Modal Collapse: Sobel's Objection to Gödel's Ontological Argument
The last ontological argument Sobel discusses is the Leibniz-inspired argument put forward by the famous logician Kurt Gödel. Gödel sets up a formal system in third-order quantified modal logic with equality and abstraction (!) and proves within that system the theorem: □∃xG(x) Where the predicate G is defined as follows: Gx ↔ ∀φ[P(φ) → φ(x)] Where P is primitive. (Sobel includes the complete source texts for Gödel's proof on pp. 144-146.) Now, unsurprisingly, given that the proof was originated by Gödel, everyone agrees that the proof is valid in the formal system. The question is whether there are any interpretations...
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Topic(s):
Contemporary Thinkers
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Dana Scott
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Existence of God
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G. W. Leibniz
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Historical Thinkers
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Jordan Howard Sobel
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Kurt Gödel
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Metaphysics
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Modality
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Ontological Argument
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Philosophy
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Philosophy of Religion
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