Dana Scott Archives

More Generally: Contemporary Thinkers (160)

September 2, 2010

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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