Gödel's ontological proof
E100625
Gödel's ontological proof is a formal, modal-logic-based argument for the existence of God that rigorously develops and refines earlier ontological arguments within a precise axiomatic framework.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Dana Scott's version of Gödel's ontological argument | 1 |
| Gödel's ontological proof canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T839974 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
Target entity: Gödel's ontological proof Context triple: [Kurt Gödel, notableIdea, Gödel's ontological proof]
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A.
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two fundamental results in mathematical logic showing that any sufficiently powerful, consistent formal system cannot prove all true statements about arithmetic, and cannot prove its own consistency.
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B.
Remarks on the Foundations of Mathematics
Remarks on the Foundations of Mathematics is a posthumously published collection of Ludwig Wittgenstein’s later writings that critically examines the nature of mathematical truth, proof, and practice from a philosophical and language-centered perspective.
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C.
Hilbert’s program
Hilbert’s program was an influential early-20th-century initiative in the foundations of mathematics that sought to formalize all of mathematics and prove its consistency using finitistic methods.
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D.
The Logical Structure of the World
The Logical Structure of the World is Rudolf Carnap’s seminal 1928 work in which he develops a rigorous, formal reconstruction of all scientific concepts from a phenomenalist basis, serving as a foundational text of logical positivism.
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E.
Tarski's undefinability theorem
Tarski's undefinability theorem is a fundamental result in mathematical logic showing that, in sufficiently strong formal systems, the notion of truth for the language of the system cannot be defined within that same language.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Target entity: Gödel's ontological proof Target entity description: Gödel's ontological proof is a formal, modal-logic-based argument for the existence of God that rigorously develops and refines earlier ontological arguments within a precise axiomatic framework.
-
A.
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two fundamental results in mathematical logic showing that any sufficiently powerful, consistent formal system cannot prove all true statements about arithmetic, and cannot prove its own consistency.
-
B.
Remarks on the Foundations of Mathematics
Remarks on the Foundations of Mathematics is a posthumously published collection of Ludwig Wittgenstein’s later writings that critically examines the nature of mathematical truth, proof, and practice from a philosophical and language-centered perspective.
-
C.
Hilbert’s program
Hilbert’s program was an influential early-20th-century initiative in the foundations of mathematics that sought to formalize all of mathematics and prove its consistency using finitistic methods.
-
D.
The Logical Structure of the World
The Logical Structure of the World is Rudolf Carnap’s seminal 1928 work in which he develops a rigorous, formal reconstruction of all scientific concepts from a phenomenalist basis, serving as a foundational text of logical positivism.
-
E.
Tarski's undefinability theorem
Tarski's undefinability theorem is a fundamental result in mathematical logic showing that, in sufficiently strong formal systems, the notion of truth for the language of the system cannot be defined within that same language.
- F. None of above. chosen
Statements (52)
| Predicate | Object |
|---|---|
| instanceOf |
argument for the existence of God
ⓘ
formal proof ⓘ modal argument ⓘ ontological argument ⓘ philosophical argument ⓘ |
| aimsToShow | existence of God is logically necessary ⓘ |
| assumes | S5 modal logic axioms or a system close to S5 ⓘ |
| basedOn | modal logic ⓘ |
| centralConcept |
God as a maximally great being
ⓘ
necessary existence ⓘ positive properties ⓘ |
| concludes |
a God-like being exists necessarily if it is possible
ⓘ
if a God-like being is possible, then it exists in all possible worlds ⓘ |
| creator | Kurt Gödel ⓘ |
| criticizedFor |
controversial notion of positive properties
ⓘ
possible modal collapse ⓘ reliance on strong modal axioms such as S5 ⓘ |
| field |
metaphysics
ⓘ
modal metaphysics ⓘ philosophical logic ⓘ philosophy of religion ⓘ |
| firstMajorPublication | Dana Scott's version circulated in the 1970s ⓘ |
| formalizationYear | 1941 ⓘ |
| furtherDevelopmentPeriod | 1940s ⓘ |
| hasComponent |
axioms about positive properties
ⓘ
definitions of God-like being ⓘ definitions of essence ⓘ definitions of necessary existence ⓘ theorems about possible and necessary existence ⓘ |
| hasFormalization | computer-verified proof in higher-order logic ⓘ |
| hasVariant |
Anderson's emendation of Gödel's ontological argument
ⓘ
Gödel's ontological proof self-linksurface differs ⓘ
surface form:
Dana Scott's version of Gödel's ontological argument
Hájek's analysis and variants ⓘ |
| inspiredBy |
Anselm of Canterbury's ontological argument
ⓘ
Leibniz's version of the ontological argument ⓘ |
| languageOfOriginalNotes | German ⓘ |
| manuscriptsCirculated | privately during Gödel's lifetime ⓘ |
| notablePublication |
appeared in print in the 1970s
ⓘ
appeared in print in the 1980s ⓘ |
| preservedIn | Gödel's Nachlass (literary estate) ⓘ |
| relatedTo |
Anselm's Proslogion
ⓘ
Leibniz's metaphysics of modality ⓘ
surface form:
Leibniz's ontological argument
|
| subjectOf |
extensive philosophical debate
ⓘ
formal logical analysis ⓘ |
| usesConcept |
essence
ⓘ
necessary existence as a property ⓘ possible world semantics ⓘ |
| usesLogicSystem | higher-order modal logic ⓘ |
| verifiedBy | automated theorem provers ⓘ |
| verifiedIn |
Coq
ⓘ
Isabelle/HOL: A Proof Assistant for Higher-Order Logic ⓘ
surface form:
Isabelle/HOL
other higher-order proof assistants ⓘ |
How these facts were elicited
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Subject: Gödel's ontological proof Description of subject: Gödel's ontological proof is a formal, modal-logic-based argument for the existence of God that rigorously develops and refines earlier ontological arguments within a precise axiomatic framework.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.