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.

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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

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Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

Kurt Gödel notableIdea Gödel's ontological proof
Gödel's ontological proof hasVariant Gödel's ontological proof self-linksurface differs
this entity surface form: Dana Scott's version of Gödel's ontological argument