Godel
Proved systems' limits
Gödel refers to Kurt Gödel (1906–1978), the Austrian-American logician and mathematician whose incompleteness theorems revolutionized mathematical logic.
His theorems demonstrated that any consistent formal system capable of expressing basic arithmetic contains true statements that cannot be proved within that system.
Gödel's proof shattered the dream of a complete mathematical foundation.
The name appears in philosophical discussions of the limits of formal reasoning and artificial intelligence.
State of lacking parts
- theoremDemonstrated logical conclusion
- proofDemonstration of truth
- consistencyReliable adherence to standards
- undecidableLacking possible proof
formal · axiom · arithmetic · mathematics · decidability · completeness · soundness · recursion
Philosophy emphasizing ideal Forms
- realismAccepting things as they are
- intuitionInstinctive immediate understanding
- truthAccordance with reality
- existenceState of being real
abstract · mathematical · ontology · certainty · knowledge · objectivity · idealism · metaphysics
Austrian capital
- AustriaCentral European alpine republic
- PrincetonIvy League university
- EinsteinByword for genius
- emigrationLeaving homeland permanently
citizenship · naturalization · Adele · paranoia · starvation · genius · prodigy · recluse
- ChurchOrganized religious denomination
- computabilityAlgorithmic solvability of problems
- haltingMarked by hesitation
- algorithmsFinite instruction sequences
Tarski · limits · foundations · crisis · revolution · modernism · twentieth-century · breakthrough
incompleteness
State of lacking parts
- theoremDemonstrated logical conclusion
- proofDemonstration of truth
- consistencyReliable adherence to standards
undecidable · formal · axiom · arithmetic · mathematics · decidability · completeness · soundness · recursion · provability
Platonism
Philosophy emphasizing ideal Forms
- realismAccepting things as they are
- intuitionInstinctive immediate understanding
- truthAccordance with reality
existence · abstract · mathematical · ontology · certainty · knowledge · objectivity · idealism · metaphysics · consciousness
Vienna
Austrian capital
emigration · citizenship · naturalization · Adele · paranoia · starvation · genius · prodigy · recluse · friendship
Turing
- ChurchOrganized religious denomination
- computabilityAlgorithmic solvability of problems
- haltingMarked by hesitation
Tarski · algorithms · limits · foundations · crisis · revolution · modernism · twentieth-century · breakthrough · landmark
GodelEinstein
Byword for genius
Bohr · Heisenberg · Feynman · physicist · empiricist
- Kurt GodelProved math's limits