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Argument

Gödel's ontological proof

Overview

Gödel's ontological proof is a formal argument by the mathematician Kurt Gödel (1906–1978) for the existence of God. The argument is in a line of development that goes back to Anselm of Canterbury (1033–1109). St. Anselm's ontological argument, in its most succinct form, is as follows: God, if He does exist, is that for which no greater can be conceived. God exists in the understanding. If God exists in the understanding, we could imagine Him to be greater by existing in reality. Therefore, God must exist. A more elaborate version was given by Gottfried Leibniz (1646–1716); this is the version that Gödel studied and attempted to clarify with his ontological argument.

The argument uses modal logic, which deals with statements about what is necessarily true or possibly true. From the axioms that a property can only be positive if not-having-it is not positive, and that properties implied by a positive property must all also be themselves positive, it concludes that (since positive properties do not involve contradiction) for any positive property, there is possibly a being that instantiates it. It defines God as the being instantiating all positive properties. After defining what it means for a property to be "the essence" of something (the one property that necessarily implies all its other properties), it concludes that God's instantiation of all positive properties must be the essence of God. After defining a property of "necessary existence" and taking it as an axiom that it is positive, the argument concludes that, since God must have this property, God must exist necessarily.

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

Possible passages

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  1. That gives rise to these eternal, and usually mistaken, contentions on necessity and contingency, on the possible and the impossible. But provided that it is understood that necessity and possibility, taken metaphysically and strictly, depend solely upon this question, whether the object in itself or that which is opposed to it implies contradiction or not; and that one takes into account that contingency is…

    Gottfried Wilhelm Leibniz, Theodicy Essays on the Goodness of God, the Freedom of Man and the Origin of Evil

    States what Gödel's ontological proof is; the author is tied to Gödel's ontological proof in the knowledge graph.

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  2. The minor contains an experience, the major reasons from a general experience to the existence of a necessary being.[68] Thus this argument really begins at experience, and is not completely à priori, or ontological. The object of all possible experience being the world, it is called the cosmological proof. It contains no reference to any peculiar property of sensuous objects, by which this world of sense might be…

    Immanuel Kant, The Critique of Pure Reason

    States what Gödel's ontological proof is.

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  3. Twenty-five of the propositions which are employed in the proof for the existence of God, or in the arguments demonstrating that God is neither corporeal nor a force connected with a material being, or that He is One, have been fully established, and their correctness is beyond doubt. Aristotle and the Peripatetics who followed him have proved each of these propositions. There is, however, one proposition which we…

    Moses Maimonides, The guide for the perplexed

    States what Gödel's ontological proof is.

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Philosophers who discussed Gödel's ontological proof

Related ideas

Place in the tradition

Part of Higher-order logic.

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