:is_fundamental_to |
proof theory
|
| gptkbp:is_influential_in |
philosophical debates about mathematics
|
| gptkbp:is_often_associated_with |
the context of mathematical paradoxes
discussions of mathematical logic literature on formal logic philosophy of mathematics curricula |
| gptkbp:is_often_compared_to |
Turing's work on computability
|
| gptkbp:is_part_of |
gptkb:Gödel's_incompleteness_theorems
|
| gptkbp:is_related_to |
gptkb:Gödel's_first_incompleteness_theorem
|
| gptkbp:is_studied_in |
mathematical philosophy
|
| gptkbp:key |
theoretical computer science
the study of formal languages discussions of mathematical intuitionism |
| gptkbp:landmark |
20th-century mathematics
|
| gptkbp:published_by |
1931
|
| gptkbp:resulted_in |
gptkb:Kurt_Gödel
philosophy of mathematics |
| gptkbp:significance |
mathematical logic
|
| gptkbp:significant_event |
the history of mathematics
|
| gptkbp:state |
no consistent system can prove its own consistency
|
| gptkbp:subject |
the philosophy of science
research in mathematical logic debate among mathematicians intense academic interest |
| gptkbp:theme |
the study of mathematical logic.
|
| gptkbp:training |
advanced mathematics courses
|