Did Kurt Gödel prove mathematically that God exists?

Gödel’s proof is logically air tight but only if you accept his premises

Kurt Gödel (c. 1906-1978) was a brilliant Austrian mathematician and good friend of Albert Einstein who created a logical proof to show that God not only does exist but must exist.

He wasn’t a particularly religious man (his father was Catholic, his mother a Protestant) but he became convinced of God’s existence entirely through philosophical and logical reflection.

His proof uses special math called modal logic, which deals with ideas like “possible” and “necessary.”

Gödel was a close friend and colleague of Albert Einstein at Princeton University’s Institute for Advanced Study

Gödel’s idea isn’t new. In fact, it goes back to a medieval thinker named St. Anselm who lived a thousand years ago.

But Gödel made it formal with math.

Here’s how it works.

Gödel starts with “positive properties.” These are good things, like being loving or kind.

He sets up five rules, called axioms, about these properties.

The Five Rules

The first rule says: if a good property always leads to another property, that second property is also good. For example, if being loving (good) always makes you kind, then being kind is good too.

The second rule says every property is either good or not good—there’s no middle ground. If being healthy is good, then being sick is not good.

The third rule says being “godlike” is a good property. Gödel defines “godlike” as having every good property and no bad ones.

So, a godlike being is perfect—it’s loving, kind, powerful, and so on.

The fourth rule says good properties stay good no matter what. If being kind is good here, it’s good everywhere.

The fifth rule says existing is good. It’s better to exist than not exist.

Conclusions from the Rules

Next, Gödel proves some ideas, called theorems. The first one says: if something is a good property, it’s possible for something to have it. So, since being godlike is good, it’s possible a godlike being exists.

This means there could be a world where God is real.

Then, Gödel defines “essence.” An essence is a property that explains everything about something. For example, if a cake’s essence is “being chocolate,” then it’s sweet, brown, and tasty because it’s chocolate.

He proves that if something is godlike, then its essence is being godlike. This means all its traits—like love or power—come from being God.

Finally, Gödel defines “necessary existence.” This means something must exist in every possible world if its essence demands it.

He says existing is a good property, and since a godlike being has all good properties, it must exist.

Plus, because its essence is being godlike, it must exist everywhere.

So, if God can exist in one world, God must exist in all worlds—including ours. Gödel concludes: God necessarily exists.

Now, is this convincing?

Let’s think about it simply. Gödel’s proof is like a airtight math puzzle.

If you accept his rules, the logic flows, and the answer is “God exists.”

It’s clever because it uses possibility—if God could exist, then God must exist.

This twists your brain a bit, but it makes sense in modal logic, where “possible necessity” becomes “necessity.”

But there are problems.

First, not everyone agrees with his rules. Why should every property be good or bad? Maybe some things, like “being tall,” are neutral. If neutral properties exist, then his second rule falls apart.

Second, saying “existing is good” feels shaky. Sure, we like existing, but is it always a good property? What about evil things—should they exist just because existence is good?

Third, “godlike” is a big leap. Gödel assumes a being with all good properties makes sense, but what if those properties clash? Can something be all-powerful and all-peaceful if power sometimes needs violence?

Plus, the proof also feels like a trick. It’s so abstract that it’s hard to connect to real life.

Logic can prove something in theory, but does that mean it’s true out here in the world?

For example, mathematicians can logically prove that infinity exists, but are there really an infinity of anything?

In short: Gödel proof is amazing as a brain exercise. It shows how far logic can stretch your mind.

But many philosophers remain unconvinced that this proof, which is known as a version of the ontological argument, provides an air-tight case that God exists.

A lot depends on accepting Gödel’s rules without proof.

If you question even one—like whether existence is always good—the whole thing becomes shaky.

Plus, it’s so complex that it feels more like a philosopher’s parlor game than a serious attempt to prove God’s existence.

In short, Gödel’s proof says: good properties exist, God has all good properties, so God must exist everywhere.

It’s a neat idea, and the logic is tight if you buy the setup.

But many people aren’t convinced by it because the rules of S5 modal logic feel a bit made-up.

What’s more, there are far more convincing arguments for God’s existence, such as the cosmological argument — that everything that comes into existence has a cause — that don’t require familiarity with the arcana of mathematical logic.

Robert J. Hutchinson is the author of numerous books of popular history, including Searching for Jesus: New Discoveries in the Quest for Jesus of Nazareth (Thomas Nelson), The Dawn of Christianity (Thomas Nelson), The Politically Incorrect Guide to the Bible (Regnery) and When in Rome: A Journal of Life in Vatican City (Doubleday). Email him at: roberthutchinson@substack.com