Questions Does God exist?If it is possible, it exists: the modal ontological argument

Does God exist?TheismOntological

If it is possible, it exists: the modal ontological argument

The modal ontological argument

Alvin Plantinga born 1932Belief in God can be rational without proof, and evil does not make it incoherent.

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What it claims

A maximally great being exists in the actual world: God exists, and even necessarily.

Why

A maximally great being is possible, so it exists in some possible world; if it exists in one world, it exists in all.

The same idea through history

Anselme de Cantorbéry1078Proslogion, chapter III: God cannot even be thought not to exist. This is already an idea of necessary existence, the seed of the modal form.

Norman Malcolm1960"Anselm's Ontological Arguments": Anselm's first argument fails, but the second, based on necessary existence, would hold.

Charles Hartshorne1962The Logic of Perfection: he writes the proof in modern modal logic, with the operators "possible" and "necessary".

Kurt Gödel1970Notes of 1970, published in 1987: God has all "positive" properties. Same modal structure, with S5, but another way of showing that God is possible.

Alvin Plantinga1974The Nature of Necessity and God, Freedom, and Evil: the version with possible worlds and the "maximally great being", the most discussed today.

In short

"If it is possible, it exists: the modal ontological argument" is an argument by Alvin Plantinga (The Nature of Necessity, ch. X; God, Freedom, and Evil (1974), 1974) on the question "Does God exist?" (answer: theism). Its claim: A maximally great being exists in the actual world: God exists, and even necessarily. According to AskPhilosophy's logic check (Z3 solver), the argument is valid only if one grants a premise the author leaves unstated (P4). AskPhilosophy presents 4 objections, 3 of them with a documented reply, and the original text behind each premise, checked word for word.

The Nature of Necessity, ch. X; God, Freedom, and Evil (1974)

Valid with an implicit premise

Kant had objected that existence is not a perfection one can draw out of a concept. In the 20th century, several philosophers (Malcolm, Hartshorne, Gödel, Plantinga) take up Anselm's proof with a new tool: the logic of possible worlds. A "possible world" is a complete way things could have been. A "maximally great" being is defined as a being that is all-powerful, all-knowing and perfectly good in every possible world. The idea: if it is merely possible that such a being exists, then it really exists. Plantinga himself does not say the argument proves God; he says it shows that believing in God is rational.

click a premise to reject it

If you accept every premise, logic forces you to accept the conclusion. So the debate is about the premises.

Checked by a logic solver: the premises cannot all be true while the conclusion is false.
Without the implicit premise: Without P4, the computer finds a two-world model: our world sees a world W where a maximally great being exists, but W does not see our world (in the model found, it sees no world at all). Seen from W, this being exists "everywhere", but that "everywhere" does not include our world, where it does not exist.

The computer confirms that the argument is valid with P4, and invalid without it. Here is why S5 matters. P2 places the maximally great being in a possible world W. P3 says that, seen from W, it exists in every world. But do "all the worlds seen from W" include our world? Only if worlds see one another (that is symmetry, at the heart of S5). In S5, what is possibly necessary is simply necessary. All the force of the argument is therefore in P1: once you accept that God is possible, logic does the rest. Beware: the same logic works the other way. If you accept instead "it is possible that no maximally great being exists", S5 leads to "such a being is impossible". The argument is valid; the whole debate is about P1.

Analogy. Imagine a rule that says of itself: "if I hold in one single country, I hold in every country". If all countries share the same list of countries (S5), it is enough for it to hold in one for it to hold here. The whole question becomes: does it really hold anywhere? You cannot check that by looking only at the rule.

Objections

Each objection is a conversation: click to see who replies and where the debate stands.

The symmetric parody (Oppy, Rasmussen and Schmid, Stanford Encyclopedia) 2024 · attacks premise 1

One can write the argument backwards: "it is possible that no maximally great being exists". With the same P3 and the same S5 logic, one concludes that such a being is impossible. Both starting premises seem as plausible as each other, and they cannot both be true. Without a reason to prefer the first, the argument does not move the debate between believers and non-believers forward. This objection has been discussed since the 1970s (van Inwagen 1977, Tooley 1981).

Plantinga replies

Alvin Plantinga 1974 · Plantinga's reply (written as early as 1974)

Plantinga grants the point: these arguments cannot perhaps be said to "prove" their conclusion. But since it is rational to accept their central premise, they show that it is rational to accept their conclusion. The aim is therefore not to force the atheist to believe, but to show that the believer is not irrational.

Graham Oppy, Joshua Rasmussen and Joseph Schmid 2024

Even this more modest aim is not achieved. Someone who thinks it is not rational to believe in God also thinks it is not rational to believe at least one premise of the argument. The reasons that stop the argument from convincing the atheist therefore also stop it from convincing that belief is rational.

The debate goes on (our summary) Present-day defenders (for instance Pruss and Rasmussen, 2018) therefore look for a "symmetry breaker": an independent reason to think God is possible rather than impossible. But each proposed reason in fact becomes a new argument, to be judged on its own.

Where the debate stands (our summary)The basic disagreement concerns the possibility premise (P1). Plantinga sees it as a premise that is rational to accept; Oppy and his co-authors judge that without an independent reason to prefer it to its opposite, it only convinces those who already believe. The search for a "symmetry breaker" is ongoing, with no universally accepted result.

William L. Rowe 2009 · attacks premise 1

The premise "a maximally great being is possible" is true only if God really exists. For such a being, if possible, exists in every world. Accepting P1 is therefore already accepting the conclusion: the argument goes in a circle (it "begs the question").

no reply

We have not yet found a direct reply by Plantinga in the texts.

The debate goes on (our summary) Defenders reply that in every valid argument the premises can be true only if the conclusion is: that is not enough to make it circular. What matters is whether one can have reasons to accept P1 without already believing in God. Critics reply that for P1 we have no such independent reasons. Seeing no contradiction in the idea of God does not show that he is possible in the strong sense the argument needs. And, as the Stanford Encyclopedia sums it up, if you do not already accept that God exists, you will not find P1 more acceptable than the reverse premise (see the first objection).

Where the debate stands (our summary)Open point: the charge of circularity rests on whether one can have reasons to accept P1 without already believing in God. No defender's reply is retained here; the discussion joins that of the first objection.

Jordan Howard Sobel (against Gödel's version) 1987 · attacks premise 3

In Gödel's version, God is defined as the being who has all "positive" properties. Sobel shows that Gödel's axioms entail a "modal collapse": everything that is true becomes necessary. Nothing would be contingent or free anymore: for example, if you wear a blue sweater today, it would be impossible for you to wear a red one. The axioms prove too much, so at least one of them is false.

a defender replies

C. Anthony Anderson defender of the argument · 1990

Anderson grants that Sobel's objection is decisive against the proof as Gödel wrote it. But he proposes small corrections (another definition of "essence" and of God, a weakened axiom), and the corrected version escapes the modal collapse: he builds a model in which not everything is necessary.

Graham Oppy, Joshua Rasmussen and Joseph Schmid 2024

Even corrected, the proof rests on the list of "positive" properties. Yet that is exactly what divides believers and atheists: the atheist may judge that some of these properties (necessary existence, for instance) are not positive, or cannot go together. Without a neutral way of knowing which properties are positive, Gödel-style arguments cannot convince.

Where the debate stands (our summary)The modal collapse of the proof as Gödel wrote it is acknowledged, including by the logicians who checked it by computer (Benzmüller and Woltzenlogel Paleo, 2014); Anderson proposes corrections that escape it. The basic disagreement then concerns what makes a property "positive", a question on which believers and atheists already disagree.

Hugh Chandler (1976), Nathan Salmon (1989) 1976 · attacks premise 4

One can challenge S5 itself: nothing guarantees that what is possible is the same from every world. If what is possible can vary from one world to another, the step from "possibly necessary" to "necessary" no longer works.

Plantinga replies

Christoph Benzmüller and Bruno Woltzenlogel Paleo 2014

For Gödel's proof, the automated provers discover that S5 is not needed: a weaker logic, KB, in which access between worlds is only symmetric, is enough. The objection against S5 therefore loses part of its force, since the argument requires less than S5.

The debate goes on (our summary) Other philosophers defend S5 as the right logic of metaphysical possibility (Williamson 2013, Pruss and Rasmussen 2018). But even symmetry alone remains an assumption: the discussion then moves back to P1, as in the first objection.

Where the debate stands (our summary)The debate concerns the right logic of metaphysical possibility: some defend S5, others dispute it. Logicians have shown that for Gödel's proof a weaker logic (KB) suffices, which reduces the force of the objection without removing it. The discussion then returns to P1.

What today's voices say

Defend it

William Lane CraigHe defends the modal ontological argument: if a maximally great being is even possible, it exists in every possible world, so it exists. He says the usual objections do not touch this version.

Trent HornHe does not use the ontological argument with atheists, though it can reassure those already inclined to it.

Philip GoffHe prefers the modal version to Anselm's and thinks it shows that a necessary being either exists or is impossible, but says in the end we do not know.

Criticize it

Alex O'ConnorHe says the modal ontological argument is toothless against atheists, since its first premise already assumes God.

In the same family · Ontological

Existence is not a predicateImmanuel Kant

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God is not a hundred thalers: Hegel defends the ontological proof against KantGeorg Wilhelm Friedrich Hegel

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That than which nothing greater can be conceived existsAnselme de Cantorbéry · 1078 · debate over 3 levels

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