The Axiom of Choice: Mathematics or Theology?
(2025) Philosophy & Theology — Vol. 37, n° 1&2, p. 35-60 (2025)
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- Through centuries, philosophers and theologians had tried to prove in many ways that God exists. Kurt Gödel gives once his own proof of existence of God based on modal logic S5 (since the modal formula □A → □A grounds the proof) and some assumptions about existence as a perfect property. Ultimately, Gödel’s ontological proof was a reforging of Leibniz’s modal proof. Mimicking Gödel, Robert K. Meyer, a distinguished logician of the last century, had re-worked and updated Aquinas’s First Three Ways (namely the versions of the ‘Cosmological Argument’ that respectively focus on the notions of change, causation and contingence) by us-ing some mathematical tools, namely set-theoretical ones as the Axiom of Choice and Zorn’s Lemma. Unfortunately, this proof is not as well-known as it merits to be, so I shall show how such a set-theoretical demonstration of the existence of God works, and what are its assump-tions. To do so, I will split my paper in two parts: first, a short discussion and, then, a proof of the Axiom of Choice in naïve-set-theory; second, a presentation and evaluation of the Mathe-matical Proofs (one cosmological due to Meyer, another ontological forged by Fisher) of the Existence of God based on the Axiom-of-Choice.
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Marion, F. (2025). The Axiom of Choice: Mathematics or Theology? Philosophy & Theology, 37(1&2), 35-60. https://hdl.handle.net/2078.5/276425 (Original work published 2025)