Gödel's second incompleteness theorem
GPTKB entity
Statements (52)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:theorem
|
| gptkbp:applies_to |
consistent formal systems
|
| gptkbp:challenges |
Hilbert's program
|
| gptkbp:consequences |
gptkb:Gödel's_completeness_theorem
|
| gptkbp:demonstrates_limitations_of |
formal proofs
|
| gptkbp:depicts |
the limits of axiomatic systems
|
| gptkbp:has_implications_for |
computability theory
the nature of mathematical knowledge |
| https://www.w3.org/2000/01/rdf-schema#label |
Gödel's second incompleteness theorem
|
| gptkbp:illustrated_by |
gptkb:Gödel_numbering
|
| gptkbp:is_a_foundation_for |
gptkb:Logic
|
| gptkbp:is_a_foundational_result_in |
philosophy of mathematics
|
| gptkbp:is_a_landmark_result_in |
20th-century mathematics
|
| gptkbp:is_a_significant_result_in |
the history of mathematics
|
| gptkbp:is_a_subject_of |
the philosophy of science
research in mathematical logic debate among mathematicians intense academic interest |
| gptkbp:is_analyzed_in |
the context of mathematical realism
|
| gptkbp:is_applied_in |
the foundations of mathematics
|
| 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_debated_in |
incompleteness of formal systems
|
| gptkbp:is_discussed_in |
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_compared_to |
Turing's work on computability
|
| gptkbp:is_often_discussed_in |
self-reference
|
| gptkbp:is_often_referenced_in |
the context of mathematical paradoxes
discussions of mathematical logic literature on formal logic |
| gptkbp:is_part_of |
gptkb:Gödel's_incompleteness_theorems
|
| gptkbp:is_related_to |
gptkb:Gödel's_first_incompleteness_theorem
|
| gptkbp:is_relevant_to |
the philosophy of language
|
| gptkbp:is_significant_for |
mathematical logic
|
| gptkbp:is_studied_in |
mathematical philosophy
|
| gptkbp:is_taught_in |
advanced mathematics courses
|
| gptkbp:key |
the study of formal languages
|
| gptkbp:key_concept |
theoretical computer science
|
| gptkbp:key_feature |
discussions of mathematical intuitionism
|
| gptkbp:main_theme |
the study of mathematical logic.
|
| gptkbp:often_includes |
philosophy of mathematics curricula
|
| gptkbp:published_by |
1931
|
| gptkbp:state |
no consistent system can prove its own consistency
|
| gptkbp:was_a_result_of |
gptkb:Kurt_Gödel
|
| gptkbp:bfsParent |
gptkb:Kurt_Gödel
|
| gptkbp:bfsLayer |
5
|