Ontological Argument (Anselm)

Anselm's argument, step by step

Anselm wrote the Proslogion as a single sustained meditation, addressed to God in the second person. He called it a fides quaerens intellectum — "faith seeking understanding." He was not trying to convince an unbeliever; he was trying to understand what he already believed. But the argument that emerges has been wielded against unbelief ever since.

The classic statement appears in Proslogion 2. The structure can be reconstructed as a deductive argument:

1. Definition. God is "that than which nothing greater can be conceived" (aliquid quo nihil maius cogitari possit).
2. The fool. Even the fool of Psalm 14 ("the fool says in his heart, there is no God") understands this definition — otherwise he could not deny it.
3. So God exists in the mind. Whatever is understood exists at least in the mind (in intellectu).
4. Premise. A being existing in reality (in re) is greater than the same being existing only in the mind.
5. Reductio. Suppose God existed only in the mind. Then we could conceive of something greater — namely the same being existing also in reality.
6. Contradiction. But that is impossible by the definition: nothing greater than God can be conceived.
7. Conclusion. God must exist in reality.

The argument's audacity is that it gets from a definition to existence without a single empirical premise. If it works, it does so by pure logic — no telescopes, no fossils, no testimony required.

Anselm's second move: necessary existence

Proslogion 3 strengthens the argument. Anselm argues that God exists not merely contingently but necessarily — God cannot be conceived not to exist. A being whose nonexistence is conceivable would be less great than one whose nonexistence is inconceivable. Since God is the greatest conceivable being, God's nonexistence must be inconceivable. So God exists necessarily.

Modern philosophers (Norman Malcolm in 1960; Charles Hartshorne earlier) have argued Proslogion 3 is the real ontological argument and far stronger than chapter 2. The reformulation is roughly: if God's existence is even possible, then since God is by definition a necessary being, God's existence is actual. (A merely possible necessary being is a contradiction in terms.) This sets up the modern modal versions.

Worked example: checking the structure

To see whether Anselm's argument is valid as stated, let G mean "God" and ">" mean "greater than":

P1. G = the being x such that ¬∃y (y > x)
P2. G ∈ Mind                              (the fool understands "G")
P3. ∀x ((x ∈ Mind ∧ x ∉ Reality) → ∃z (z > x))   ("real > merely-imagined")
P4. Suppose G ∉ Reality.                   (assumption for reductio)
P5. From P2, P4, P3: ∃z (z > G)
P6. P5 contradicts P1.
∴ G ∈ Reality.

The argument is valid — the conclusion follows from the premises. The question is whether the premises are true. Three premises are doing all the work:

• P1: that the definition of God picks out a coherent being. Critics: maybe "greatest conceivable being" is incoherent, like "largest integer."
• P2: that mere understanding of "G" puts God in the mind. Critics (Aquinas): we don't fully grasp the divine essence, so what we have in mind isn't really God.
• P3: that real existence makes a being greater. Critics (Kant): existence isn't a property, so it can't be a great-making property.

Most attacks on the ontological argument target one of these three premises.

Ontological vs cosmological vs teleological

	Ontological	Cosmological	Teleological
Type	A priori (definition)	A posteriori (existence)	A posteriori (design)
Starting point	The concept of God	That anything exists at all	The order in nature
Empirical input	None	Bare existence of the world	Specific features (eyes, laws, fine-tuning)
Form	Reductio from definition	From contingency or causation	Inference to best explanation
Classic proponent	Anselm, Descartes	Aquinas, Leibniz, Craig	Paley, modern fine-tuning
Concludes to	A maximally great being	A first cause / necessary being	An intelligent designer
Standard objection	Existence is not a predicate	Why must the chain end?	Hume: bad analogy; Darwin: alternative

Each argument tries to bridge a different gap. The ontological argument is the most ambitious — it claims to prove God from logic alone — and consequently the most controversial. Even theologians who accept the cosmological and teleological arguments often reject the ontological one. Aquinas himself, in Summa Theologiae I.2.1, rejects Anselm's argument (while accepting his Five Ways) on the ground that we don't know God's essence well enough to derive existence from it.

Gaunilo's lost island

The first major objection came from a contemporary, the Benedictine monk Gaunilo of Marmoutiers, in a short reply titled Pro Insipiente ("On Behalf of the Fool"). Gaunilo offered a parody:

Imagine an island somewhere in the ocean, more excellent than any other island. Define it as "that island than which no greater island can be conceived." Now, you understand this definition; the island therefore exists in your mind. But an island existing in reality would be greater than one existing only in the mind. Therefore, the lost island must exist in reality.

Since obviously no such island exists, the form of argument must be invalid. Gaunilo's parody is the canonical objection: the ontological argument "proves too much."

Anselm's reply, in his Responsio, distinguished God from islands. Only an absolutely greatest being — one without any limitation — has existence as part of its very nature. Islands, by being islands, are finite and limited. There is no upper bound on island-greatness (any island could be improved by being slightly larger or sandier), so "greatest conceivable island" is incoherent in a way "greatest conceivable being" is not. The objection assumes the parallel structure transfers; Anselm denies this.

Whether Anselm's reply succeeds is contested. Modern critics including J. L. Mackie argue Gaunilo's logic generalizes: any concept of a "perfect X" runs into the same difficulty.

Aquinas's and Kant's objections

Aquinas (Summa Theologiae I.2.1, ad 2) granted that if we understood God's essence as Anselm assumes, the argument might work. But we do not. Our concept of God is derived from God's effects (causality, motion, design), not from a direct grasp of essence. The argument therefore moves illegitimately from words to reality. Aquinas preferred a posteriori arguments — the Five Ways — which start from observable facts about the world and reason backward.

Kant delivered the most famous attack in the Critique of Pure Reason (1781), in the section "On the Impossibility of an Ontological Proof of the Existence of God." Kant's central claim: existence is not a real predicate (Sein ist offenbar kein reales Prädikat).

The thought is this: when you describe an object — "a triangle has three sides," "God is omnipotent" — you are listing properties that constitute the concept. When you then say "and it exists" or "God exists," you are not adding a further property; you are positing that there is an instance of the concept. "Existing" is not in the same logical category as "wise" or "powerful." A thaler in your pocket has the same predicates as a thaler you merely imagine — what differs is whether the concept is instantiated.

If existence is not a property, then it cannot be a "great-making" property, and step 4 of Anselm's argument collapses. Adding "existing in reality" to the concept of God does not improve the concept — it just claims an instance.

Kant's objection has been enormously influential, and most analytic philosophers consider it decisive against the classical version. But it is also contested: contemporary defenders argue Kant's point depends on a particular logical theory (where existence is captured by the existential quantifier), and the argument can be reformulated in modal logic where the issue is necessary existence, not bare existence.

Descartes's version

Descartes revived the argument in Meditation 5 (1641). His version is more streamlined and abstract:

1. God is, by definition, a supremely perfect being.
2. Existence is a perfection.
3. Therefore God has existence — i.e., God exists.

Descartes compares this to mathematical necessity: just as a triangle's three angles necessarily sum to two right angles, existence necessarily belongs to the supremely perfect being. To conceive of God lacking existence is as incoherent as conceiving of a valley without a mountain.

This is the version Kant primarily targeted. Leibniz refined it further, observing that Descartes assumed without proof that the concept of a supremely perfect being is coherent (i.e., that all perfections are mutually compatible). Leibniz tried to plug this gap with a separate argument that perfections, being simple positive properties, cannot conflict.

Plantinga's modal version

Alvin Plantinga's The Nature of Necessity (1974) recast the ontological argument in possible-worlds modal logic. The key concept is maximal greatness:

• A being has maximal excellence in a world W if it is omniscient, omnipotent, and morally perfect in W.
• A being has maximal greatness if it has maximal excellence in every possible world (i.e., necessarily).

The argument:

1. It is possible that maximal greatness is instantiated. (= there is some possible world W in which a maximally great being exists.)
2. If a maximally great being exists in W, it exists in every possible world (by definition of maximal greatness).
3. So it exists in the actual world.
4. Therefore a maximally great being actually exists.

The inference from "exists in some possible world" to "exists in every possible world" relies on the modal axiom S5, which says ◇□p ⟹ □p. S5 is the standard system for metaphysical necessity, and the inference is logically valid.

Plantinga himself was scrupulous. He explicitly said the argument does not prove God exists. It only shows that the rationality of believing in God reduces to the rationality of believing the possibility premise. The opponent must claim it is impossible for a maximally great being to exist — a much stronger claim than mere agnosticism. Whether this premise is more reasonable than its denial is, Plantinga concedes, ultimately a substantive judgment.

Critics (e.g., Graham Oppy, J. L. Mackie) reply with parody arguments: define a "maximally great no-being" — one that necessarily entails God's nonexistence. The parody has the same structure, so we can't accept Plantinga's possibility premise without good reason to reject the parody's possibility premise. The dialectic stalemates on intuitions about possibility.

Gödel's version

Kurt Gödel formulated a precise modal version (privately, in notes published posthumously in 1987). It uses higher-order modal logic and a few axioms about "positive properties": positive properties are closed under entailment, the conjunction of any positive properties is consistent, and necessary existence is positive. Gödel's argument is more rigorous than its predecessors and has been formally verified by automated theorem provers (Benzmüller and Paleo, 2013). The catch: it works only on the assumption that those axioms are correct, and several of them are contested.

Hume's broader skepticism

David Hume, in Dialogues Concerning Natural Religion (1779), didn't focus on the ontological argument specifically — his main targets were design and cosmological arguments — but his general principle bears on Anselm: "Whatever we conceive as existent, we can also conceive as non-existent. There is no being whose non-existence implies a contradiction." If Hume is right, no a priori argument for God's existence can succeed, because every existential claim is contingent. The ontological argument requires that some existential claim — God's — be necessary, which Hume's principle directly denies.

Variants and family members

• Anselm's Proslogion 2 (1078) — the classical version above.
• Anselm's Proslogion 3 — necessary existence; precursor to modal versions.
• Descartes's Fifth Meditation (1641) — existence as perfection.
• Spinoza, Ethics I, Prop. 11 (1677) — God's essence involves existence; pantheistic framing.
• Leibniz's repair (1676) — supplements Descartes by arguing the concept of God is consistent.
• Hegel (1827) — reads the ontological argument as expressing the unity of thought and being; not a proof in the standard sense.
• Hartshorne / Malcolm modal versions (1962, 1960) — necessary existence in S5.
• Plantinga's maximal greatness (1974) — the standard contemporary version.
• Gödel's ontological proof (published 1987) — formal modal logic with positive properties.

Common confusions

• "It's an argument from authority." No — the argument is purely deductive. It's actually the opposite of an argument from authority: no premise depends on revelation or tradition.
• "It proves any concept exists." Anselm's distinction with Gaunilo is precisely that only a maximally great being has the right structure for the argument to apply. Whether that distinction holds is what's contested.
• "Kant disproved it." Kant disproved the Cartesian version that treats existence as a predicate. Modal versions sidestep this by talking about necessary existence, which most contemporary philosophers do treat as a genuine modal property.
• "It assumes what it sets out to prove." The argument doesn't assume God exists — it assumes the concept of God is coherent. Critics dispute whether that assumption already smuggles in too much.
• "Believers don't actually use this argument." True for most believers, but the argument has been deployed seriously by Anselm, Descartes, Leibniz, Hegel, Hartshorne, Malcolm, Plantinga, Gödel, and Robert Adams. It is the intellectual high-wire act of theistic philosophy.
• "It's just word games." The argument is genuinely controversial — competent philosophers continue to defend and attack it. Calling it "word games" usually substitutes for engaging with the modal versions, which are technically rigorous.