Gödel's ontological proof
Gödel's formalization of the ontological argument for the existence of God using modal logic
| rdfs:label |
"Gödel's ontological proof"@en
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skos:alt |
"ゲーデルの神の存在論的証明"@ja
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| schema:description |
"Gödel's formalization of the ontological argument for the existence of God using modal logic"@en
|
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schema:date |
"2026-08-31T20:04:49+00:00"^^xsd:dateTime |
| schema:version | 2538725052 |
| wikibase:identifiers | 3 |
| wikibase:sitelinks | 13 |
| wikibase:statements | 11 |
| p:P13772 | wd:statement/Q598840-4B546CF1-3FC9-4649-B09F-4A12850646FA |
| p:P138 | wd:statement/q598840-539062e1-4746-abc8-9654-6c558fa70de4 |
| p:P2283 | wd:statement/Q598840-3b7e2c6c-4e39-b77e-8ea6-427e4c712af2 |
| p:P2534 | wd:statement/Q598840-b7717f50-4e25-dc00-8c08-49e828254d77 |
| p:P31 | wd:statement/Q598840-9008ae8b-49e2-60a4-e1aa-ed15acea2558 |
| wd:statement/Q598840-ce323425-4d2e-daa8-2d99-1534067670fa | |
| p:P575 | wd:statement/Q598840-353bab85-4234-ebe5-dab2-cca1f62afcc3 |
| p:P61 | wd:statement/Q598840-2739cb28-4053-bd67-853c-497d71fc1164 |
| p:P6104 | wd:statement/Q598840-759E9671-9BFC-4833-A33C-4FADD2ACC9C8 |
| p:P6366 | wd:statement/Q598840-EF83CFE9-98FC-4E14-AA2C-C771DE6CE0EA |
| p:P646 | wd:statement/Q598840-5F24825C-C3AB-4F89-8EC3-B5C71F0F2621 |
|
p:direct- |
<https:/ |
| wdt:P13772 | "ontological-proof-of-god" |
| wdt:P138 | Kurt Gödel |
| wdt:P2283 | modal logic |
| wdt:P2534 | "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable columnspacing="1em" rowspacing="4pt" columnalign="right left "><mtr><mtd><mi>A</mi><mn>1</mn></mtd><mtd><mo stretchy="false">(</mo><mi>P</mi><mo stretchy="false">(</mo><mi>p</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi>◻</mi><mi mathvariant="normal">∀</mi><mi>x</mi><mo stretchy="false">(</mo><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false" accent="false">→</mo><mi>q</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false" accent="false">→</mo><mi>P</mi><mo stretchy="false">(</mo><mi>q</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mn>2</mn></mtd><mtd><mi>P</mi><mo stretchy="false">(</mo><mi mathvariant="normal">¬</mi><mi>p</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>⟺</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mi mathvariant="normal">¬</mi><mi>P</mi><mo stretchy="false">(</mo><mi>p</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>T</mi><mn>1</mn></mtd><mtd><mi>P</mi><mo stretchy="false">(</mo><mi>p</mi><mo stretchy="false">)</mo><mo stretchy="false" accent="false">→</mo><mi>◊</mi><mi mathvariant="normal">∃</mi><mi>x</mi><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>D</mi><mn>1</mn></mtd><mtd><mi>G</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>⟺</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mi mathvariant="normal">∀</mi><mi>p</mi><mo stretchy="false">(</mo><mi>P</mi><mo stretchy="false">(</mo><mi>p</mi><mo stretchy="false">)</mo><mo stretchy="false" accent="false">→</mo><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mn>3</mn></mtd><mtd><mi>P</mi><mo stretchy="false">(</mo><mi>G</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>T</mi><mn>2</mn></mtd><mtd><mi>◊</mi><mi mathvariant="normal">∃</mi><mi>x</mi><mi>G</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>D</mi><mn>2</mn></mtd><mtd><mi>S</mi><mo stretchy="false">(</mo><mi>p</mi><mo>,</mo><mi>x</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>⟺</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">∧</mo><mi mathvariant="normal">∀</mi><mi>q</mi><mo stretchy="false">(</mo><mi>q</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false" accent="false">→</mo><mi>◻</mi><mi mathvariant="normal">∀</mi><mi>y</mi><mo stretchy="false">(</mo><mi>p</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false" accent="false">→</mo><mi>q</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mn>4</mn></mtd><mtd><mi>P</mi><mo stretchy="false">(</mo><mi>p</mi><mo stretchy="false">)</mo><mo stretchy="false" accent="false">→</mo><mi>◻</mi><mi>P</mi><mo stretchy="false">(</mo><mi>p</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>T</mi><mn>3</mn></mtd><mtd><mi>G</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false" accent="false">→</mo><mi>S</mi><mo stretchy="false">(</mo><mi>G</mi><mo>,</mo><mi>x</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>D</mi><mn>3</mn></mtd><mtd><mi>E</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>⟺</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mi mathvariant="normal">∀</mi><mi>p</mi><mo stretchy="false">(</mo><mi>S</mi><mo stretchy="false">(</mo><mi>p</mi><mo>,</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false" accent="false">→</mo><mi>◻</mi><mi mathvariant="normal">∃</mi><mi>y</mi><mi>p</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mn>5</mn></mtd><mtd><mi>P</mi><mo stretchy="false">(</mo><mi>E</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>T</mi><mn>4</mn></mtd><mtd><mi>◻</mi><mi mathvariant="normal">∃</mi><mi>x</mi><mi>G</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mtd></mtr></mtable></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P31 | mathematical proof |
| ontological argument | |
| wdt:P575 | "1941-01-01T00:00:00+00:00"^^xsd:dateTime |
| wdt:P61 | Kurt Gödel |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "2778817621" |
| wdt:P646 | "/m/03855" |
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