Difference between revisions of "Gödel's completeness theorem"
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(Actually, it's real; it was just stated incorrectly. I fixed it and added another ref.) |
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'''Gödel's completeness theorem''' was proven by [[Kurt Gödel]], which states: | '''Gödel's completeness theorem''' was proven by [[Kurt Gödel]], which states: | ||
<blockquote> | <blockquote> | ||
| − | Any | + | Any proposition in [[mathematics]] is true only if it is [[sound]]; that is, if it can be proven to be true. <ref>http://www.math.uchicago.edu/~mileti/museum/complete.html</ref> |
</blockquote> | </blockquote> | ||
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The nature of The Completeness Theorem has far-reaching implications in the field of Theistic Creation. For instance, it is clear that God made the world, as only He could make first order logic complete. The soundness of the statement "God exists and is all things to all men" is proven within first-order predicates, meaning that The Completeness Theorem provides a mathematical proof for the existence and omnipotence of God. Kurt Gödel himself once claimed, "Even my surname is simply 'God,' with an added 'el' and an umlaut."<ref>http://www.godelandtheology.org/quotes/quote54.htm</ref> | The nature of The Completeness Theorem has far-reaching implications in the field of Theistic Creation. For instance, it is clear that God made the world, as only He could make first order logic complete. The soundness of the statement "God exists and is all things to all men" is proven within first-order predicates, meaning that The Completeness Theorem provides a mathematical proof for the existence and omnipotence of God. Kurt Gödel himself once claimed, "Even my surname is simply 'God,' with an added 'el' and an umlaut."<ref>http://www.godelandtheology.org/quotes/quote54.htm</ref> | ||
| + | {{reflist}} | ||
[[Category:Logic]][[category: mathematics]] | [[Category:Logic]][[category: mathematics]] | ||
Revision as of 17:35, December 9, 2009
Gödel's completeness theorem was proven by Kurt Gödel, which states:
Any proposition in mathematics is true only if it is sound; that is, if it can be proven to be true. [1]
Theological Implications
The nature of The Completeness Theorem has far-reaching implications in the field of Theistic Creation. For instance, it is clear that God made the world, as only He could make first order logic complete. The soundness of the statement "God exists and is all things to all men" is proven within first-order predicates, meaning that The Completeness Theorem provides a mathematical proof for the existence and omnipotence of God. Kurt Gödel himself once claimed, "Even my surname is simply 'God,' with an added 'el' and an umlaut."[2]