Ontological Arguments

Ontological arguments are arguments for the conclusion that God exists from premises supposed to derive from reason alone — from what are typically alleged to be analytic, a priori, and necessary premises, rather than from observation of the world. The first and best-known ontological argument was proposed by Anselm of Canterbury in the eleventh century, who derived the existence of that than which no greater can be conceived from the very concept of such a being. ¹

A Simplifying Introduction

An ontological argument tries to show that God’s existence follows from the very concept of God — no empirical evidence needed. Anselm’s version: God is “that than which nothing greater can be conceived.” If such a being existed only in the mind, then a greater being could be conceived — one that exists in reality too. But nothing can be greater than God. Therefore, God must exist in reality. Two famous later versions:

• Descartes’ version: God has every perfection; existence is a perfection; therefore God exists.
• Modal version (Leibniz, Plantinga): If God’s existence is possible, then God exists necessarily (via S5’s ◇□A → □A reduction). See s5-modal-logic and gottfried-wilhelm-leibniz.

The core philosophical puzzle: can you reason your way from a definition to the existence of something in the world? Critics (most famously Kant) argue that “existence is not a predicate” — you cannot build existence into a concept and then claim it exists. ¹

The Modal Ontological Argument (MOA)

The modal ontological argument proceeds from God’s possible existence to God’s actual existence. Standard formulations (Malcolm 1960, Hartshorne 1965, Plantinga 1974) share four parts: ¹

1. Characterisation of the being: typically a maximally great being — one that exists necessarily and is essentially omnipotent, omniscient, and morally perfect (Plantinga 1974).
2. Possibility premise: the characterised being is metaphysically possible.
3. Necessity premise: in any possible world in which the being exists, it is necessary that it exists.
4. A modal logic strong enough to validate the inference from possible necessary existence to necessary existence — typically S5, whose characteristic axiom ◇p → □◇p entails ◇□p → □p. (A weaker system like B validates ◇□p → p and could be used instead.)

The argument runs:

i. Possibly, God exists. (Possibility premise) ii. Necessarily, if God exists, then it is necessary that God exists. (Necessity premise) iii. Hence, it is necessary that God exists.

From (i) and (ii), there is some possible world where God exists necessarily — i.e., it is possibly necessary that God exists. By S5’s ◇□p → □p, it is necessary that God exists. By axiom (M) (□p → p), God exists simpliciter. ¹

This is precisely the argument alvin-plantinga defends and gottfried-wilhelm-leibniz anticipated with his dictum: “If a necessary being is possible, it follows that it exists actually.”

Ways to Challenge the MOA

There are three corresponding challenges, one per part: ¹

1. Challenge the modal logic: dispute whether S5 accurately captures metaphysical modality (Chandler 1976, Salmon 1989). Defenders include Pruss & Rasmussen 2018, Williamson 2016, Hale 2013.
2. Challenge the necessity premise: while “maximally great being” makes the premise definitionally true, other characterisations (e.g., “perfect being”) require substantive argument that necessary existence is a great-making property.
3. Challenge the possibility premise: this is where the action usually lies — can we really assert that a maximally great being is possible? Proving real (metaphysical) possibility is much harder than proving logical consistency. This connects directly to the possibilism-actualism debate about the status of possible objects.

General Objections

The SEP’s general assessment is that none of the extant ontological arguments is persuasive — each is either invalid, has premises no reasonable non-theist should accept, or yields a conclusion with no religious significance. However, it remains an open question whether some hitherto undiscovered argument could succeed; there is fairly widespread consensus, even amongst theists, that no known ontological argument is successful in giving non-theists reason to accept its conclusion. ¹

Common objections alleged to explain the failure of (some) ontological arguments:

• Existence is not a predicate (Kant): existence adds nothing to the concept of a thing, so it cannot be a perfection.
• The argument begs the question (Gaunilo): one could “prove” the existence of any conceivable perfect thing (e.g., a perfect island) by the same reasoning.
• Conflation of logical and metaphysical possibility: consistency of the concept does not establish real possibility.
• Failure of the S5 reduction in multimodal contexts: “possibly necessary in the epistemic sense” does not entail “necessary in the alethic sense.” ¹

History and Key Figures

• Anselm of Canterbury (11th c.) — Proslogion II: the first ontological argument.
• René Descartes (17th c.) — the Cartesian version: God has every perfection; existence is a perfection.
• Gottfried Wilhelm Leibniz (17th–18th c.) — modal version; “If a necessary being is possible, it follows that it exists actually.” See gottfried-wilhelm-leibniz.
• Immanuel Kant (18th c.) — the “existence is not a predicate” objection.
• Gödel (20th c.) — formalised a complex modal ontological argument in higher-order modal logic.
• Plantinga (1974) — contemporary modal version based on possible worlds semantics; see alvin-plantinga and kripke-semantics.
• Hegel — dialectical version in the 19th century.

Relationship to the Wiki’s Modal Logic Cluster

Ontological arguments are the philosophical payoff of the s5-modal-logic reduction principle ◇□A → □A. The possibilism-actualism debate determines whether the possibility premise is metaphysically respectable, and kripke-semantics provides the formal framework in which the argument is stated. See also humes-argument-against-miracles for the contrasting empirical argument strategy.

See Also

• s5-modal-logic — The modal system whose ◇□A → □A validates the MOA
• gottfried-wilhelm-leibniz — Originated the modal ontological argument
• alvin-plantinga — Contemporary defender of the modal ontological argument
• possibilism-actualism — Metaphysical backdrop for the possibility premise
• kripke-semantics — Possible worlds framework in which the argument is stated
• modal-logic — The family of modal logics underlying the argument
• fine-tuning-argument — The leading a posteriori (physical) argument for theism, complementing this a priori family

References

• Oppy, G. (2024). “Ontological Arguments.” Stanford Encyclopedia of Philosophy. ¹
• Anselm. Proslogion (1078).
• Plantinga, A. (1974). The Nature of Necessity. Oxford University Press.
• Malcolm, N. (1960). “Anselm’s Ontological Arguments.” Philosophical Review, 69(1), 41–62.
• Hartshorne, C. (1965). Anselm’s Discovery. Open Court.
• Kant, I. Critique of Pure Reason (1781/1787), “The Impossibility of an Ontological Proof.”

Footnotes

1. raw/articles/sep-ontological-arguments.md ↩ ↩² ↩³ ↩⁴ ↩⁵ ↩⁶ ↩⁷ ↩⁸